Characterization of an Erbium
Atomic Beammaster thesis in physics

byJohannes Schindler

submitted to the Faculty of Mathematics, Computer Scienceand Physics of the University of Innsbruckin partial fulfillment of the requirements
for the degree of Master of Science

Supervisors:
Ass.Prof. Dr. Francesca Ferlaino
Univ.Prof. Dr. Rudolf Grimm

Innsbruck, July 2011

Zum Besten aller Wesen.

Abstract
In this thesis we study and characterize an erbium atomic beam emerging froma high-temperature oven system. This is the first step towards the productionof a quantum-degenerate gas of Er. Er is a rare-earth element and its quantum
mechanical interaction properties are yet rather unexplored. Its exceptionallylarge magnetic moment of 7 µB makes Er especially interesting, since it allows
studies on the physics of dipolar quantum gases. In addition, Er shows an unusual electronic configuration and a complex energy level scheme, promising richscattering properties and offering many possibilities for laser cooling.
Since Er has a high melting point temperature of more than 1500 ◦ C, the ovensystem for the production of a thermal atomic beam requires specific engineering.
This includes thermal shielding, heated apertures, special crucible materials aswell as reliable control- and security systems. We characterize the atomic beam
emerging from the oven by absorption spectroscopy and fluorescence imaging on
the strong 401 nm transition. Based on our measurements, we optimize the collimation setup and we find the ideal operation temperature to be T ≃ 1250 ◦ Cwith a corresponding atomic flux of 3 × 1010 s−1 injected into the Zeeman slower.

iii

Zusammenfassung
Im Rahmen dieser Arbeit untersuchen wir einen Erbium-Atomstrahl, welchen wir
mittels eines Hochtemperaturofens erzeugen. Dies ist der erste Schritt zur Erzeugung eines Quantengases von Erbium Atomen. Erbium gehört zur Gruppe derseltenen Erden, seine quantenmechanischen Wechselwirkungseigenschaften sindnoch weitgehend unerforscht. Erbium ist besonders interessant, da durch sein
aussergewöhlich großes magnetisches Moment von 7 µB zahlreiche Experimente
zur Physik dipolarer Quantengase ermöglicht werden. Ebenso sind aufgrund derkomplexen elektronischen Struktur dieses Elements mannigfaltige Streueigenschaften zu erwarten und zudem zahlreiche Möglichkeiten zur Laserkühlung
gegeben.
Der hohe Schmelzpunkt von Erbium von über 1500 ◦ C stellt besondere Anforderungen an das Ofendesign. Unter anderem verwenden wir eine thermische
Abschirmung, beheizte Blenden, spezielles Material für den Tiegel sowie eigene
Kontroll- und Sicherheitssysteme. Durch Absorptionsspektroskopie und Fluoreszenzmessungen mit dem starken atomaren Übergang bei 401 nm charakterisieren wir den erzeugten Atomstrahl. Basierend auf unseren Messungen optimieren wir die Ofenblenden und bestimmen die ideale Betriebstemperatur zu
T ≃ 1250 ◦ C, bei welcher der Atomfluß in den Zeeman Slower 3 · 1010 s−1 beträgt.

iv

Contents
Contents

v

Introduction

1

1 Thermal atomic beams
1.1 Effusive oven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Atomic beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Determination of the atomic flux . . . . . . . . . . . . . . . . . . .
1.4 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4
4
6
8
9

2 Erbium
2.1 General properties . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Electronic properties . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Laser cooling of erbium atoms . . . . . . . . . . . . . . . . . . . . .
2.5 Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Scattering properties . . . . . . . . . . . . . . . . . . . . . . . . . .

12
12
14
16
18
20
21

3 Experimental setup
23
3.1 Vacuum chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Cooling and trapping lights . . . . . . . . . . . . . . . . . . . . . . 26
4 Erbium oven
4.1 Oven system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Control system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Atomic beam shutter . . . . . . . . . . . . . . . . . . . . . . . . . .

29
29
31
33

5 Characterization of the atomic beam
5.1 Measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Collimation setup 1 . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Collimation setup 2 . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37
37
40
51
57

v

Contents

Conclusion and Outlook

62

A Magnetic moments of the lanthanides

65

B Erbium oven control

67

C Atomic beam shutter control
69
C.1 Control box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
C.2 Source code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
D Calibrations
78
D.1 Laser frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
D.2 CCD camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Bibliography

81

List of Symbols and Abbreviations

88vi

Introduction
By cooling atoms to ultralow temperatures, we gain extraordinary high control
over their external as well as their internal degrees of freedom. Therefore, ultracold atoms empower us to study and to understand phenomena belonging tovery different branches of research, such as quantum chemistry, condensed matterand few-body physics, high-temperature superconductivity, and quantum simulations [1–5].
The field of ultracold quantum gases has been subject to vast developmentsin the past two decades. The first Bose-Einstein condensation, a phase transition
that leads to the macroscopic occupation of the system's ground state at ultralow
but finite temperatures, was attained in 1995 [6–8]. Subsequently, also fermions,representing the basic building blocks of matter were cooled to quantum degeneracy [9–11]. The ability to modify the two-body interaction by magnetic or optical
Feshbach resonances [12] increased dramatically the level of control on the systems. This opened the way of studying tunable quantum gases in the weak andin the strong interacting regime and of creating more complex structures such as
weakly bound dimer states [13–16]. All of this pioneering works were performedon elements from the alkali series and rely on the isotropic and short-ranged contact interaction. Alkali atoms provide comparatively simple systems with justone valence electron in the electronic s-shell and convenient optical transitions
for laser cooling experiments. At ultralow temperatures, the interaction between
those atoms can simply be described by a single scattering parameter known as
the s-wave scattering length a.
In further advance, the laser cooling and trapping techniques were extended tomore complex atomic species, which provide additional challenges and prospects[17–19]. In particular, atoms or molecules that interact via the dipole-dipole
interaction (DDI) lead to totally new phenomena. In contrast to the contact
interaction, the DDI has anisotropic and long-range nature. This gives rise to
new quantum phases and offers geometry dependent tunability [20,21]. Two candidate systems exhibit strong DDI: polar molecules and magnetic atoms. Polar
molecules carry a large electric dipole moment but require a complex production sequence since direct laser cooling can hardly be applied [22, 23]. Magnetic

1

Introduction

atoms exhibit smaller magnetic dipole moments but offer more robust systems.
Chromium has been so far the only strongly magnetic species to be Bose condensed1 [24]. In this system, the dipolar character manifests itself in spectaculareffects such as the d-wave collapse of the trapped gas [25], the geometry dependent stability of the system [26] and suppression of collisional relaxation in an
optical lattice [27]. Nowadays, exotic atoms with high magnetic moments, as
found in the lanthanide series are subject of increased interest in our community
and represent the cutting-edge research on the DDI [28–30].
Erbium is one of those elements with highly magnetic atoms. It is a rather
unexplored species, which shows a very rich energy structure and many favorable properties like a large number of isotopes, a high mass, a high magnetic
moment and a variety of narrow as well as broad laser cooling transitions. In
addition, erbium's unusual electronic configuration leads to complex scattering
properties [31–34].
The primary goal of our experiment is to Bose condense Er atoms and to investigate their scattering properties. Besides studies of ultracold dipolar Bose or
Fermi gases, also the formation of Feshbach molecules with even higher magnetic
moments or few body physics with DDI are of interest. Our vision is to admix
Li atoms to Er, leading to a crystal like system with extreme mass imbalance toobserve novel effects on the field of Efimov physics or of the BEC-BCS crossover.
At the moment, our experiment is in the construction phase. We set up thecomplete vacuum apparatus and the main laser setup for cooling and trapping.
During my master thesis time, I contributed to the mounting of the vacuum
apparatus, the installation of the cooling water system and the construction ofvarious coils to generate magnetic fields including the winding of the Zeeman
slower coils. Furthermore, I had the possibility to gain some experience with adye laser that we plan to use for the narrow line magneto-optical trap. Besides
the above mentioned tasks, the main focus of my work is the setting up and characterization the Er oven system. I installed and programmed a control- and safetysystem for the oven as well as an atomic beam shutter control system. Once theEr oven was operating, I characterized the atomic beam by means of laser spectroscopy and optimized the beam collimation setup based on these measurements.
This thesis is structured as follows. Chapter 1 gives an overview on thefundamental theoretical concept to understand the atomic beam behavior. In
Chap. 2 we review the main properties of Er atoms with emphasis on its laser
cooling transitions and trapping potential. Chapter 3 gives an overview on ourcomplete experimental setup including the vacuum chamber and the laser setup.
The detailed setup and working principle of the Er oven is explained in Chap. 4.
1

Recently, also Dysprosium atoms have been Bose condensed in the group of B. Lev atUniversity of Illinois at Urbana-Champaign (private communication 07.2011).

2

Introduction

Finally, in Chap. 5 we present the results of the laser spectroscopy measurementsthat characterize the Er atomic beam and that we used to adapt the Er oven
design to our requirements.

3

Chapter 1

Thermal atomic beams
The starting point of our experiment is a thermal beam of Er atoms produced
from an effusive high-temperature oven. The atomic beam is then decelerated
via the Zeeman slower technique and later trapped in a magneto-optical trap.
In this Chapter, we introduce the working principles of an effusive oven and themethods to characterize the atomic beam emerging from the oven.

1.1

Effusive oven

There exist many different kinds of sources for the production of a thermal atomic
beam, depending on its demands and source material [35]. For source materials
with high melting points, coated heated-filaments or laser deposition generate
free atoms, but provide only limited atomic flux. Wicking recirculation sources
offer higher flux and are a clever way to conserve source material in applications
with needs for long source life, such as in atomic clocks. For our purpose, we use
an effusive heated oven combined with a bright wall collimator that we discuss inSec. 1.2. It provides a robust system with a high, well controllable atomic flux.
The oven itself consists of a tube with an aperture. It is heated by surrounding
heating wires and is water cooled for thermal shielding. The technical details are
given in Chap. 4, in the following we describe the theoretical working principle
on a simplified system.
We consider an ideal atomic gas in thermal equilibrium at temperature T
stored in a box. It is described by the ideal gas law
p = kB n T ,(1.1)

where p is the pressure, kB the Boltzmann constant and n the atomic density.
If the box is surrounded by vacuum and has a circular aperture with diameter
b1 , the atoms escape from it because of the pressure gradient between the box
and the vacuum. Here, it is important to distinguish different regimes of the41. Thermal atomic beams

oven operation. Depending on p, the atoms suffer collisions with each other. The
mean distance atoms travel between two successive collisions, the so called mean
free path λmf , is given by1
λmf = √,
(1.2)
2 π d20 n
where d0 is the atomic diameter [36]. If λmf is smaller than the size of theaperture, the atoms encounter many collisions while emerging from the box. This
leads to a hydrodynamic flow, a collective transport process, and is described by
fluid dynamics. In contrast, for
λmf & b1

(1.3)

atom-atom collisions are rare and atom-wall collisions dominate. This is theeffusive- or molecular flow regime, in which our effusive oven works. The expansion is an individual transport process where mechanisms as so called diffusivereflection can occur: an atom hits a wall, sticks to it and is re-emitted in an angle
that is independent of its incident angle. By this, in contrast to hydrodynamic
flow, an atom that hits the inner face of the aperture can return to the box.
Furthermore, in the effusive regime, the emergence of atoms from the box does
not change the spatial- nor the velocity distribution of the atoms inside the box.
In the effusive regime, we can calculate the flux emerging from the box asfollows. The velocity v = |~v | of the atoms inside the box is described by the wellknown 3D Maxwell-Boltzmann velocity distribution
Pv (T ) = C



m
kB T

3
2



− m v2v exp
2 kB T
2



,

(1.4)

with C a normalisation constant and m the mass of an atom. The most probablep√velocity is vmp = 2 kB T / m and the mean velocity is v̄ = 2 vmp / π.
Figure 1.1 illustrates the atomic volume V = v̄ dt · A cos α leaving the box in
the time interval dt [37]. Here, α is the angle of emergence and A = b21 π / 4 isthe area of the aperture. Only a part dω / (4 π) of the atoms travels on a solid
angle dω. The number of atoms dN per unit time dt leaving the box into dω isgiven by the unit flux dΘ and reads as
dN = dΘ dt =dωn v̄ cos α A dt ,
4π

(1.5)

where n is the atomic density. Integrating Eq. (1.5) over the solid angles dω =2 π sin α dα with α from 0 to π/2 gives the total flux coming out of the box
Θ=1n v̄ A .
4

(1.6)

5

1. Thermal atomic beams

Acos(α)tvd

αFigure 1.1: In the time interval dt, an atomic volume of V = v̄ dt · A cos α leaves thebox at an angle of emergence α. A is the area of the aperture, v̄ is the mean velocity of
the atoms. Integration in spherical coordinates over ϕ from 0 to 2 π and over ϑ from 0
to α gives the volume emerging into the solid angle dω.

1.2

Atomic beam

The angular distribution of the atoms leaving the box from the aperture is proportional to cos α, as given in Eq. (1.5). Only atoms travelling at small angles areuseful for the experiment, since they can travel through the apparatus without
hitting it. A large fraction of atoms is unused and it is needed to block it to
avoid or reduce source material deposition in the apparatus. The atomic beam
can be narrowed by collimating it by a second aperture, aperture 2, in front of thefirst aperture, aperture 1. This is a so called dark wall collimator that provides
simple geometric shading by cutting off the unused part of the source beam. This
technique is not suitable for our experiment, since Er deposited at the apertures
can overgrow and close the aperture. Therefore, we use heated apertures that
re-emit the blocked atoms. This is a type of a so called bright wall collimatorthat conserves the source material and extends the source life time [35]. In termsof simplicity, in the following we neglect that the apertures are heated. Provided
that the mean free path of the atoms is larger than the typical geometry of theoven, this is a valid approximation.
Figure 1.2 shows the oven with and additional aperture 2 with diameter b2 at
a distance a from aperture 1. Only atoms inside the dotted lines contribute to
the atomic beam leaving the oven. The beam emerges into a solid angle aroundthe z-axis of
b1 /2 + b2 /2−1
ω = 2 π (1 − cos α) , where α = tan f and f =, (1.7)a6

1. Thermal atomic beams

Figure 1.2: Scheme of an effusive oven with aperture 1 of diameter b1 and aperture 2
at a distance a with diameter b2 . Inside the box, the atoms have temperature T andvelocity distribution Pv (T ). Only atoms inside the dotted lines contribute to the atomic
beam. The beam emerges into a solid angle ω = 2 π (1 − cos α) and has diameter d at
a distance l from aperture 2. The atoms in the beam have velocity distribution Pv′ (T )and longitudinal and transversal velocity components vz (T ) and vx (T, f ). A laser beamcrosses the atomic beam transversal at distance l from aperture 2.

where f is the collimation ratio. At a distance l from the aperture 2, the beam
has a diameter d ofb1
d = 2 (a + l) f −
.
(1.8)
2
The flux Θ′ through the aperture is obtained by integrating Eq. (1.5) over dω =2 π sin α dα from α = 0 to α = tan−1 f :
Θ′ =

1
f2
n v̄ A.
4
1 + f2(1.9)

A different type of bright wall collimator uses a long channel instead of a circular hole for aperture 1. In the effusive regime, wrongly directed atoms hit the
tube wall and by diffusive reflection they can return to the source or contributeto the directed beam. This changes the angular distribution of the atoms from
Eq. (1.5) considerably. The flux of atoms travelling along the tube is undiminished, whereas the total atomic flux Θtube is reduced toΘtube =1Θ.
κ

(1.10)

The factor 1/κ depends on the geometry of the channel and for a long circularcylindrical tube it is given by 1/κ = (8 b1 ) / (3 a1 ), where b1 is the diameter anda1 the length of the tube [37]. However, as the longitudinal flux is not alteredby such a collimator, Eq. (1.9) also holds in this case, given that f is small andλmf & a1 .
In an atomic beam the velocity distribution of the atoms is no longer describedby Eq. (1.4) as in the box. Since, as shown in Eq. (1.5) and Fig. 1.1, the probabilityof an atom to emerge from the box is proportional to its velocity, the velocity
distribution changes to




m 2 3
− m v2′′
Pv (T ) = C
v exp,(1.11)kB T
2 kB T7

1. Thermal atomic beams

with normalisation constant C ′ and Pv′ (T ) ∝ v 3 . Thus, the most probable velocpp′′
ity changes to vmp= 3 kB T / m and the mean velocity is v̄ ′ = vmp
3 π / 8 [37].
We can distinguish two components of the velocity distribution: a longitudinal
distribution with velocities vz (T ) and a transversal distribution with velocities
vx (T, f ). The longitudinal distribution is determined by the temperature T of thesource, whereas the transversal distribution has to fulfil the boundary conditionof the apertures and is determined by the collimation ratio f from Eq. (1.7). The
individual velocities must obeyvx ≤ f v z

1.3

[38].

(1.12)

Determination of the atomic flux

We can control the flux by the source temperature. The source should emit
as many atoms as necessary for the experiment but as few atoms as possible
to extend the source life-time. To monitor the flux, we measure it by laser
spectroscopy.
In a simple model we consider the atoms as pure two level systems (2-LS) withground state |gi and excited state |ei. The energy difference of the two statesis ∆Eeg = h ν0 with the transition frequency ν0 . If an atom absorbs a photon
from a resonant laser beam with frequency ν0 , the atom is excited from |gi to |ei.
After the lifetime τ of |ei, the atom decays back to |gi by spontaneous emissionof a photon with energy h ν0 and can be re-excited. The photon is emitted in
random directions and can be observed as fluorescence light [39]. Therefore, theintensity of the transmitted light is reduced by the amount of absorbed light andis proportional to the atomic density.
As shown in Fig. 1.2, we cross the atomic beam transversely with a resonant
laser beam at the distance l from aperture 2. For laser beam intensities below
the saturation intensity Isat of the transition, the Beer-Lambert law describes thetransmission of light with incident intensity I0 through the atomic beam [40]:I = I0 exp(−D) .

(1.13)

D is related to the optical density (OD) of the atomic beam by D = ln (10) OD ≈2.3 OD. For the laser beam interacting with the atomic beam from x1 to x2 , D
is defined as
Z x2
D=n(x) σ0 dx ≈ n σ0 j ,(1.14)
x1

where σ0 is the cross-section for the absorption of a resonant photon by an atom[38]. For small angles α from the beam axis, the density can be estimated as
constant over the light-atom interaction length j = x2 − x1 . In general, j is notequal to the atomic beam diameter d, since atoms that are not in center havevelocity components in the direction of the laser beam. Hence, their resonance81. Thermal atomic beams

frequencies are Doppler shifted and these atoms do not interact with the light.
In a 2-LS, the absorption cross-section is given by
3 λ2(1.15)
2π
for resonant light with wavelength λ = c / ν0 [41]. Combining Eq. (1.13 - 1.15)
yields to the atomic density:
 
2π 1
I
ln
.
(1.16)
n=−
2
3λ j
I0
σ0 =

In this way, by measuring I0 , I and j, we can calculate the total flux Θtot out ofan source with aperture diameter b1 and temperature T by inserting Eq. (1.16)
into Eq. (1.6): r
3
π 2 b21I
2 kB TΘtot = −ln.
(1.17)
24 λ2 jI0m
Respectively, by Eq. (1.9), we can calculate the flux injected into a certain angle
around the beam axis.

1.4

Spectrum

To characterize the atomic beam in further detail, we scan the frequency ν of thelongitudinally crossed laser light over the atomic resonance at ν0 . The transmitted light intensity I as a function of ν represents the absorption spectrum. We
find an absorption peak around ν0 and its exact position, width and shape reflect
the physics of the atomic beam. The natural line shape and -width of the unperturbed atoms get altered and broadened by their thermal motion, atom-atomcollisions or interaction with light. By understanding the underlying broadening
mechanisms, we can conclude from the absorption spectrum on the collimation,
temperature or flow regime of the source and the atomic beam.

Natural linewidth
The natural linewidth ∆νnat is the fundamental limit of the linewidth. Due tothe finite lifetime τ of the exited state, the Heisenberg energy uncertainty relation∆E τ = h limits the width to∆E
1∆νnat ==.
(1.18)h2 πτ
The natural line shape can be derived from a classical model of a damped harmonic oscillator for the excited electron [38]. In this model, the atomic potential
is approximated as a harmonic potential and radiative energy loss results in
damping. This leads toInat (ν) = I0(Γ/4π)2,(ν − ν0 )2 + (Γ/4π)2(1.19)
9

1. Thermal atomic beams

which is a Lorentzian function with peak intensity I0 and full width half maximum(FWHM) ∆νnat = Γ/2π. Γ = 1/τ corresponds to the spontaneous decay rate of
the excited state.

Doppler broadening
Moving atoms see the frequency of a laser beam Doppler shifted. Accordingly,
the resonant condition for an atom moving at a non-relativistic velocity v is
ν = ν0 +


~k ~v
vk 
= ν0 1 +,2πc(1.20)

where ~k is the wave vector of the light wave, vk = ~v ~ek is the velocity component
in its direction and c is the speed of light. Since in a thermal gas the atoms have
distributed velocities, this shift leads in first order to a broadening of the spectral
line. For the interaction with the light, only vk needs to be considered, thus a 1D
Maxwell-Boltzmann distribution with normalization constant C ′′ describes thevelocity distribution of free atoms:rm− m v2′′
Pvk (T ) = C
exp.
(1.21)kB T
2 kB T
Substituting v = c (ν/ν0 − 1) gives the probability distribution Pν (T ) that is
proportional to the line shape 2− c m (ν − ν0 )2,(1.22)
ID (ν, T ) = I0 (T ) exp
2 kB T ν02
which is a Gaussian function with peak intensity I0 (T ). It has a Doppler widthp√
FWHM = 2 ln 2 ∆ν .
∆νD = (ν0 /c) 2 kB T / m = ν0 vmp / c and a FWHM of ∆νD
D
In an atomic beam the velocity distribution is not a pure Maxwell-Boltzmann
distribution, but is additionally proportional to v. Therefore, according to′′ = ν v ′ / c. However, the main
Eq. (1.11), vmp
has to be used and thus ∆νD
0 mp
difference to the free gas is that the distribution has two components with velocities vx and vz . Thus, the Doppler width also has two components and according
to Eq. (1.12):
ν0 ′
v f.
(1.23)∆νD,x = ∆νD,z f =c mpThis means that the Doppler broadening of a spectral line is reduced by collimating the atomic beam. Thus, the resolution can be increased and, more importantfor us, conclusions on the collimation can be drawn.

Other broadening mechanisms
Saturation- or power broadening occurs when the intensity of the laser beam exceeds or is comparable to the saturation intensity Isat of the transition. Then,101. Thermal atomic beams

the optical pumping rate is larger than the relaxation rate and the line is broadened [38]. The resulting line has a Lorentzian shape with FWHMp∆νS = ∆νnat 1 + I/Isat .
(1.24)For I ≪ Isat it is thus negligible.
Collisional- or pressure broadening results from the deformation of the electronic wave function during an atom-atom collision. Thus, the transition frequency is shifted and the line is broadened [38]. The resulting line has a
Lorentzian shape with FWHM√
∆νcol = n σat vmp ∝ n T .
(1.25)
Since the collision cross-section σat for Er is not known yet, we cannot makepredictions on the strength of this mechanism besides that for a constant density√
n, the linewidth scales with T . In general, due to the limited collisions in theeffusive regime, this effect should be negligible.
If several different mechanisms contribute to the broadening of a line, theresulting total line shape is represented by the convolution of the individual line
shapes. For instance, a line broadened due to Doppler broadening as well as due
to saturation broadening has a line shape described by a Voigt profile:Z +∞V (ν; ∆νG , ∆νL ) =G(ν ′ ; ∆νG ) L(ν − ν ′ ; ∆νL ) dν ′ .
(1.26)−∞F W HM ,G(ν; ∆νG ) represents the Gaussian contribution with width ∆νG = ∆νD
L(ν; ∆νL ) represents the Lorentzian contribution with width ∆νL = ∆νnat +∆νS .
In this case, the resulting total linewidth ∆νV is estimated asq2∆νV ≈ 0.5346 ∆νL + 0.2166 ∆νL2 + ∆νG[42].
(1.27)

If we do not consider the spectrum of a free gas, but the transversal spectrum ofan atomic beam, according to Eq. (1.23), we have to employ the reduced Doppler
F W HM in Eq. (1.26) and Eq. (1.27).
width ∆νD,x11

Chapter 2

Erbium
Erbium is a very interesting and rather unexplored element for ultracold gas
experiments. It is a soft, silver-colored metal with an atomic number of 68. It
belongs to the rare earth elements and is part of the lanthanide series. Thereis an increasing interest in elements from this series, since they can exhibit highmagnetic moments and have exotic electronic configurations, which opens up
many possibilities for laser cooling applications. In this Chapter, we present
relevant properties of erbium atoms, including the electronic, the magnetic andthe scattering properties. We also discuss the optical transitions that we want touse for laser cooling and trapping Er atoms.

2.1

General properties

Erbium was discovered in 1843 in a quarry near the village of Ytterby in Sweden,
as other rare earth elements such as Ho, Tm and Yb. Today, Er is almost exclusively mined in China. It finds many commercial applications in laser technology.
For instance, it is used as doping element for fiber lasers. Here, trivalent Er ionsare pumped with 980 nm or 1480 nm light and emit light at wavelengths around1550 nm [43,44]. In optical communication, this is used for fiber amplifiers, whichallow fast and relatively cheap signal amplification at low noise [45–47]. Also the
Er:YAG solid state laser finds common use in medical photo-ablation treatments
due to the strong absorption of its 2940 nm infrared light in water [48, 49].
Erbium is a soft, silver-colored rare earth metal. Macroscopically it has afibroid structure, microscopically it forms a hexagonal close packed crystal [50].
Similar to Cr [51], Er has a comparatively high melting point temperature of
Tmelt = 1529 ◦ C [52]. Figure 2.1 shows its vapor pressure as a function of thetemperature. For comparison, we also plot the vapor pressure of other rare earth
elements such as Tm, Yb and Sa, of the magnetic Cr atoms and of the alkali
metal Li, which we will in future experiments admix to the Er machine. The
122. Erbium

6

10

Tmelt(Er)=1529°C
4

10

2

10

0

pvapor [mbar]

10

−2

10

−4

10

Er − points
Li − points
Yb − points
Sm − points
Tm − points
Cr − plot

−6

10

−8

10

−10

10

0

500

1000

1500
T [°C]

2000

2500

3000

Figure 2.1: Vapor pressure as a function of the temperature for Er, Li, Yb, Sm, Tm and
Cr. Erbium requires high temperatures for vapor pressures suitable for the productionof a thermal atomic beam. The solid and dashed lines are fits to the data [53] using
Eq. 2.1. The vertical dotted line shows the melting point temperature Tmelt of Er.

data points are extracted from [53] and fitted to an Antoine equation [54], whichapproximates the relation between vapor pressure and temperature:


b
,
(2.1)
Pvapor (T ) = exp a −c+Twith the fit parameters a, b and c. Erbium and Cr show the lowest vapor pressures
for a given temperature. Although Er, Tm and Yb are neighboring elements, themelting point of Yb is much smaller than that of Er and Tm1 . It is likely that
this is due to the different crystal structure, which is hexagonal for Er and Tm,
but cubic for Yb [50, 55]. For Er, the required high temperatures for sufficiently
high vapor pressures make the production of an oven technologically challenging. As we will discuss in Sec. 5.4, we estimate that temperatures of 1200 ◦ C leadto a reasonable Er atom flux for Zeeman slower (ZS) and magneto-optical trap
(MOT) applications.
Erbium has the advantage of showing good getter properties. As reported
in Ref. [56], Er films have exceptionally high adsorption activity especially forhydrogen, which commonly limits the achievable pressure in a vacuum chamber.
1

Tmelt (Yb) = 824 ◦ C,

Tmelt (Tm) = 1545 ◦ C, [53].

13

2. Erbium

When the Er oven is turned on, a part of the atoms coats the inner walls of thevacuum chamber. Remnant atoms hitting the wall stick to it, and the pressure
drops. This eases the production of ultra high vacuum (UHV) conditions in thevacuum chamber. It is the same principle as that of a Ti-sublimation pump, butsince the surface area of Er films is much larger than that of Ti films, the effectshould be even stronger with Er.
Erbium is very appealing for quantum gas experiments. First, it has a comparatively high magnetic moment of 7 µB 2 . Nowadays, highly magnetic atoms
are attracting great attention in our community because of the many possibilities
to study dipolar effects [20]. Second, Er has a rich energy structure, which resultsfrom its unusual electronic configuration, where an incomplete f-shell with twoelectron vacancy is submerged by a full s-shell. This offers many possibilities
for various laser cooling schemes and leads to novel collisional behavior. In addition, the numerous Zeeman levels open opportunities for quantum computing,as recently proposed in [57]. Third, six stable isotopes provide flexibility for theexperiment and allow investigation of bosonic as well as fermionic systems.
The group of Jabez J. McClelland at the National Institute of Standards andTechnology (NIST) has been the first to demonstrate laser cooling of a magnetic
rare earth species. They produced a blue MOT with 105 atoms at temperatures
below 25 µK [33, 58], as well as a narrow-line MOT with temperatures below
2 µK [34].

2.2Electronic properties

The electronic ground state of Er is in a [Xe]4f 12 6s2 configuration. The [Xe]means that, as in the noble gas Xe, all shells energetically up to the 5p shell are
fully occupied. From the 14 valence electrons, two of them fill the 6s shell and theremaining 12 are arranged in the 4f shell, leaving it with a two electron vacancy.
Therefore the incomplete 4f shell is subjacent to the complete 6s shell, what
is called submerged shell structure. This results in very rich scattering properties [31, 32] and a complex energy level scheme [29, 59], as shown in Fig. 2.2.
Since the bosonic isotopes have nuclear spin quantum number I = 0, the relevant quantum number is the total angular momentum quantum number J. Er
has 110 states with J values ranging from 2 to 12. In Fig. 2.2 even parity3 states
are indicated with red horizontal lines, odd parity states with black horizontal
lines. The arrows mark transitions from the even parity ground state at J = 6
to odd excited states at J = 7. This is because in an electric dipole transition,
2e~
The Bohr magneton is defined as µB = 2m
with e the elementary charge, ~ the reducedePlanck constant and me the electron rest mass.
3
Parity is a symmetry property of the electronic wave function. The parity operator P̂
inverts the wave function through the origin. If P̂ Ψ(~r) = Ψ(−~r) = Ψ(~r) the wave function haseven parity, if P̂ Ψ(~r) = Ψ(−~r) = −Ψ(~r) it has odd parity [60].

142. Erbium

Figure 2.2: The energy level scheme of Er. Even parity states are indicated with red
horizontal lines, odd parity states with black horizontal lines. The arrows show electric
dipole transitions investigated in [29], for our experiment the transitions at 401 nm andat 583 nm are of special interest. Plot and data from [29] and [59].

which is the most dominant type of transition, the total angular moment J has
to change by ±1 and the parity of the state must change [61].
The different energy levels arise from the occupation of different shells andfrom the coupling scheme of the electrons. The well known Russell-Saunders or
spin-orbit (LS-) coupling is common for light elements, where the Coulomb interaction is dominant over the spin-orbit interaction. In this scheme, all individual
electronic orbital angular momenta ~l and spins ~s of each electron add separately~ and a total spin S,~ which finally couple toto a total orbital angular moment L~ +S~ [39]. The resulting state is denoted by thea total angular moment J~ = L(2s+1)
term symbol
LJ . Accordingly with the usual spectroscopic notation [61],the L-states are labeled with letters as follows: .
L valuesymbol

0
S

1
P

2
D

3
F

4
G

5
H

6
I

...
...

In the case of heavy elements, the spin-orbit interaction is comparable orstronger than the Coulomb interaction. The resulting coupling scheme is known15

2. Erbium

as jj-coupling. A special case of this is the J1 J2 -coupling, which is relevant for
many excited states of the lanthanides [62]. In this scheme, the 4f electrons andthe outer, remaining electrons couple independently in a LS-coupling scheme tostates with total angular momentum J~1 and J~2 . They add to a overall total
angular momentum J~ = J~1 + J~2 and the resulting state is denoted as (J1 , J2 )Jterm.
In the ground state of Er, the 4f 12 6s2 electrons are coupled in a LS-coupling
scheme to a 3 H6 term with a total orbital momentum quantum number L = 5.
This is exceptionally high, compared to the ground states of the alkali atoms,
which all have L = 0. The excited states usually experience a higher spinorbit interaction and follow the J1 J2 -coupling scheme. For instance, the excitedstate associated with the strong laser cooling transition at 401 nm is labeled as[Xe]4f 12 (3 H6 )6s6p(1 P10 ) (6, 1)07 , see Fig. 2.2. Here, one of the ground state 6s electrons is excited to the 6p shell. The 12 4f electrons couple in a LS-scheme to a
3 H term, the 6s and the 6p electron couple in a LS-scheme to a 1 P 0 term. These
6
1
two states couple to a (J1 , J2 )J0 = (6, 1)07 term, where J = 7 and '0 ' indicates theodd parity.

2.3

Isotopes

Erbium possesses six stable bosonic and fermionic isotopes with relatively highmasses m from 162 amu to 170 amu. Tab. 2.1 shows the natural abundance andnuclear spin quantum number I of the stable Er isotopes.
element
erbiummass m [amu]
162
164
166
167
168
170

abundance [%]
0.1
1.6
33.5
22.9
27.0
14.9

nuclear spin I
0
0
0
7/2
0
0

statistic
boson
boson
boson
fermion
boson
boson

Table 2.1: Natural abundance and nuclear spin of the stable erbium isotopes. Data
from [63].

In the electronic ground state, Er has a total angular momentum quantum
number J = 6. No bosonic isotope shows hyperfine structure, being I = 0. The
ground state of the fermionic 167 Er with I = 72 splits up into eight hyperfine
5
states from F = 19
2 to F = 2 . Compared to other fermionic alkali systems
that were brought to quantum degeneracy as 40 K [9] or 6 Li [64], 167 Er shows an
exceptionally high abundance of 22.9 %. The richness in isotope number gives us
more flexibility in terms of scattering properties. This can be very facilitative, as
in the case of Sr. Here, the least abundant of the four isotopes, 84 Sr, has been the16

2. Erbium

first to be Bose condensed thanks to its favorable scattering properties4 [17, 18].
Later on, it even was used to cool the fermionic 87 Sr by interisotope collisions toquantum degeneracy [65].

Figure 2.3: Natural abundance versus isotope shift for the 401 nm, the 583 nm and the841 nm transition. 166 Er is taken as a reference. Data from [32, 66, 67], no values known
for 162 Er and 167 Er at the 401 nm transition.

The laser cooling transition frequencies depend on the particular isotope.
The different number of neutrons leads to different atom core masses and charge
distributions and in that way the transition frequencies are shifted, what is calledisotope shift [60]. Figure 2.3 shows the isotope shift of all stable isotopes for threetransitions [32,66,67]. Taking 166 Er as a reference, the isotope shift is always lessthan 2.2 GHz for the 401 nm and the 583 nm transition. This is convenient since
we can reach all isotopes at each transition within the same mode of the laser
system.
4
The scattering properties determine the thermalization of the atoms and thus are the key
parameter for evaporative cooling.

17

2. Erbium

2.4

Laser cooling of erbium atoms

The group of Jabez J. McClelland has identified five different transitions that
could be used for laser cooling experiments, as illustrated in Fig. 2.2. Tab. 2.2
shows the accordant laser cooling parameters such as the natural linewidth ∆ν,the saturation intensity Isat , the Doppler temperature TDoppler and the recoil
temperature Trecoil given in Ref. [29] with corrections from Ref. [68, 69].
parameterΓ (1/s)τ∆ν
Isat
TDopplervDoppler
Trecoilvrecoil

400.91 nm
2.2 × 108
4.5 ns35.6 MHz72.2 mW/cm2
854 µK
0.210 m/s
357 nK
6.0 mm/s

582.84 nm
1.2 × 1060.857 µs
0.19 MHz
0.13 mW/cm2
4.8 µK
15 mm/s
170 nK
4.1 mm/stransition
631.04 nm
1.8 × 105
5.6 µs
28 kHz
15 µW/cm2
680 nK
5.8 mm/s
140 nK
3.8 mm/s

841.22 nm
5.0 × 104
20 µs
8.0 kHz1.8 µW/cm2
190 nK
3.1 mm/s
81 nK
2.8 mm/s

1299.21 nm
1375 ms
2.1 Hz0.13 nW/cm2
51 pK
50 µm/s
34 nK
1.8 mm/s

Table 2.2: The laser-cooling parameters for several transitions in Er [29, 68, 69]: spontaneous decay rate Γ, lifetime τ , linewidth ∆ν, saturation intensity Isat , Doppler temperature TDoppler, Doppler velocity vDoppler , recoil temperature Trecoil and recoil velocity
vrecoil .

The 401 nm transition has a broad natural linewidth ∆ν = 36 MHz, resulting
in a strong scattering force
Fscat = ~ kΓI / Isat,
2 1 + I / Isat + 4 δ2 / Γ2

(2.2)

where Γ = 2 π ∆ν the spontaneous decay rate, Isat = π h c Γ / (3 λ2 ) the saturation
intensity, I the intensity, ~ k the photon momentum and δ the detuning from thetransition [60]. Therefore, we use this transition for the ZS to slow the thermal
atomic beam, for transversal cooling (TC) to focus the atomic beam and for theimaging. This transition can also be used for a MOT [33], but for our MOT wewant to take advantage of the narrow linewidth ∆ν = 0.19 MHz of the 583 nm
transition, which has a lower Doppler temperature5 TDoppler of 4.8 µK. Due tothe high mass m of Er, the recoil temperature6 Trecoil of 170 nK is also very low.
The ZS is designed to slow the atoms to 5 m/s, which is on the order of the capture
velocity of the MOT. Therefore, it will be feasible and benefical to use the 583 nm
transition to capture and further cool the slowed atoms in the MOT.
5

The Doppler temperature TDoppler = 2~kΓB is the fundamental temperature limit for the
Doppler cooling mechanism [60].
2 2
6The recoil temperature Trecoil = ~ mk is the fundamental temperature limit for sub-Doppler
cooling mechanisms [60].

18

2. Erbium

In usual alkali gas experiments, the cooling transition needs to be opticallyclosed. Otherwise atoms leaking to metastable states get lost from the coolingcycle. As demonstrated in Ref. [33], this requirement is much less restrictive for
Er atoms. Considering the energy level diagram in Fig. 2.2 and the electric dipole
selection rules7 , it is clear that the 401 nm cooling transition is optically open. In
particular, excited atoms can decay8 to any energetically lower lying metastablestate of opposite parity and J = 6, 7 or 8. In Ref. [33] the branching ratio forthis transition is determined to 8 × 10−6 , so in every 1.3 × 105 transitions to theground state, the excited state once decays to a metastable state. Dependingon the number of required cooling cycles, this can limit the atomic population.
However, atoms in such metastable states can be trapped by the quadrupole
magnetic field of the MOT because of their high magnetic moment µ, as reported
first in Ref. [33] and later in Ref. [70]. Thus, non-resonant metastable atoms
cascade back to the ground state, from where they can be recaptured by the
MOT beams. So in the 401 nm transition, despite the numerous loss channels,
the atoms can be recycled due to the high magnetic moment that confines theatoms to the vicinity of the MOT beams.
We find the 583 nm transition particularly suitable for MOT operation. Here,
excited atoms can decay to two metastable states, but since the energy changesuch transitions is very small, the transition rate is also small according to the
Fermi golden rule, leading to a branching ratio of 2 × 10−8 .
Erbium is very favorable for the use of polarization gradient cooling, since
the magnetic moments of many excited states are very similar to the one of its
ground state. The Landé g-factors9 of ground and excited state differ only by
0.004 for the 401 nm transition and by 0.03 for the 583 nm transition10 [59]. SubDoppler cooling mechanisms rely on Zeeman shifts of the ground state sublevels,
whereas Doppler cooling relies on Zeeman shifts of the ground state versus theexcited state. Therefore, there is a critical magnetic field value above which the
Doppler cooling dominates, as explained in [71,72]. Clearly, for smaller differencesof the g-factors of ground and excited state, this critical magnetic field value ishigher and the sub-Doppler cooling is less sensitive to magnetic fields. Therefore,
especially the 401 nm transition is very suitable for polarization gradient cooling,
as demonstrated in Ref. [58] and also in similar work on Dy [28].
7
In emission, J can change to J ′ = J ± 1 (stimulated emission) and also to J ′ = J (except
for J = 0) (spontaneous emission). The parity symmetry has to change in both cases [61].
8
In a first order approximation, we only consider decay via the electric dipole radiation andneglect the weaker decay via electric quadrupole or via magnetic dipole transitions, which would
involve odd parity states with J values from 5 to 9.
9
The magnetic moment µ is proportional to the Landé g-factor of the state, see Eq. (2.3).
10
g[4f 12 6s2 3 H6 ] = 1,16381, g[4f 12 (3 H6 )6s6p(1 P01 ) (6, 1)07 ] = 1,160,
12 3
g[4f ( H6 )6s6p(3 P01 ) (6, 1)07 ] = 1,195

19

2. Erbium

2.5

Magnetic properties

Compared with the maximum magnetic moment µ = 1 µB of alkali atoms, mostof the lanthanide elements have high magnetic moments. Tab. 2.3 shows theelectronic configuration and the ground state magnetic moment µ of all lanthanide
atoms [59]. There is a direct relation between the vacancy of the 4f -shell andthe magnetic moment [73]. As we explain in more detail in App. A, the Hund's
rules [60] determine the ground state quantum numbers, which determine theLandé g-factor of the state. Sinceµ = g MJ µB ,(2.3)

with g the Landé g-factor, and MJ the magnetic quantum number of the total
angular momentum, the magnetic moment is related to the occupation of the
4f -shell. Erbium has µ = 7 µB , resulting from its 4f 12 6s2 electronic ground state
occupation: According to Hund's rules this configuration leads to a 3 H6 groundstate term with MJ = 6. This gives a Landé g-factor of 1.16 and results in amagnetic moment of 6.98 µB .
element
e.c. ([Xe]-)µ [µB ]

La
5d1 6s2
1

Ce
4f 1 5d1 6s2
4

Pr
4f 3 6s2
3

Nd
4f 4 6s2
2

Pm
4f 5 6s2
1

Sm
4f 6 6s2
0

Eu
4f 7 6s2
7

Gd
4f 7 5d1 6s2
5Tb
4f 9 6s2
10

Dy
4f 10 6s2
10

Ho
4f 11 6s2
9Er
4f 12 6s2
7Tm
4f 13 6s2
4Yb
4f 14 6s2
0

Table 2.3: The ground state electronic configuration ('e.c.') and ground state magnetic
moment µ (rounded, in units of µB ) of all lanthanides listed by rising atom number. All
lanthanides have a complete Xe configuration, µ / µB = g MJ , values from [59].

The quantum behavior of Er gas is expected to be strongly affected by its
magnetic properties. The interaction energy of two magnetic dipoles aligned bya polarizing magnetic field is
Udd =Cdd 1 − 3 cos2 (θ)
,
4π
|~r|3

(2.4)

where Cdd = µ0 µ2 is the coupling constant, ~r the relative coordinate of the twodipoles and θ is the angle between ~r and the dipole axis [20]. This means that for
Er with µ = 7 µB the dipole-dipole interaction (DDI) is 49 times stronger than20

2. Erbium

for alkali atoms with µ = 1 µB since Cdd ∝ µ2 . Furthermore, the DDI is longrange and anisotropic since Udd ∝ |~r|−3 cos2 (θ). This has many consequences
and is expected to give rise to novel collisional behavior. In the case of identical fermions ultracold collisions are blocked by the Pauli exclusion principle dueto the symmetry of s-wave scattering. The anisotropy of the DDI could enable
such collisions by introducing higher partial waves [21]. In the case of bosons,the long-range character of the DDI might fundamentally change the universal
scaling law of Efimov physics [74].
The dipolar-length add = (m µ0 µ2 ) / (4 π ~), where µ0 is the magnetic constant, is a measure for the absolute strength of the DDI [20]. Thus, the highmass m of Er further enhances its dipolar character. Additionally, the high µ
and m should result in the observation of many Feshbach resonances already at
low magnetic fields. Controlling the scattering length via Feshbach resonances is
an important tool to reach quantum degeneracy and to produce tunable quantum
gases [12].

2.6Scattering properties

Important quantities as the background scattering length a, which determines
the interaction at low temperatures are so far unknown. Its determination is thefirst goal of our experiment.
The use of evaporative cooling [75] is an important step for the achievement of quantum degeneracy. It is mostly performed in magnetic traps, but for
non-S-state atoms collisional relaxation of the magnetic moments leads to rapid
loss of atoms in a magnetic trap [76, 77]. Erbium is in an electronic H-state, but
has a submerged shell structure, where the spherical symmetric 6s-shell could suppress the interaction anisotropy of the H-state and effectively make it a S-state.
This competition between open and closed shells can also be seen in the development of the investigation of the spin relaxation rates of Er in magnetic traps.
In 2004 Hancox et al. studied collisions of He with Er in a He buffer gas cooledmagnetic trap at temperatures below 1 K [31]. They successfully trapped Er andmeasured a suppression of the collisional transfer of angular momentum. Therefore, they concluded that in Er-He collisions the interaction anisotropy of the Er
atoms is shielded by the two unpaired electrons. This gave hope that this would
also hold for Er-Er collisions. However in 2010, Connolly et al. measured large
spin relaxation rates of Er in a magnetic trap at temperatures of 500 mK [32].
The rates are significantly higher than those of highly magnetic S-state atoms
and in striking contrast to the previous work. Although there are currently no
theoretical predictions for Er-Er collisions, they explain the rapid loss by an additional spin relaxation mechanism despite spin exchange, dipolar relaxation orsecond-order spin-orbit coupling, which is induced by the electronic interaction21

2. Erbium

anisotropy. This means that magnetic trapping of Er will be highly inefficient.
Therefore, in our experiment, we will use an optical dipole trap (ODT) to perform
evaporative cooling of Er.

22

Chapter 3

Experimental setup
For the production of an Er BEC and further experiments on ultracold Er and
Er-Li mixtures, we set up a vacuum apparatus and several laser systems. In
the vacuum chamber, a thermal beam of Er atoms is produced in an oven andsubsequently the atoms are slowed, trapped and further cooled by magnetic fields
and laser light. In this Chapter, we give an overview of the experimental setup
and the cooling strategy to produce a BEC of Er atoms.

3.1

Vacuum chamber

Figure 3.1 shows a drawing of the complete vacuum chamber, which is composedof five main sections: (a) Er oven chamber, (b) Li oven chamber, (c) Zeeman
slower (ZS), (d) magneto-optical trap (MOT) chamber and (e) pumping chamber.
The Er oven chamber consists of a commercial oven system, which produces
an Er atomic beam by the effusion of solid Er at temperatures up to 1350 ◦ C. A
detailed discussion of the Er oven is found in Chap. 4. In brief, the oven system
consists of a crucible surrounded by a water cooled thermal shield. The crucible
is divided in two parts: the effusion cell, where solid Er is placed and the hotlip, which contains two heated apertures. The emerging atomic beam has a mostprobable velocity of about 415 m/s at a temperature of 1350 ◦ C. The oven system isfollowed by an octagon, which gives optical access at five CF40 viewports. Here,as indicated with the blue arrows, we can apply transversal cooling (TC) [78]using the strong 401 nm transition. By cooling the atoms transversely with red
detuned light in a 2D optical molasses, their transversal velocity components
are reduced and thus the atomic beam is further collimated. Via the moveable
bellow on top, it is possible to place an Al mirror at the beam axis under anangle of 45 ◦ in respect to the beam axis. In this way, we can check the atomic
beam path towards the MOT chamber and the injection of the ZS light. On the

23

24

3. Experimental setup

Figure 3.1: Drawing of the complete vacuum chamber, which consists of: (a) Er oven chamber, (b) Li oven chamber, (c) ZS, (d) MOT chamberand (e) pumping chamber. Red arrows indicate the 1064 nm light, which we use for the ODT, yellow arrows show the 583 nm MOT beams,
blue arrows mark the 401 nm light for the ZS and TC.

3. Experimental setup

backside of the octagon we connect an ion pump1 , an ionization gauge2 and an
all metal angle valve, which is used to attach a turbomolecular pump system3
for pre-pumping. The Er oven chamber is separated by an all metal transition
valve from the rest of the chamber to allow refilling of the oven without loosing
the vacuum conditions in the whole chamber.
In the adjacent Li oven chamber, we can admix Li atoms to the atomic beam.
The Li oven4 is situated below the beam axis and emits Li atoms in verticaldirection. In a tube along the beam axis, which is divided alongside in threeparts, Er and Li are combined to a joint atomic beam. In 2/3 of the tube's crosssection, the Er atomic beam travels from the Er oven towards the ZS and MOT.
Li atoms can enter the remaining 1/3 of the tube from below and are collimatedto a longitudinal beam by microtubes inserted along the beam axis [79]. At theend of the tube, Er and Li atoms emerge towards the ZS and merge into a two
species atomic beam. In the prime setup, where we focus on Er itself, this Li ovensection is replaced by an ordinary tube. After the Li oven section, a four-way
cross connects another pump section with an ion pump1 , an ionisation gauge2 andan angle valve. On top, a Ti-sublimation pump5 gives further pumping capacity
on demand. From below, the atomic beam shutter can mechanically block theatomic beam via a tiltable bellow and a servo motor. Past this, another cubewith four viewports allows further transversal cooling to collimate the beam. A
bellow, which we use for the alignment of the complete chamber, connects thesecond valve, which is integrated for the same reason as the prior one.
The ZS is a spin-flip type σ − slower with an independent magnetic offset
field. For the ZS we use the 401 nm light, red detuned by about 16 ∆ν =b 580 MHz.
The ZS is water cooled and contains a differential pumping tube. This 8 mm indiameter and 30 cm long tube maintains a pressure gradient of 103 between theoven chambers, where pressures of 10−9 mbar are sufficient, and the experimental
chamber, where pressures of about 10−12 mbar are needed. After the ZS, theslowed Er atomic beam is expected to have a longitudinal velocity of 5 m/s.
The slowed atoms are captured in the MOT chamber. We use the narrow
583 nm transition for MOT operation. The MOT consists of a six beam opticalmolasses and a quadrupole magnetic field. Depending on the available laser power
and on the desired MOT size, the beams each have a diameter of up to 30 mm
and the coils generate a magnetic field gradient of about 10 G/cm. The Feshbachand the curvature coils give an homogeneous offset magnetic field for the useof Feshbach resonances [12] and add curved magnetic fields for compensation
1

Varian Star cell 20 l
Varian UHV-24
3
Pfeiffer HiCube classic
4
The Li oven has the same design as the one already used in the FeLiKx experiment in
Innsbruck [79].
5
Varian TSP filament-type
225

3. Experimental setup

or magnetic trapping. A pair of compensation coils, which compensates themagnetic field of the ZS is mounted on the front and back of the MOT chamber.
All coils are water cooled. To compensate for residual magnetic fields of any
direction, we install a compensation cage around the MOT chamber, which is
not shown Fig. 3.1. To cool the atoms towards quantum degeneracy, we load theatoms from the MOT into a crossed optical dipole trap (ODT) at 1064 nm. For
this, another four, smaller, CF16 viewports give optical access for two beams,
which are sketched as red arrows.
To provide and measure pressures as low as 10−12 mbar, the pumping chamber
is equipped with an ion pump6 , a Ti-sublimation pump5 and an ionisation gauge2 .
For pre-pumping and the baking of the experimental chamber, a turbomolecular
pump3 can be attached by an angle valve. Since not all atoms from the atomic
beam are captured by the MOT, but a large part will hit the end of the chamber,
it is not possible to inject the 401 nm light for the ZS directly from the backside,
because a coated window looses transmittance rapidly. A coated mirror suffers
only small loss of reflectivity, as we measured in a test setup with the movablemirror from the Er oven section. The reflectivity of the Al mirror coated with Er
was only 3 % lower than that of the uncoated mirror. Therefore, in the four way
cross, we inject the ZS light towards the atomic beam with a 45 ◦ Al mirror fromthe side.

3.2

Cooling and trapping lights

A single-mode single-frequency (smsf) frequency doubled diode laser7 provides
light at 401 nm. It has an output power of 120 mW, which we use for ZS, TC
and imaging. The linewidth of the laser diode of about 100 kHz is well below thenatural linewidth of the 401 nm transition in Er. To prevent long-term frequency
drifts we lock the laser to the atomic transition by a phase modulation transfer
locking scheme. Figure 3.2 shows the optical setup of the locking scheme.
To lock the laser to the atomic transition frequency, we generate free Er atoms
that can get resonant with the laser light. Since Er has a very high melting pointtemperature, it is inapplicable to use a vapor cell, as it is done for all alkali
atoms [80]. Therefore, we use a hollow cathode lamp (HCL), which is a glass
tube with Er coated cathodes and is filled with Ar buffer gas at a pressure of
4 mbar. By applying high voltage8 to the electrodes, we produce an Ar plasma.
The Ar ions are accelerated towards the cathode, hit it and sputter off Er atoms.
This generates free, neutral Er atoms that we can use to lock the laser. To obtainan error signal for the lock, we use modulation transfer spectroscopy [81, 82], a
6Varian Star cell 75 l
Toptica DL-SHG pro
8
Typical values are a voltage of 125 V at a current of 7 mA.
726

3. Experimental setup

Figure 3.2: Scheme of the optical setup for the modulation transfer lock. In a hollow
cathode lamb (HCL), free Er atoms interact can get resonant with the lower beam branch,
the probe beam . The upper beam branch, the pump beam, is modulated with an electro
optic modulator (EOM) before it enters the HCL. The probe beam signal is detected witha photodiode (PD). By mixing it with the local oscillator (LO) signal used for the EOM
we gain an error signal for locking the laser to a certain Er transition.

pump-probe technique, which gives a Doppler-free spectrum. For this, the lightfrom the laser is split with a polarizing beam splitter (PBS) into a probe and apump beam. The pump beam is phase modulated with an electro optic modulator (EOM), which is driven with a local oscillator (LO) at a frequency of
about 14.7 MHz. With another PBS we overlay counter propagating pump- andprobe beam in the HCL. If the light is resonant with the Er atoms, the phasemodulation of the pump beam is transferred to an amplitude modulation of theprobe beam by nonlinear effects in the atoms. We detect the probe beam with aphotodiode (PD) and mix it with the LO signal to allow phase sensitive detection. The generated signal has a flat baseline and a zero-crossing exactly at thetransition frequency and thus can be fed directly to the laser system as an error
signal for stable long-term locking. A typical signal of this modulation transfer
spectroscopy is shown in Fig. 3.3. Here, four of erbium's five stable bosonic isotopes are clearly visible at the major zero-crossings of the signal, separated by
the isotope shift. The residual zero-crossings, mainly in-between 166 Er and 168 Er,
arise from the fermionic 168 Er, which is split into several hyperfine states. We canlock the laser to a certain isotope by the steep signal slope at the corresponding
zero-crossing.
The MOT light at 583 nm is generated by a dye laser9 , which we pump witha 10 W smsf solid state laser10 . The current master work of Alexander Rietzler isthe development of a locking scheme for the dye laser. It needs to have smsf operation at an output power of 700 mW and a stability and linewidth of 100 kHz11 .
9Radiant Dyes cw-ring-laser
Coherent Verdi V10
11This is required, since the natural linewidth of the 583 nm transition in Er is 170 kHz.
1027

3. Experimental setup

Figure 3.3: A typical signal of the modulation transfer spectroscopy on the HCL. Fourof erbium's five bosonic isotopes are clearly visible at the major zero-crossings of thesignal, separated by the isotope shift. The residual zero-crossings, mainly in-between
166
Er and 168 Er, arise from the fermionic 168 Er, which is split into several hyperfine
states. Due to the signal's steep slope at the transitions and its flat baseline, it provides
an excellent error signal for the locking of the laser system.

For this, he will stabilize and lock the laser with an external cavity. The lightfor the ODT at 1064 nm is produced by a smsf solid state laser12 . Since a ODToperates far off detuned and the laser offers a good intensity stability, no special
frequency- or intensity stabilization is needed.

12

InnoLight MEPHISTO MOPA 18 W

28

Chapter 4

Erbium oven
We produce a thermal Er atomic beam from a commercial oven operating at
about 1200 ◦ C. The oven consists of an effusion cell, where few gram of solid Er
are sublimated, and two separately heated apertures, which collimate the atomic
beam. For thermal shielding, the high-temperature oven is water cooled. In this
Chapter, we first describe the setup, the working principle and the home built
control- and safety system. Later, we discuss the atomic beam shutter, which we
use to block the atomic beam prior the ZS.

4.1

Oven system

The complete oven system is manufactured by CreaTec Fischer & Co. GmbH1 .
The oven has a special design to fulfill the requirement of high-temperature operation, as needed for Er, which has a melting point temperature of 1529 ◦ C [52].
The central part is the effusion cell (EC), where solid Er is heated. The adjacent hot lip (HL) consists of two apertures that collimate and direct the atomic
beam emerging from the EC towards the ZS tube. For heat shielding, the wholecrucible is surrounded by a water cooled cylinder. Figure 4.1 shows a technicaldrawing of the detailed setup.
The tantalum (Ta) crucible consists of the EC part, where we can insert
10 cm3 of solid material, and the HL part, where a spacer fixes the first and second aperture. The apertures both have 5 mm inner diameter and are separated
by 50 mm. The EC and the HL part are heated separately with Ta wires, fixed bya pyrolytic boron nitride spacer that provides mechanical stability and electricalinsulation even at high temperatures. This whole section is surrounded by a water cooled cylinder and integrated in a steel tube with a CF40 flange connection
to the main chamber. A bellow allows to adjust the orientation of the oven. The
power supply for the heating wires and the temperature sensors are feed through1

Model: Dual Filament Effusion Cell DFC-40-10-290-WK.

29

4. Erbium oven

Figure 4.1: Schematic, sliced view of the Er oven. It consists of a crucible with EC
and HL, two separate heating wires, a water cooling system and a tiltable housing withconnections for power supply and temperature sensors.

at the back end of the oven by ceramic spacers.
The heating wires heat the EC and the HL radiatively. The specified temperature range is 100 − 1400 ◦ C, the PID controller provides a stability of better
than 0.1 ◦ C. Temperature ramps should not exceed 30 ◦ C/min, to allow thermalization with Er and reduce the stress on the crucible. The maximum EC and HL
heating wire currents and the corresponding heating powers are 3.5 A and 6.1 A
as well as 84 W and 220 W respectively [83]. Typical operation temperatures for
the EC range between 1000 ◦ C and 1350 ◦ C, depending on the required flux. Thistemperature is still well below the melting point of Er of 1529 ◦ C because liquidmaterial can break the crucible when cooling down the oven. Since we can heat
EC and HL separately, we typically use the HL at 100 ◦ C higher temperatures
than the EC to prevent material condensation at the apertures. This is an essential feature, since in related experiments2 with Cr, condensed Cr has been
observed to grow over the aperture and to lead to a short circuit of the heating
wires.
The thermocouple temperature sensors are attached outside of the crucible.
This implies that the measured temperature can differ from the actual temperature of the Er inside the crucible by few percent and we thus can use it only as
a guiding value. The water cooling system shields the vacuum chamber from thehigh temperatures. It requires a water flow of 2 l/min at 5 − 10 ◦ C water temperature and maintains a temperature of less than 100 ◦ C all over the oven section
vacuum chamber. The oven system has to be operated in vacuum, it is specified
from a maximum pressure of 1 × 10−5 mbar down to the UHV regime. To provide
this, we use a turbomolecular pump and an ion pump, as discussed in Sec. 3.1.
The high temperatures involved also require a careful material engineering.
We chose Ta for all parts of the crucible and for the wires. Tantalum has the advantage to have a very high melting point of more than 3000 ◦ C and to not create2

Private communication: Tilman Pfau, Universität Stuttgart.

30

4. Erbium oven

low-temperature-melting alloys with Er, as demonstrated by the Er experimentat the NIST. In contrast, Ta and Cr form a low-temperature-melting alloy, so inthis case, ceramic or other materials have to be used for the crucible [51].
A valve separates the oven chamber from the UHV part, so that we can keep
the vacuum in the MOT chamber while refilling the oven. For the first oven operation, we clean the parts in a supersonic bath of acetone first, then of isopropanol
and work in a clean environment. We cut Er pieces from an Er block and fill thebare crucible with typically 6 g of Er before we reassemble the crucible and theoven system. The insertion or removal of the crucible into the oven system must
be done carefully in order to guarantee collinear alignment, since the heating
wires can easily be damaged. Also the power and temperature connection mustbe handled with special care, since the ceramic spacers of the feedthroughs canbreak.

4.2

Control system

To control the high-temperature oven system and to secure it against power break
down and cooling water failure, we set up a control system as schematically illustrated in Fig. 4.2.

Figure 4.2: Structure of the Er oven control system. We control the oven from thecomputer via the oven control. We protect the oven control against power failure withan uninterrupted power supply (UPS), which we coordinate with the safety systems.

A CreaTec power supply unit with two power circuits supplies the heating
wires of EC and HL. It is controlled by two Eurotherm precision proportionalintegral-derivative (PID) controllers, which get feedback from the thermocouple
sensors. The controllers can be monitored and set manually onboard, or by acomputer connected via Ethernet. The iTools OPC Server program manages
the PID controller variables, which we read and write in the LabVIEW oven31

4. Erbium oven

control program. In this way we monitor the actual temperature, the working
setpoint temperature and the current output power and can set the temperature
setpoints3 and the temperature ramps.
Power failure can cause repeatedly, abrupt temperature ramps that damage
the crucible. Therefore, we backup the power supply and the PID controller withan uninterrupted power supply (UPS), which is connected to the computer via
an USB port. Here, the MGE UPS program manages the UPS variables, andexecutes the command line in case of variable changes. The command line itself
starts a LabVIEW subVI executable that updates the UPS status in the LabVIEW oven control program. Therefore, in case of power failure, if the remaining
supply time of the battery falls below a preset value, we cool down the EC and
HL heating wires in a controlled way to the standby temperature, from which asudden power-off does not harm the crucible.
The status of the cooling water system and the emergency off system are connected to the interlock of the UPS. In case of failure of the cooling water supply
for the oven, as too low water backflow or leaks, this triggers an instant power offof the UPS and thus of the heating wires. This is crucial since without sufficientcooling water flow, the oven will overheat and vaporize the cooling water, which
can damage the oven.
Hence, to operate the oven, the emergency-off system has to be inactive, thecooling water must run, the UPS and the power supply unit have to be switchedon and the program iTools OPC Server must run. Then, the LabVIEW oven
control program can be started to control the heating wires.
Figure 4.3 shows the user interface of the oven control program, App. B gives
a detailed description of the program code. The user sets the EC and HL temperatures and the heating or cooling ramps in the commensurate displays of thetwo upper sub windows. Note that both values are protected against fault input.
For operation at preset temperature setpoints, the 'ON' button changes between
default temperature setpoints for working or standby operation. Further displays
show the present temperatures, working setpoints, target setpoints, the thermocouple sensor status and the actual output power. The central part is a graphshowing the actual and the working setpoint temperature in real time. In Fig. 4.3,
the graph displays the initial heating up phase from 'OFF' to 'ON' mode. The
straight lines mark the evolution of the working setpoints, which result of the target setpoints and the temperature ramps. The actual temperature values oscillate
around the ideal values since the current limitation on the power supply is set tovalues that are optimized for the 'ON' mode. EC and HL temperature oscillate
alternately; this shows that although the two PID controllers work independentof each other, the EC and HL system are coupled via radiation inside the oven.
The 'enable values' button in the lower left of the screenshot allows to adjust3

The setpoint is the final obliged value, the working setpoint is the present obliged value.

32

4. Erbium oven

Figure 4.3: A screenshot of the oven control program user interface. We can set andmonitor EC and HL temperatures on the computer. The program also reacts to thestatus the UPS.

the preset values for the temperature limits and the 'ON/STANDBY' temperatures. The 'EMERGENCY OFF' button at the lower middle of the interface
sets the temperature setpoints and working setpoints to zero. This switches off
the heating and the oven cools down as fast as possible. The subwindow 'UPS
status' shows the status of the UPS variables. The program automatically reacts
to changes of the backup time of the UPS.

4.3

Atomic beam shutter

For each experiment cycle, we will load the MOT with atoms coming from the
Zeeman slowed beam. After the MOT phase, the atoms are lead into an ODT.
At this point, the atomic beam should be blocked to leave the already opticallytrapped atoms unperturbed. Therefore, it is of prime importance to install an
atomic beam shutter between Li oven and ZS section. The beam shutter is amechanical shutter, which is driven by a servo motor. A control box connected33

4. Erbium oven

(a)

(b)

(c)

Figure 4.4: Technical drawings of the atomic beam shutter. (a) The shutter unit, in
position (1): 'blocked beam' and in position (2): 'unblocked beam'. (b) The servo motorwith mounting. (c) The complete assembly to the vacuum chamber, here the atomic
beam enters from the front and is blocked.

with the experiment computer controls the shutter operation.
Figure 4.4 (a) shows the beam shutter for the 'blocked beam' and the 'unblocked beam' position. The disc has a diameter of 20 mm and since this isconsiderably larger in diameter than the 275 mm distant differential pumping
tube of the ZS with 8 mm in diameter, this ensures adequate blocking of theatomic beam. A little bar connects the disc with the lower end of a bellow,
which we attach to the vacuum chamber. Two ball bearings on the side arms,
which we tighten with springs4 allow tilting of the bellow. Figure 4.4 (b) shows
the mounting of the servo motor. It is fixed to the posts of the chamber, andconnected to the lower end of the bellow with a little bar. The servo motor hasa metal gear to provide a long lifetime, and a torque of approximately 150 Ncm,
which is sufficient to tilt the bellow. It is specified to rotate by 40 ◦ in 0.17 s at
a supply voltage of 6 V, this sets the limit of the shutter speed. As common for
servo motors, it is controlled with a pulse width modulated (PWM) signal. Thissignal has a period of 20 ms and an amplitude of 5 V. By modulating the width
between 1 ms and 2 ms, we can set the position of the shutter. Figure 4.4 (c)illustrates the complete assembly of the shutter system. In this view, the atomic
beam enters from the front and is blocked by the shutter.
The atomic beam shutter control box connects the servo motor with the digital output box of the experiment control. For this, we use a microcontroller5(µC), which coordinates manual or digital adjustments and control. In App. C.1
the circuit diagram and the operating guidelines for the electrical details and right4
5

Not shown in the drawing.
Atmel AVR ATmega128

34

4. Erbium oven(a) front view(b) side view

Figure 4.5: The atomic beam shutter control box with all connections, status LEDs
and most switches. Switches for the adjustment of the shutter position are inside thebox.

usage are given. The source code for the µC, which we wrote in the programming
language C, and comments on it in App. C.2 give insight into the firmware structure. Below, we describe the features of the control box according to Fig. 4.5 andgive a brief overview of the firmware structure.
The control box is powered with 5 V to 8 V via a BNC connector. This directly supplies the servo motor, whereas we supply the electric circuit with a 5 V
voltage regulation. This division avoids unintentional resets of the µC and protects the µC against too high voltage. In case of a low signal on the emergency
off connector, the control box aborts operation and blocks the atomic beam. The
experiment control sends a TTL signal to the control box. It has either a 'high'or a 'low' value and thus triggers the shutter position 'blocked beam' and 'unblocked beam'. To avoid groundloops, we do not connect the TTL signal directly
to the µC, but via an opto-isolator6 , therefore it is inverted, the same holds forthe emergency off signal. The switch 'pc/manual' changes from computer control
to manual control, where the shutter position is set by the 'unshut/shut' switch.
To calibrate the shutter position, we open the box, choose the manual mode andadjust the 'unshut' or 'shut' position by turning on the according potentiometer
inside the control box. The connector 'con3' in Fig. 4.5 (b) offers to reprogram
the µC via the programming adaptor without opening the box. Aside, the servo
is attached. This connector7 supplies the servo with power and sends the PWM
control signal. The status LEDs display position and mode of the shutter and the
shutter control. At initialisation, all LEDs shine for 1 s, blinking LEDs indicate
an emergency blocking.
All these features result from the firmware of the µC. The basic working
scheme relies on the following segments. A main while-loop uses interlaced ifloops to check the status of the control variables ordered by their importance:
6

An integrated circuit (IC), providing galvanic separation by translating electrical information into optical information and backwards.
7
For convenience, the connector is a case insensitive six pin connector, although only threepins for power, ground and signal are needed.

35

4. Erbium ovenemergency off', 'pc control', 'manual control', 'shutter positioning'. To control
the servo, a timer interrupt runs every 10 ms8 . If the value of the variable 'shutterpos', which determines the blocking of the atomic beam, changed within thelast second, it sends the appropriate signal to the servo motor. Otherwise, it
sends no signal and so leaves the motor at rest to avoid needless vibrations.
The interrupt, the PWM signal output and the analog to digital conversion9(ADC) are all features provided by the µC itself and are initialized together withthe pin configuration in the beginning. In the end of the source code, we define
the user defined functions for the positioning of the shutter via the potentiometers and the setting of the shutter position according to the manual- or the TTL
signal input. The included header file defines constants, macros, variables andfunctions.
'

8This delay is negligible compared to the angular speed of the servo motor.
The ADC converts the analog voltage values of the potentiometers, which we use for adjustment of the shutter position, to digital values, which the µC can process.
936Chapter 5

Characterization of the atomic
beam
We characterize the Er atomic beam using differential absorption spectroscopy.
Already well below the melting point of Er, we observe a comparatively highatomic flux from the oven and an unexpected large spatial divergence of theatomic beam, indicating a large Doppler broadening. Based on our observations,
we designed an optimized, new generation atomic beam collimation setup, which
includes two apertures and a reducing-flux tube. In this Chapter, we describe themeasurement setup and present our observations on beam divergence and atomic
flux, performed on both the original and the optimized collimation setup, here
referred to setup 1 and setup 2 respectively. A comparison of the performance ofboth setups is also given.

5.1

Measurement setup

To measure the atomic flux emerging from the Er oven and the divergence of theatomic beam, we perform spectroscopic measurements using the 401 nm transition. This is a comparatively strong transition with a linewidth of 36 MHz anda saturation intensity of 72 mW/cm2 . It is well suitable for such a measurement
since the resulting spectra provide strong signals. Figure 5.1 illustrates the opticalsetup. As discussed in Chap. 4, the Er oven system creates an atomic beam travelling longitudinally towards the MOT chamber, see Fig. 3.1. Our spectroscopic
measurements are performed in the octagon chamber, which is located just before
the Li oven section and the ZS tube. Here, five viewports guarantee good opticalaccess. The 401 nm light enters the chamber and is intersected transversely withthe atomic beam. If the light is resonant with the atomic transition, the atoms
absorb the light, which then is spontaneously re-emitted.

37

5. Characterization of the atomic beam(a) side view(b) front view

Figure 5.1: The optical setup of the differential absorption spectroscopy and the imaging of the atomic beam fluorescence. (a) In the sliced side view of the oven chamber, acollimated atomic beam, drawn in red, leaves the Er oven. We split 401 nm light by a
PBS into a reference beam, which falls directly on a PD and into a probe beam. The
probe beam enters the octagon where it interacts with the atomic beam before it isdetected by a PD. The difference of the two PD signals gives a signal free of global intensity fluctuations. (b) As shown in the front view, a CCD camera images the fluorescence
perpendicular to laser and atomic beam, which travels into the plane of projection.

Absorption spectroscopy
We measure the absorption of light in a differential absorption spectroscopy setup
as illustrated in Fig. 5.1(a). The absorption of light is detected by the photodiode
PDprobe . By scanning the laser frequency, we record the absorption spectrum of
the 401 nm transition for all stable isotopes. Since the atomic beam and the laser
beam are perpendicular to each other, the spectral width provides information on
the transversal velocity of the atoms and on the transversal Doppler broadening.
To remove the background of the absorption signal, we use a differential setup.
Here, a PBS splits the 401 nm light, transported with a fiber1 from the lasertable to the experiment-table, into a probe beam and a reference beam. The
intensity ratio of the two beams is adjustable by a half-wave plate. The reference
beam power is measured directly by PDref . The probe beam passes through thechamber and interacts with the atoms before it is detected at PDprobe . Lenses2
focus the laser beams onto the photodiodes. Within few percent, both beam paths
have the same length of ≃ 45 cm to equalize distortion effects that scale with1

In the setup characterized in Sec. 5.2 we use a polarization-maintaining singlemode Thorlabs PM-S350-HP-custom fiber of 10 m length. In the setup characterized in Sec. 5.3 we use apolarization-maintaining singlemode Schäfter + Kirchhoff PMC-400Si-3.1-NA010-3-APC-800P
fiber followed by an additional PBS to clean the polarization further.
2
With a focal lenght of 50 mm.

38

5. Characterization of the atomic beam

the length. The differential signal PDprobe − PDref is free from global intensitychanges, but is sensitive to intensity changes of the individual beams. To improve
the signal further, we shield the chamber and the photodiodes from stray lightand install an additional aperture in front of PDprobe to avoid back-reflections
into the chamber.
The parameters and settings of the actual measurement are as follows. The
laser beam power before the PBS is 60 µW, the radius of the laser beam is about
0.07 cm. Therefore, the intensity of the light is I = 1 mW/cm2 , which is well below
the saturation intensity, I ≪ Isat . To operate the laser on resonance, we lock thefrequency externally via the HCL to the 401 nm transition of 166 Er, as discussed
in Sec. 3.2. To scan the frequency, we use the scan mode of the laser systemthat simultaneously tilts the grating and changes the diode current of the seed
diode laser. This results in a triangular frequency signal with more than 5 GHz
peak-to-peak frequency amplitude and a period of 3 s at default settings. By this,the laser frequency can be scanned over the resonance without mode-hops in the
doubling cavity. The differential PD signal is recorded with a digital storage
oscilloscope. To achieve a good signal-to-noise ratio, all spectra are obtained byaveraging the signal over more than 30 frequency scans. To calibrate the laser
frequency in the scanning region, we measure the wavelength with a wavemeter3
and combine this with the scan rate of the laser system. As discussed in moredetail in App. D.1, this gives the frequency axis to the spectra recorded with theoscilloscope.

Fluorescence imaging
Additional to the absorption spectroscopy, we also image the fluorescence ofatoms emitted in random directions with a CCD camera4 . As shown in Fig. 5.1(b), we mount the camera in front of an octagon chamber viewport, perpendicular
to the laser beam. By this, we determine the laser-atom interaction length andestimate the cross section of the atomic beam. We place the camera about 20 cm
from the chamber and we use a camera objective with large focal length, focusedto the center of the chamber. A cover shields the camera from stray light. We
calibrate the pixel size and the exposure time of the camera as described in detailin App. D.2. The exposure time needs to be short, not to saturate the CCD chipat high fluorescence light intensities and it needs to be long enough to detect low
intensities. In setup 1, the optimal exposure time is 100 ms and the pixel size is
1 px =
b 58.1 µm. In setup 2, the optimal exposure time is 1 s and the pixel size is
1 px =
b 42.8 µm.
Figure 5.2 shows a typical CCD image of the fluorescence light of the atomic
beam. In this view, the atomic beam is entering the image from the right side,3
4

HighFinesse WS/7
MATRIX VISION blue fox

39

5. Characterization of the atomic beam

atomic beamlaser beam

Figure 5.2: A typical CCD image of the fluorescence light of the atomic beam. In thisview, the atomic beam is entering the image from the right side, the laser beam fromthe bottom, as indicated by the arrows (not in scale). Reflections of the light in thechamber are removed by a reference image. Only the parts of the atoms whose resonancefrequencies are Doppler shifted by less than the natural linewidth of the transition areresonant and fluoresce. From such an image we derive the light-atom interaction length.

the laser beam from the bottom. Reflections of the light in the chamber are
removed by a reference image. Only the parts of the atoms whose resonance frequencies are Doppler shifted by less than the natural linewidth of the transition
are resonant and fluoresce. From such an image we derive the light-atom interaction length. In combination with the differential absorption measurement, we
can deduce the flux of the atomic beam, as discussed in Sec. 1.3 and in Sec. 5.4.

5.2

Collimation setup 1

The collimation setup of the oven consists of a number of apertures placed rightafter the effusive oven. It determines the divergence of the atomic beam and its
flux. The setup has to compromise between high flux and low atom loss. On the
one hand, highly divergent atomic beams are useless in the experiments since only
atoms in the central part of the beam can enter the ZS tube because of geometriclimitation. On the other hand, strong collimation leads to an insufficient atomicflux.
In setup 1, we place two apertures in the oven section as schematically illustrated in Fig. 5.3. The first aperture, aperture 1, has an inner diameter b1 ≃ 5 mm
and it is situated between the EC and the HL. At a distance a ≃ 50 mm aperture2, is installed with an inner diameter b2 ≃ 5 mm. This second aperture has themain scope of collimating the atomic beam. At a distance of l ≃ 83 mm fromaperture 2, the probe laser beam transversely intersects the atomic beam. To
characterize this setup before mounting the complete vacuum chamber, we assembled first the Er oven chamber, named section (a) in Fig. 3.1. Instead of thevalve terminating the chamber, we placed a CF40 viewport.
As already pointed out in Chap. 1, the oven operates in the effusive regime.
Using Eq. (1.1) and Eq. (1.2), we estimate the mean free path to be λmf ≈ 4 cm
40

5. Characterization of the atomic beam

Figure 5.3: Scheme of collimation setup 1. Aperture 1, which separates EC and HL
section and aperture 2, which collimates the atomic beam have both an inner diameterof b1 = b2 ≃ 5 mm and are spaced by a ≃ 50 mm. At a distance of l ≃ 83 mm from theaperture 2, the probe laser beam transversely intersects the atomic beam. The atomic
beam diameter is expected to be d1:2 = 22 mm.

at a temperature of 1350 ◦ C. Since the aperture dimensions are lower than λmf
by an order of magnitude, we assume to be in the effusive regime.

Beam divergence
The atomic beam diameter at a certain distance from the EC is a measure of
the beam divergence. By Eq. (1.8), for the geometry of setup 1 as illustrated inFig. 5.3, we expect a diameter of d1:2 = 22 mm at a distance of a + l from theEC. We estimate the actual beam diameter dex by imaging the fluorescence of theatomic beam at the intersection with the laser beam. Since atoms with a radial
velocity component vx 6= 0 experience a Doppler shifted resonance frequency ν0′ ,we need to scan the laser frequency on a range exceeding the Doppler shift toimage the complete atomic beam spectrum. Figure 5.4 shows such a measurement. Frames (a) to (i) represent negative fluorescence image sections, which
are recorded in a time sequence. The atomic beam enters each frame from theright, the laser beam from the bottom, identical to Fig. 5.2. The laser frequency
is scanned and increases from frame (a) to (i). Therefore, different sections of
the atomic beam with different Doppler shifted resonance frequencies fluoresceon each frame, leading to an apparent motion of the fluorescence. The inhomogeneous shape of the fluorescence in frames (d) and (e) results from the fact thatduring the exposure time of 100 ms, the laser frequency is scanned by 200 MHz
over the transversal atomic beam profile, leading to a distorted image. Fromframe (b) to (h) the fluorescence is visible in between the red dotted lines, spacedby 41 mm, which serve as a guide to the eye. However, the field of view of the
CCD camera is of equal size and the edges of the total fluorescence region, aresharp and not smooth. Thus, it is likely that the actual atomic beam diameteris larger than the field of view. Therefore, we determine the lower bound of theatomic beam diameter to be dex & 41 mm.
41

5. Characterization of the atomic beam

1cm

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Figure 5.4: Fluorescence images, which are recorded in a time sequence. The atomic
beam enters each frame from the right, the laser beam from the bottom. The laser
frequency is scanned and thus is increased from frame (a) to (i). Therefore, different
sections of the atomic beam with different Doppler shifted resonance frequencies fluoresceon each frame. The red dotted lines serve as a guide to the eye and signalise the region offluorescence. A scale is given in frame (a) and to improve visibility we show the negative
images.

Figure 5.5: Scheme of the actual atomic beam in collimation setup 1. Atomic vapor
fills both EC and HL part leading to an atomic beam that emerges from aperture 2 andis collimated at the inner edges of the octagon at a distance a3 ≃ 66 mm from aperture 2
with a diameter of b3 ≃ 38 mm. For geometrical arguments, the resulting atomic beamis highly divergent and has a large diameter d2:3 = 49 mm.

42

5. Characterization of the atomic beam

Figure 5.6: Transversal absorption spectrum at TEC = 1350 ◦C and THL = 1450 ◦C.
The black line shows the differential signal, the red curve is a five peak Voigt function
fit to the data. Five of the six stable Er isotopes are clearly resolved. The signal isnormalized to the maximum absorption corresponding to a maximum optical density
ODmax ≃ 0.21.

This is a factor of 2 bigger than the value of d1:2 = 22 mm, which was expected
for this collimation setup. A possible explanation for the large value of dex is toconsider both the EC and the HL behaving as an effusive oven, as schematicallyillustrated in Fig. 5.5. As a consequence, the first aperture will not play anyrole in the collimation since similar to the EC, also the HL is filled with atomic
vapor. This leads to an effectively shifted collimation setup: the atoms emerge
from aperture 2 and are collimated at the proximate limiting structure, whichis the octagon. The inner edges of the octagon chamber, which have a diameterof b3 ≃ 38 mm and a distance of a3 ≃ 66 mm from aperture 2, act as a third
aperture. For such a collimation, we expect a beam diameter of d2:3 = 49 mm
what is in agreement with the lower bound of dex .

Spectrum
The large transversal divergence of the atomic beam is also confirmed by theabsorption spectra. We measure the transversal absorption spectrum as describedin Sec. 5.1. By this, we can directly measure the Doppler broadened width of theabsorption signal and get information on the transversal velocities. Therefore, we
can characterize the oven system also in dependence of its operation temperature.
Figure 5.6 shows the absorption spectrum recorded with the above described43

5. Characterization of the atomic beam

Figure 5.7: Abundance relative to 166 Er of the stable Er isotopes. The measured values,
indicated as black squares, are in well agreement with the literature values [63], indicatedas red circles. Since 162 Er has very low abundance, no reliable measurement result exists.
167
Er is split into eight hyperfine states and is not resolved in the measurement. The
error bars are statistical over seven measurements.

setup 1. Since the EC and the HL part are operated at high temperatures of
TEC = 1350 ◦ C and THL = 1450 ◦ C, the atomic beam has a high flux and absorbs
40 % of the incident light, leading to a distinct signal. All five stable bosonicisotopes of Er are clearly resolved. According to Eq. (1.26), we fit a Voigt function
to the data from which we determine the peak positions and the width. The fitted
Voigt function shows a vanishing small Lorentzian contribution, thus we can treat
it as a pure Gaussian function.
Isotopic composition and isotope shift
The area of each individual absorption peak gives information on the isotope
abundance. For an accurate determination, we average over seven different measurements at different operation temperatures. Comparing the measured values
normalised to 166 Er with the natural abundance reported in literature [63], we
find overall good agreement for 164 Er, 168 Er and 170 Er as shown in Fig. 5.7. Because of the low abundance of 162 Er of 0.1 %, we can not give a precise value.
167 Er is split into eight hyperfine states and is not resolved in the spectrum. The
error bars account for the statistical error of the seven measurements.
The peak positions provide information on the isotope dependent frequency
shift. Figure 5.8 compares the measured values to the literature values [32]. As
44

5. Characterization of the atomic beam

Figure 5.8: Frequency shift of the 401 nm transition relative to 166 Er for all stablebosonic isotopes of Er. The measured values, indicated as black squares, are in very
good agreement with the literature values [32], indicated as red circles (no known value
for 162 Er). The error bars are statistical over seven measurements.

before, the results are mean values of seven measurement sets, leading to a statistical error estimation. All values known from literature, also shown in Fig. 2.3,
agree very well with our results. For 162 Er, to our knowledge no literature value
exists, but our measured value fits to the slope of 400 MHz frequency change peratomic mass unit (amu) observed at the other bosonic isotopes.
Line shape and linewidth
In absence of any broadening mechanisms, the absorption spectrum has a Lorentzian line shape with a width given by the natural linewidth ∆νnat , which is determined by the inverse lifetime of the excited state. For the 401 nm transition∆νnat is 36 MHz. In our measurements, we always observe a linewidth bigger
than the natural one, meaning that the spectrum is affected by some broadening
mechanism. The shape of the absorption spectrum gives information on the underlying broadening mechanism. A Gaussian shape is most probably ascribed to
Doppler broadening, while a Lorentz type shape can arise from saturation or collisional broadening. For mechanisms of equal strength, the profile is represented
by a convolution of the contributing line shapes, namely a Voigt profile. In thisfirst measurement set, we always observe a pure Gaussian profile and assume that
Doppler broadening is the most dominant broadening mechanism. The error bars
shown in all following graphs refer to the statistical error coming from the fit of45

5. Characterization of the atomic beam

Figure 5.9: The Gaussian linewidth ∆νG of 170 Er in setup 1 as a function of the EC
temperature corresponding to the Doppler broadening of the line. The measured values
do not fit to the ones expected from Eq. (1.23) for√ collimation at apertures 1 and 2
drawn with a solid red line. A free fit to ∆νG = α TEC , indicated by the dashed blueline, suggest α = 10.0(3) corresponding to a collimation at aperture 2 and the octagon
chamber.

a Voigt profile to the absorption data.
The linewidth of all isotopes should not differ more than 1 % since the massdependence of Doppler broadening is weak. However, the linewidth of the threemost abundant bosonic isotopes differs by 8 % what we explain by the influenceof the fermionic 167 Er. 167 Er is split into eight hyperfine states and not resolved
individually in the measurement, but nevertheless alters the absorption peaks of
166 Er and 168 Er. Therefore, in the following we will only focus on the propertiesof the 170 Er isotope, which shows the most isolated but yet distinct absorption
peak.
The linewidth of a Doppler broadened line depends on the transversal velocity
component of the atoms and is thus proportional to the beam divergence and thetemperature. In Fig. 5.9 we show the measured values of the Gaussian contribution ∆νG to the linewidth of the Voigt profile, corresponding to the Doppler
width, as a function of TEC , where THL = TEC + 100 ◦ C. From Eq. (1.23), we
expectp√∆νD = (ν0 /c) f 3 kB T / m = α T ,(5.1)
where f is the collimation ratio and α a constant for a fixed f . For a collimationof the atomic beam at apertures 1 and 2, as illustrated in Fig. 5.3, α = 3.1
and ∆νG should follow the solid red line. The calculated values strongly differ
46

5. Characterization of the atomic beam

Figure 5.10: Spectrum in setup 1 for different HL temperatures. Dotted red line:
TEC = 1350 ◦C, THL = 1450 ◦C; solid black line: TEC = 1350 ◦C, THL = 970 ◦ C, signal
magnified by a factor of 5. For low HL temperatures, the peaks get narrower and thesignal is reduced. Therefore hyperfine states of 167 Er appear, whereas 162 Er is longer
resolved. The signal is normalized to the maximum absorption of the signal indicated by
the dotted red line corresponding to a maximum optical density ODmax ≃ 0.21. For thesolid black line, ODmax ≃ 0.07.

from the measured ones, which always show larger values of the linewidth. This
trend is consistent with our fluorescence measurements. The dashed blue line
corresponds to a fit of the measured values by Eq. (5.1), suggesting α = 10.0(3).
If we consider the first aperture is not playing any role and that the collimation
is provided by aperture 2 and the inner edges of the octagon chamber, we expect
α = 10.1. This agrees well with the measured values and further confirms thefluorescence measurements.
Varying the HL temperature
To investigate the reason for the apparent failure of aperture 1, we decrease the
HL temperature whilst maintaining constant EC temperature. Due to radiative
heating the lowest attainable temperature is THL = 970 ◦ C at TEC = 1350 ◦ C.
The corresponding spectrum is shown as a solid black curve in Fig. 5.10. The
signal has lower intensity and is magnified by a factor of 5 to compare it to thespectrum at TEC = 1350 ◦ C, THL = 1450 ◦ C, drawn as dotted red line. We seethat the absorption peaks are narrowed by decreasing the HL temperature. Dueto the narrower absorption spectra, hyperfine states of 167 Er appear for instance
between the 166 Er and the 168 Er peak. This clear change of the signal strength47

5. Characterization of the atomic beam

Figure 5.11: Change of the spectrum shape for TEC < THL . The solid green line representing a fit to a pure Lorentzian function, fits the spectrum at TEC = 1350 ◦C,THL =1150 ◦C better than the dashed red line representing a fit to a pure Gaussian function.
The signal is normalized to the maximum absorption corresponding to a maximum optical density ODmax ≃ 0.09.

and linewidth emphasizes that the HL temperature affects the atomic beam andthat it does not only play the secondary role to avoid source material condensation at the apertures.
The line shape of the absorption peaks changes with decreasing the HL temperature while keeping the EC temperature constant, as visible in Fig. 5.11. Thisobservation demonstrates that not only the EC, where the Er material is placed,
but also the HL has an oven-like behavior. The solid green line representing a fit
to a pure Lorentzian function, fits the spectrum at TEC = 1350 ◦ C, THL = 1150 ◦ C
better than the dashed red line representing a fit to a pure Gaussian function. We
find that in contrast to temperature sets with THL & TEC , where the spectrum
evolves towards an almost pure Gaussian profile, for THL . TEC a Lorentzianfunction is the dominant contribution to the total line shape. According to
Eq. (1.27), the Voigt profile has a Gaussian contribution ∆νG and a Lorentzian
contribution ∆νL to the total width ∆νV . For TEC = 1350 ◦ C, THL = 1450 ◦ C,(∆νG / ∆νL ) ≈ 1021 and for TEC = 1350 ◦ C, THL = 1150 ◦ C, (∆νG / ∆νL ) ≈ 0.6,
signifying the change of the line shape. This implies that for THL . TEC Doppler
broadening is not the only broadening mechanism present. The underlying mechanism for the Lorentzian line shape is not fully understood and suggests thatcomplicated atom dynamics occur in the HL part. Saturation- and collisional
broadening have Lorentzian line shapes. The first mechanism can be neglected48

5. Characterization of the atomic beam

due to the low intensity of the laser beam of I ≈ 0.01 Isat . As follows, collisional
broadening can partially explain the observed behavior.
The HL part has EC-like character
We explain the strong influence of the HL temperature on the linewidth and theline shape as follows. Erbium atoms that emerge from the EC at too large solid
angles will not pass aperture 2, but stick to the walls of the HL part. Since thesewalls are heated, the atoms are re-emitted in random directions. Re-emitted
atoms collide with atoms emerging from the EC and create an atomic vapor in
the HL. This disables the creation of an atomic beam and gives the HL part anEC-like character. From aperture 2, an atomic beam emerges into the octagon
chamber, where it can propagate freely since no atoms are re-emitted from thewalls. This corresponds to the situation illustrated in Fig. 5.5: both the EC andthe HL part are filled with atomic vapor and thus aperture 1 and the EC itself
are effectless to the atomic beam. Consequently aperture 2 and the HL inherit
this role and the HL becomes EC-like character. This mechanism depends on two
parameters: the flux from the EC, and the temperature of the HL. For low flux
from the EC the collisions will be limited and the beam can propagate throughthe HL part. For low HL temperatures the re-emission of atoms from the walls
is reduced and the emergence of atomic vapor in the HL is limited.
We check our speculation by measuring the linewidth as a function of the HLtemperature for a constant EC temperature of 1250 ◦ C, as shown in Fig. 5.12.
The total linewidth ∆νV consists of a Gaussian contribution ∆νG , shown as
black squares, and Lorentzian contribution ∆νL , shown as red circles. The HLtemperature strongly determines the ratio of both contributions. For THL ≥1200 ◦ C, the profile is purely Gaussian and the Lorentzian contribution is not
resolved. At high HL temperatures ∆νG is on the order of magnitude of the
expected Doppler broadening for an atomic beam collimated at aperture 2 andthe octagon chamber, indicated as a dotted line. For THL ≤ 1150 ◦ C, ∆νG dropsand ∆νL dominates. In this region, ∆νG is even lower than the expected Doppler
broadening for an atomic beam collimated at apertures 1 and 2, indicated as adashed line. This confirms the considerations above: for low HL temperatures thebeam can propagate freely from the EC through the HL part, and an additional
broadening mechanism with Lorentzian line shape is resolved. ∆νL increases withrising HL temperature. In first order this agrees with Eq. (1.25), which describes
the width of a line broadened by collisional broadening.
Conclusion
We conclude that in the original collimation setup for operation temperatureswith THL & TEC , the emerging atomic beam is highly divergent as pointed out
directly by the fluorescence imaging measurement as well as by the large linewidth49

5. Characterization of the atomic beam

Figure 5.12: Gaussian contribution ∆νG , shown as black squares, and Lorentzian
contribution ∆νL , shown as red circles, to the total linewidth ∆νV of the 170 Er absorption
peak as a function of the HL temperature for TEC = 1250 ◦C. For THL ≥ 1200 ◦C, theprofile is purely Gaussian and the Lorentzian contribution is not resolved. For THL ≤1150 ◦C, ∆νG drops and ∆νL dominates. The horizontal lines correspond to the expectedvalues of the Doppler broadening of an atomic beam at TEC = 1250 ◦C. Dashed line:
collimation at apertures 1 and 2, dotted line: collimation at aperture 2 and the octagon
chamber.

of the absorption peaks. This is explained by a collimation of the atomic beam
at aperture 2 and the inner edges of the octagon. Consequently, the HL partis also filled with atomic vapor and has an EC like character. This results intoa strong influence of the HL temperature on the line shape and the linewidthof the absorption peaks. For THL & TEC Doppler broadening is the dominantbroadening mechanism, leading to a broad, Gaussian shaped absorption peak.
We assume that collisional broadening also contributes to the total broadening,as for THL . TEC the line shape changes to a Lorentzian function and as thetemperature dependence of the linewidth cannot solely be explained by Doppler
broadening.
At an oven operation with heated apertures, the high divergence of the atomic
beam results in a strong contamination of the chamber with unused Er atoms.
This exhausts the source material quickly, requiring frequent refilling of the ovenand is thus not providing a good system for long-term operation. To operate theoven at low HL temperatures does also not provide a good long term performance.
Although in this case, the reduced linewidth suggests a well collimated beam, on
longer timescales, Er atoms condensing on the colder apertures would grow over50

5. Characterization of the atomic beam

Figure 5.13: Scheme of the optimized collimation setup, referred to as setup 2. Aperture1′ is a tube aperture with length a′1 ≃ 30 mm and inner diameter b′1 ≃ 3 mm. Aperture 2′
and the additional aperture 3′ have inner diameters of b′2 ≃ 3 mm and b′3 ≃ 8 mm and arespaced by a′2 ≃ 50 mm and a′3 ≃ 65 mm. At a distance of l′ ≃ 106.5 mm from aperture
2′ , the probe laser beam transversely intersects the atomic beam. For a collimation on
apertures 1′ and 2′ , the atomic beam diameter is d1′ :2′ = 11 mm.

and block the atomic beam. Therefore, we designed a new-generation collimation
setup.

5.3

Collimation setup 2

The optimized collimation setup, setup 2, is illustrated in Fig. 5.13. Aperture 1 is
replaced by aperture 1′ , which is a tube aperture with a length of a′1 ≃ 30 mm andan inner diameter b′1 ≃ 3 mm. According to Eq. (1.10), such a tube should reduce
the total flux emerging from the EC by a factor of 0.27, leaving the longitudinal
flux density almost equal. The second aperture, aperture 2′ , at a distance a′2 ≃50 mm from aperture 1′ also has a reduced inner diameter b′2 ≃ 3 mm, whichguarantees a better collimation. Additionally, at a distance a′3 ≃ 65 mm fromaperture 2′ , we insert a dark wall collimator, aperture 3′ , which in contrast to
aperture 1′ and 2′ is not heated. It has inner diameter b′3 ≃ 8 mm and reduces
the material accumulation in the octagon chamber. This setup will not eliminate
the effusive-oven like behavior of the HL section but will reduce its influence on
the atomic beam.
Although the geometry of the first aperture of 30 mm is larger than in setup
1, Eq. (1.3) is still fulfilled and so we assume that the EC section still operates inthe effusive regime. We performed measurements similar to the ones describedin the previous section. The 401 nm probe light intersects the atomic beamtransversely at a distance of l′ ≃ 106.5 mm from aperture 2′ . The measurements
were performed on the completely mounted vacuum chamber.

51

5. Characterization of the atomic beam

Figure 5.14: Spectrum of setup 1 (dotted red line) and of setup 2 (solid black line,
magnified by a factor of 5), both at TEC = 1350 ◦C and THL = 1450 ◦C. In setup 2, thepeaks are narrowed, and the intensity is reduced. Therefore hyperfine states of 167 Er
appear, whereas 162 Er is no longer resolved. The signal is normalized to the maximum
absorption of the signal indicated by the dotted red line corresponding to a maximum
optical density ODmax ≃ 0.21. For the solid black line, ODmax ≃ 0.07.

Beam divergence
We first perform fluorescence imaging of the atomic beam. We observe a lower
fluorescence signal due to the reduced atomic flux. As a consequence, we image
with a long exposure time, much longer than the inverse of the laser scan rate.
We evaluate the beam diameter from a single fluorescence image. We observea smaller beam divergence compared to the one of setup 1. For instance, thefluorescent region is not anymore cut from the field of view as in setup 1. We
evaluate the beam diameter to be dex′ = 17(3) mm.
Compared to setup 1, in which dex ≥ 41 mm, the beam diameter is strongly
reduced. But also in this setup, the measured value significantly deviates fromthe expected value corresponding to proper collimation at apertures 1′ and 2′ ofd1′ :2′ = 11 mm. If we consider again, that the first aperture does not play a roleand that the beam is collimated at apertures 2′ and 3′ , we expect a diameterof d2′ :3′ = 15 mm, which is in better agreement with the measurement. This
corresponds to a situation similar to the simplified scheme for setup 1 in Fig. 5.5,
except that the aperture setup is different.

52

5. Characterization of the atomic beam

(a)

(b)

Figure 5.15: Absorption peak of 170 Er fitted to different functions: Gaussian function(solid red line), Lorentzian function (dotted blue line) and Voigt profile (dashed greenline) at (a) TEC = 1200 ◦C and (b) TEC = 1350 ◦C. The Voigt profile fit gives for (a)∆νG = 5(3) × 102 MHz and ∆νL = 9(2) × 102 MHz and for (b) ∆νG = 101(4) MHz and∆νL = 84(4) MHz. The Gaussian and the Lorentian fit give for (a) ∆νG = 119(5) MHzand ∆νL = 108(7) MHz and for (b) ∆νG = 164(1) MHz and ∆νL = 141(2) MHz.

Spectrum
In collimation setup 2, the spectrum shows narrowed absorption peaks and has
lower intensity. In Fig. 5.14 we compare the absorption spectrum obtained using
setup 1 (dotted red line) and setup 2 (solid black line). Both spectra are observed
at TEC = 1350 ◦ C and THL = 1450 ◦ C. The spectrum of setup 2 is magnified bya factor of 5 and resolves hyperfine states of 167 Er, whereas 162 Er is no longer
visible because of its very low abundance.
Line shape and linewidth
In contrast to setup 1, where we find the spectrum to be described by a pure
Gaussian function for most temperature sets, for setup 2 we observe almost
equal contributions from both a Lorentzian as well as a Gaussian function to53

5. Characterization of the atomic beam

Figure 5.16: Gaussian linewidth ∆νG as a function of the EC temperature for setup
1, indicated by red circles, and for setup 2, indicated by black squares. The linewidth insetup 2 is reduced by a factor of 3 compared to setup 1, which also corresponds to thevalue expected by Eq. (1.23). The temperature dependence of ∆νG is reduced in setup
2.

the Voigt profile of the absorption peaks for all temperature sets. Figure 5.15 (a)and (b) shows the absorption peak of 170 Er for low (TEC = 1200 ◦ C) and for high
(TEC = 1350 ◦ C) EC temperatures. We evaluate the peak profile using different
fit functions. The solid red line represents a Gaussian function, the dotted blueline a Lorentzian function and the dashed green line a Voigt profile. For both low
and high temperatures, we observe that all these functions give a good descriptionof the observed profile. For lower EC temperatures, a fit of the Voigt profile tothe data gives the Gaussian and Lorentzian width with an uncertainty of 50 %,indicating that due to the low signal-to-noise ratio the fit cannot discriminate
between the two contributions. At high EC temperatures, we can distinguish theGaussian and Lorentzian contributions, which have almost the same weight. For
convenience and to have a direct comparison with setup 1, we choose to fit all
the absorption spectra with a pure Gaussian function. The extracted values represent an upper limit to the Gaussian width and overestimate thus the Doppler
broadening, since the Lorentzian contribution is neglected. However, these values can give us a qualitative trend on the temperature dependence. The error
bars shown in all following graphs refer to the statistical error from the fit of a
Gaussian function to the absorption data.
Our results are summarized in Fig. 5.16. We compare the Gaussian linewidth∆νG as a function of the EC temperature for setup 1, indicated by red circles, with54

5. Characterization of the atomic beam

Figure 5.17: Different fits to ∆νG (TEC ) in setup 2 (c.f. Fig. 5.16) by ∆νG = α (TEC )x .
For fixed x = 0.5 corresponding to pure Doppler broadening, we find α = 8.1 (dashed
red line). For fixed α = 1.0 corresponding to collimation at apertures 1′ and 2′ , we findx = 0.8 (solid blue line).

setup 2, indicated by black squares, where THL = TEC + 100 ◦ C. The linewidth insetup 2 is reduced by a factor of 3 compared to setup 1, which also corresponds
to the value expected by Eq. (1.23) if we consider a purely Doppler broadenedline.
The linewidth is affected by both the effective collimation and the type ofbroadening mechanism. If we consider a pure Doppler broadening and fit thedata corresponding to the black squares in Fig. 5.16 to Eq. 5.1, as shown by thedashed red line in Fig.5.17, we find α = 8.1. This suggests an atomic beam thatis much less collimated than by apertures 2′ and 3′ . If we consider a collimationof the atomic beam at apertures 1′ and 2′ corresponding to α = 1.0 and fit thedata to a function T x , as shown by the solid blue line in Fig. 5.17, we find a temperature dependence of T 0.8 . Our data suggests that we are in an intermediatecase. Further experiments at lower temperatures could clarify this point.
In general, we observe that Doppler broadening is not the sole broadening
mechanism contributing to the absorption line suggesting complicated atom dynamics inside the HL part. From the linewidth at TEC = 1350 ◦ C we estimate an
upper limit of the transversal Doppler velocity to 65 m/s.

55

5. Characterization of the atomic beam

Figure 5.18: Gaussian linewidth ∆νG as a function of the HL temperature, where
TEC = 1250 ◦C for setup 1, indicated by red circles, and for setup 2, indicated by blacksquares. While for THL . 1150 ◦C, the width is for both setups of the same magnitude,
for THL > 1150 ◦C the influence of the HL temperature on ∆νG is strongly reduced in
setup 2.

The influence of the HL temperature
In Fig. 5.18 we show the Gaussian linewidth ∆νG as a function of the HL temperature, where TEC = 1250 ◦ C for setup 1, indicated by red circles, and for setup
2, indicated by black squares. The influence of the HL temperature on ∆νG is
reduced by setup 2. While for THL . 1150 ◦ C, the width is for both setups ofthe same magnitude, for THL > 1150 ◦ C the influence of the HL temperature on∆νG is strongly reduced in setup 2. We conclude that the emergence of atomic
vapor in the HL is hindered in setup 2. This agrees well with the picture drawn
above of the EC-like character of the HL, which is dependent on THL and on theflux from the EC. Compared to setup 1, in setup 2 the flux is reduced and so are
the collisions in the HL part. Therefore, the influence of the HL temperature on∆νG is reduced.
Conclusion
Similar to setup 1, for oven operation with THL > TEC in setup 2, the HL has EClike character and is filled with atomic vapor disabling aperture 1′ . But although
the atomic beam is not collimated as intended, this optimized setup shows good
improvements. The atomic beam divergence is reduced and so is the part of theunused atoms. Also the influence of the HL temperature on the atomic beam is56

5. Characterization of the atomic beam

Figure 5.19: The flux density in units of sr−1 measured in the octagon chamber asa function of the EC temperature, where THL = TEC + 100 ◦C. The flux in setup 1,
indicated by red circles, is an order of magnitude higher than in setup 2, indicated as
black squares. The linear temperature dependence of the flux in both setups exhibits the
exponential dependence of the vapor pressure on the temperature.

strongly reduced. Due to equally strong Gaussian and Lorentzian contributions
to the line shape, we assume that besides Doppler broadening also collisional
broadening contributes to the total broadening.

5.4

Flux

The atomic flux is a very important quantity to characterize the oven system since
it determines the number of atoms per unit time that enter the ZS tube and thatcan be captured by the MOT. According to Sec. 1.3, we can estimate the flux atthe position of the probe laser beam by measuring I, I0 and j. From the 166 Er
absorption peak amplitude of the differential signal and the magnitude of thereference signal, we obtain the transmitted intensity I and the incident intensity
I0 . By imaging the fluorescence on resonance of the 166 Er transition, we measure
the light-atom interaction length j. We normalise the total flux obtained from
Eq. (1.17) to the unit solid angle of emergence, and account for the fact that
we measured the optical density only for 166 Er by scaling it with the inverse
abundance of 166 Er. The resulting flux density Θex / sr includes all isotopes andholds only for small solid angles. It provides a suitable quantity to analyse theflux measured in the octagon chamber in dependence of the collimation setup
and of the operation temperature.
57

5. Characterization of the atomic beam

Figure 5.20: The flux density in units of sr−1 measured in the octagon chamber as afunction of the HL temperature, where TEC = 1250 ◦C. Both in setup 1, indicated by
red circles, and in setup 2, indicated by black squares, the flux is dependent on the HLtemperature for THL & 1050 ◦C.

Setup 1 vs. setup 2
Figure 5.19 shows the flux density Θex / sr measured in the octagon chamber as afunction of the EC temperature on a logarithmic scale, where THL = TEC +100 ◦ C.
The flux in setup 2, indicated as black squares, is reduced to 9 % of the flux ofsetup 1, indicated as red circles. This agrees well with the flux reduction due
to the different collimation setup expected from Eq. (1.9), which also predicts
a value of 9 %. In both setups we see a linear temperature dependence withequal slope, which reflects the exponential temperature dependence of the vapor
pressure shown in Eq. (2.1), which is proportional to the atomic flux [51].
Influence of the HL temperature
As expected, the HL temperature influences the flux in both setups. We show in
Fig. 5.20 the flux density Θex / sr measured in the octagon chamber as a functionof the HL temperature. The EC temperature is constant at TEC = 1250 ◦ C. Bothin setup 1, indicated by red circles, and in setup 2, indicated by black squares,
the flux depends on the HL temperature for THL & 1050 ◦ C. In this region,
the increase of the flux with the HL temperature is of similar strength in both
setups. In contrast to this, as show in previous measurements (c.f. Fig. 5.18),
the linewidth ∆ν in setup 2 shows reduced dependence on the HL temperature.
Therefore, we conclude that in both setups for increasing HL temperatures, more58

5. Characterization of the atomic beam

(a)

(b)

Figure 5.21: Accumulation of Er in the vacuum chamber. (a) View through a viewportof the octagon while operating the oven in setup 1. On the inner edges, Er starts toaccumulate in tiny rolls. (b) The connection tube of oven and octagon after operating
the oven in setup 1. The inner walls are all over coated with Er, and the Er layer peels
off.

and more atoms are re-emitted by the HL walls and contribute to the flux out of
the oven. However, in setup 2, the total amount of re-emitted atoms is less andso are the collisions in the HL part. This explains that the HL temperature has
reduced influence on the linewidth in setup 2, but that the relative increase of
the flux with the HL temperature is similar in both setups.
Material deposition
The high flux in setup 1 also leads to undesirable accumulation of Er material.
Already after some hours of oven operation, tiny rolls of accumulated Er emergedat the inner edges of the octagon, as show by Fig. 5.21 (a). When changing theapertures from setup 1 to setup 2, we opened the oven chamber and realized that
Er material coated the inner walls of the connection tube of oven and octagon all
over, as seen in Fig. 5.21 (b). Due to gravity, the Er layer peeled off the wall. In
long-term operation, this would give additional contact surface for Er atoms fromthe beam that stick to it, grow new structures and finally block the atomic beam
emerging from the oven. Thus, it was an important step to adapt the apertures
to setup 2, since this setup provides a better collimated beam with reduced flux
in contrast to setup 1, which could neither provide reliable long-term operation
nor a well-collimated atomic beam.
Extracted flux at the MOT position
To estimate the number of atoms that reach the MOT region per second from ourmeasured value for the atomic flux in the octagon chamber, we need to take into59

5. Characterization of the atomic beam

Figure 5.22: Derived atomic flux that can be captured by the MOT as a function of theEC temperature in setup 2. According to Eq. (5.2), several loss factors determine ΘMOT ,where in our setup ξ2 is variable. We plot ΘMOT (TEC ) for three different values of ξ2 :0.324 (black squares), 0.140 (red circles) and 0.061 (blue triangles). The dotted black,dashed red and dash-dotted blue lines correspond to exponential fits to the measured
values and are also shown for lower temperatures to indicate the trend.

account several loss factors [84]. For geometrical arguments, only a fraction ofΘex can enter the ZS tube, what gives rise to a loss factor ξ0 . The isotope factor
ξ1 considers that only a certain isotope is slowed and captured. The ZS factor
ξ2 corresponds to the ratio of atoms that can be slowed by the ZS to the total
Rv
R∞
number of atoms injected into the ZS: ξ2 = 0 0 P ′ (v)dv / 0 P ′ (v)dv, where v0 is
the capture velocity of the ZS and P ′ (v) is the velocity distribution in the beam.
Since we can vary v0 by the magnetic offset field of the ZS to adjust the magnetic
field profile to the available slowing light power, also ξ2 varies. The last loss factor
ξ3 accounts for that the slowed atomic beam leaving the ZS has a large divergence,since only longitudinal velocity components are slowed in the ZS. Therefore onlyRrR∞
a part of those atoms passes the MOT region: ξ3 = 0 0 I(r)dr / 0 I(r)dr, whereI(r) is the intensity and r0 is the radius of the MOT region. Combining this,yields to the number of atoms that can be captured in the MOT per unit time,
if we assume that the capture velocity of the MOT is larger or equal to the final
velocity of the slowed atoms from the ZS:ΘMOT ≈ ξ0 ξ1 ξ2 ξ3 Θex .

(5.2)

For our setup, ξ0 = 1.3 × 10−4 , ξ2 can vary from 0.061 to 0.324, depending on thecapture velocity and ξ3 = 0.011. If we consider 166 Er, ξ1 = 0.336. In Fig. 5.22
60

5. Characterization of the atomic beam

we plot ΘMOT (TEC ) for three different values of ξ2 : 0.324 (black squares), 0.140(red circles) and 0.061 (blue triangles). The dotted black, dashed red and dashdotted blue line correspond to exponential fits to the measured values and arealso shown for lower temperatures, at which we could not probe the flux with
our measurement. These lines indicate the presumable development of ΘMOT ,which should only be considered as a rough estimation. All values suggest thatwith setup 2, we can have a sufficient supply of Er atoms for tapping and further
cooling large atomic samples.

61Conclusion and Outlook
During my master thesis work, I focused my efforts in producing and characterizing an Er atomic beam, emerging from a high-temperature oven. The knowledgeof the atomic beam behavior is fundamental for all future experiments on laser
cooling and Bose condensation of Er atoms. Due to erbium's high melting point,
the operation temperatures of the oven are unusually high for standard ultracold
gas experiments based on alkali and alkaline earth elements. A big experimental
effort was then necessary to design and operate the oven system. To shield thehigh temperatures, the oven system is water cooled. To avoid material condensation on colder parts of the system, the apertures that collimate the atomic
beam are heated to higher temperatures than the effusion cell. To backup thesystem against power failure we protect it with an UPS. To secure safe operation, the oven system is connected to the cooling water system control and to
the emergency-off system. The oven control program provides not only the userinterface, but also coordinates the safety systems.
We characterize the atomic beam emerging from the oven by laser spectroscopy. Our measurements clearly reveal a complex beam behavior in the ovenchamber leading to a highly divergent atomic beam and the deposition of Er
material at the walls of the vacuum chamber. To minimize both effects, we had
to design and mount a novel atomic beam collimation setup. The optimized
setup consists of a tube aperture combined with two circular apertures. The
measurements on this new setup show that it provides a much better collimationof the atomic beam with a reduced but sufficient atomic flux for large cooled andtrapped ensembles of Er atoms. We find the optimal operation temperature to be
1250 ◦ C. At this temperature, the estimated total atomic flux, which is injected
into the ZS slower tube is 3 × 1010 s−1 with a transversal Doppler velocity of
65 m/s. We expect correspondingly a number of the order of 107 atoms/s that canbe captured by the MOT. This is a large enough value to guarantee a good MOT
operation.
Currently, we are baking the complete experimental apparatus at a temperature of 200 ◦ C to lower the background pressure in the chamber further. In
the MOT chamber, we measure a background pressure of 2 × 10−11 mbar, which
62

Conclusion and Outlook

(a)

(b)

Figure 6.1: The vacuum chamber, (a) almost completely mounted. The ZS is clearlyvisible in the center in white, to the left hand side is the golden colored MOT chamber,and to the very right side is the Er oven. (b) The experimental chamber whilst thebaking. To lower the background pressure, we heat the chamber to temperatures of200 ◦C for several days. Thereby, residual gases that are enclosed in the stainless steel
walls of the chamber and that limit the vacuum are released and pumped off.

assures a good enough vacuum level for our purposes. The next step is the adjustment and testing of the ZS as well as the setup of the narrow-line MOT. Once
the MOT is working, we can load the ODT and start to study the collisional
behavior of cold Er atoms in detail by Feshbach spectroscopy, which is a major
step on our way to the Bose-Einstein condensation of Er.

63

Appendices64

Appendix A

Magnetic moments of thelanthanides
The magnetic moment µ is calculated asµ = g MJ µB ,(A.1)

where MJ is the projection of the total angular momentum quantum number J
towards its quantization axis. g is the Landé g-factor, which for LS-coupling of
the electrons can be estimated as
g = 1 + (gs − 1)

J (J − 1) − L (L − 1) + S (S − 1),
2 J (J − 1)

(A.2)

where gs is the Landé g-factor of the electron, which is can be approximated by
gs = 2. S is the total spin quantum number and L is the total orbital angularmomentum quantum number. So, to evaluate the magnetic moment for a certain
electronic configuration one has to know the specific quantum numbers S, L and
J of the state. These quantities can be derived with the aid of Hund's rules [60].
Those rules only apply to the lowest term of the ground state configuration forcases where there is only one incomplete subshell and where the electrons couple
in a LS-coupling scheme. This is the case for most of the lanthanide atoms in
the ground state, as one can see in Tab. A.1. Except for Ce and Gd, the fourHund's rules determine S, L and J.
The calculated µ agrees well agreement with the measured values from [59]as shown in Tab. A.1. This underlines the validity of the assumptions and the
explanation of the magnitude of the magnetic moments by the occupation of the
4f shell.

65

A. Magnetic moments of the lanthanides

el.

4f n

5dn

S

L

J

term

g (lit.)g (calc.)µ (lit.)µ (calc.)

La
Ce
Pr
Nd
Pm
Sa
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb

0
1
3
4
5
6
7
7
9
10
11
12
13
14

1
1
0
0
0
0
0
1
0
0
0
0
0
0

1
2

2
4
6
6
5
3
0
2
5
6
6
5
3
0

3
2

2D

4
9
2

1G
4
4I

4

5I

0.79755
0.945430.73104
0.603290.30500
0
1.993402.65140
1.325131.24159
1.195141.163811.1411900.80000
1.00000
0.727270.60000
0.2857102.00000
2.666671.33333
1.25000
1.20000
1.16667
1.14286
0

1.20
3.78
3.29
2.41
0.76
0
6.98
5.30
9.94
9.93
8.96
6.98
3.99
0

1.20
4.00
3.27
2.40
0.71
0
7.00
5.33
10.00
10.00
9.00
7.00
4.00
0

0
3
2

2
5
2

3
7
2

4
5
2

2
3
2

1
1
2

0

5
2

0
7
2

3
2

9
2

4
6H

5
2

7F
0
8S
7
2

15
2

9D
2
6H

2

15
2

8

5I

15
2

4I

6

3H

7
2

2F

0

1S

8

15
2

6

7
2

0

Table A.1: Occupation of the 4f shell, occupation of the 5d shell, resulting total spinquantum number S, resulting total orbital momentum quantum number L, resulting
total angular momentum quantum number J, the according term symbol, the Landé gfactor found in literature [59], the estimated Landé g-factor calculated for LS-coupling,
the resulting magnetic moment µ for the Landé g-factor from literature and from thecalculation, for all ground states of the lanthanide elements ('el.').

66

Appendix B

Erbium oven control
The screenshot of the LabVIEW block diagram in Fig. B.1 shows the structure of
the oven control program code. After initialization in a flat sequence, the main
program starts. Here, the datasockets in the upper left manage the 'On/Stby'
switch and access the network variables, which connect the control program with
the PID controllers via the iTools OPC server. The while-loop on the upper
right, plots the EC and the HL temperature and the working setpoints versus
the absolute time. The environment variables in the right of the lower while loop
acquire the UPS status. The MGE UPS personal solution pack program triggers
the command line if one of the UPS variables changes. The command line has the
new variable values as argument and starts the executable subVI UPS-triggerLabVIEW.exe. The subVI reads the command line argument and distributes thecontained information to the according environment variable. The oven control
program displays the UPS status and sets the oven to standby mode for too little
remaining backup time of the UPS, this is realized in the attached case structure.
The central part of the VI is the case structure in the lower while-loop. The
screenshot only displays one out of 14 cases, which manage and secure the workingof the control program:case 0: default case

case 1: reacts to the 'EMERGENCY OFF' button1

case 2-9: set safety limits for the input values of the OPC server variables
and manages the 'On/Stby' switchcase 10: preset values changeable via the 'enable changes' switchcase 11-13: aid the scaling and appearance of the temperature plot

1

As seen in Fig B.1, in an emergency case, the temperature ramps are set to 0 ◦ C/min.
However, due to the interpretation of the PID controller, this sets the temperature immediately
to the new setpoints of 0 ◦ C.

67

B. Erbium oven control

68
Figure B.1: A screenshot of the LabVIEW block diagram, which displays the oven control program code.

Appendix C

Atomic beam shutter control
C.1

Control box

We use an Atmel AVR ATmega128 µC mounted on a Crumb128-light µC module.
An external resonator with a frequency of 14.7456 MHz is the clock source for theprocessor. The detailed pin configuration and the whole electric circuit are shownin the circuit diagram in Fig. C.1. The settings to program the µC via the Atmel
AVR Studio 4 program with the AVRISP mkII programming interface are: ISP
frequency 2 MHz, Fuses: (no M103C; SUT CKSEL = ext. crystal/resonator highfreq., start-up time: 16 K CK +64 ms). We repeat a part of the manual text,
which gives the main operating guidelines:
The control box has on its face the following switches and connectors: power,
emergency stop, ttl, power switch, reset push button (red), pc/manual control
switch and the unshut/shut switch. On the side the servo can be plugged in,as well as, if necessary the programming interface. To access the potentiometers
and the pushbutton (green), one has to open the box.
When everything is connected, the power switch starts the controller (no morethan 8 V), the orange LED shines. All three other LEDs shine for 1 second (default led test at initialisation) (also if system is reset). The red push button resets
the controller in case this is needed.
For control via the pc (TTL signal), set the pc/manual control switch to pc.
The blue LED shines as well as either the green or the red one, indicating thestatus of the shutter (beam unshut or beam shut respectively).
For control by hand, set the pc/manual control switch to manual. The blue
LED doesn't shine. The unshut/shut switch allows control over the shutter position, which is indicated by the green or the red LED.
For positioning the shutter positions, one has to operate in the manual control mode, has to keep the green push button pushed and turn at the same time''69

C. Atomic beam shutter control

the screw at the according potentiometer. According means that you can onlychange the position of the choice you have made at the unshut/shut switch. The
potentiometer marked 'u' will change the position of the shutter at unshut, if theunshut/shut switch is set to unshut. The potentiometer marked 's' will change
the position of the shutter at shut, if the unshut/shut switch is set to shut. If thegreen push button is released, normal manual operation continues.
If an emergency stop occurs, the shutter will be set to 'beam shut' and block
the atomic beam. The red, blue and green LED blink to indicate the interrupt.
If the emergency stop ends, normal operation mode continues automatically.''

C.2

Source code

The explanation below, describes the source code shown in List.B.2, and is also
contained in the control box manual.
The header file, abs.h (see List. C.2), defines constants, macros and variables
and links functions. In the program, after the including the needed header andlibraries (order is not commutative) the main loop starts. The initialisation of
input/output, interrupts, PWM and analog-to-digital conversion take place andinterrupts are activated.
The while-loop keeps the program running and checks switches and the emergency stop. If this is not activated, the main loop checks whether the operation
mode is manual control or pc control. In the fist case there's distinction between
normal operation and positioning of the shutter via the potentiometers (setting
the values for 'beam shut' and 'beam unshut'). If the emergency stop is active(signal at BNC connection is low, signal at µC is high (opto-isolator)), the shutter
is set to the position 'beam shut' , and all LEDs are blinking.
The controlling of the servo is accomplished by an timer interrupt that runs
every 10 ms. Here, basically some if-loops decide whether the value of shutterpos
has changed in the last second (period is dependent on j, see code). If so, thenew value is set and the signal is changed accordingly. If not, no signal is sent
to the servo (just high, no PWM). The reason for that is that, in this way, theservo is only driven when needed and left passive when not needed, what preventsneedless vibrations of the system. At the start of the interrupt SREG is backsaved and reloaded in the end to make the program more robust and save.
At the input output initialization the pins are set in the needed configurations (input, output, internal pull-ups). For a default check of the LEDs, bydelay ms(1000), all LEDs shine for 1 s. At the interrupt initialization, the timer
interrupt frequency is set, as well as the mode of the external interrupt. At thePWM initialization, the mode, as well as the pulse of the signal (50 Hz) is set''

70

C. Atomic beam shutter control

71

Figure C.1: The circuit diagram of the atomic beam shutter control box, which operates a servo motor. An Atmel AVR ATmega128 µC withexternal resonator is mounted on the Crumb128-light µC module. Opto-isolators give galvanic separation, the voltage regulator protects theµC from high voltage

C. Atomic beam shutter control(ICR1). At the analog to digital conversion initialization, the mode is selected
and a dummy readout takes place, for reserving the variable for the upcoming
results.
The measurement functions do a simple ADC k times to give a stable average(important: clear the channel before selecting it). The flashing of the LEDs isdone by a simple counting of b. Manual control checks the switch for choosing the
shutter position manually and sets the value of shutterpos accordingly. Whereas
in pc control shutterpos is set according to the TTL signal from the pc (which isinverted ↔ optocoupler).''Listing C.1: Source code of the µC firmware.
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/ * **************************
atom beam−s h u t t e r c o n t r o l l e r************************** * /// v e r s i o n 1 . 0// a u t h o r : j o g y s c h i n d l e r// d a t e : 0 7 . 0 7 . 0 1 0#include <a v r / i o . h>#include <a v r / i n t e r r u p t . h>#include ” a b s . h”
#include < u t i l / d e l a y . h>//−−−−−−−−−//main l o o p//−−−−−−−−−
i n t main ( void ){c l i () ;i n i t i o () ;i n i t i n t () ;i n i t p wm ( ) ;init adc () ;sei () ;while ( 1 ){e = PIND ;// c h e c k and f i l t e r emergency s t o p
e &= (1<<PD0) ;statusi f ( e==0)// s i g n a l @ bnc i s h i g h ( no emergency s t o p ) −> s i g n a l @ p ini s low ( o p t o c o u p l e r ) , normal o p e r a t i o n{l = PINA ;// c h e c k and f i l t e r s w i t c h p o s i t i o nl &= (1<<PA1) ;i f ( l ==0)// s w i t c h [MANUAL CONTROL <−> PC CONTROL] ==MANUAL CONTROL{
m = PINA ;// c h e c k and f i l t e r s w i t c h p o s i t i o nm &= (1<<PA5) ;m /= 3 2 ;i f (m==1)// s w i t c h [SHUTTER POSITIONING <−> OPERATING] ==OPERATING{
manual control () ;}72

C. Atomic beam shutter control

50

else

51
52

{
m e a s u r e p o t i 1 ( ) ; // measure p o t e n t i o m e t e r 1 f o r v a l u e o fbeam unshut
m e a s u r e p o t i 2 ( ) ; // measure p o t e n t i o m e t e r 2 f o r v a l u e o fb e a m sh u t

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// s w i t c h [SHUTTER POSITIONING <−> OPERATING] ==SHUTTER POSITIONING

manual control () ;}}// s w i t c h [MANUAL CONTROL <−> PC CONTROL] == PC CONTROL

else{

pc control () ;led b on () ;
}
}
else
{

// s i g n a l @ bnc i s low ( emergency s t o p ) −> s i g n a l @ p in i s h i g h (o p t o c o u p l e r ) , emergency s t o p
OCR1A = ( 3 * beam shut ) +1000; // s e t s e r v o t o b e a m s h u tl ed fl ash () ;// f o r i n d i c a t i o n o f emergency s t o p
h = 0;//h r e s e t f o r b u s i n e s s as u s u a l a f t e r emergency s t o p}}
return 1 ;}//−−−−−−−−−// i n t e r r u p t//−−−−−−−−−// t im e r i n t e r u p t f o r s e t t i n g s e r v o
ISR ( TIMER3 COMPA vect){
stemp = SREG;// b a c k s a v i n g SREG
TCNT3 = 0 ;// r e s e t
i f ( s h u t t e r p o s != h )// i f s h u t t e r p o s changed{
j =0;
OCR1A = ( 3 * s h u t t e r p o s ) +1000;// s e t p u l s e l e n g h t ( e m p i r i c a l formula, by t h e o r e t i c a l e s t i m a t e , and e x p e r i m e n t a l t r i a l an e r r o r )h = s h u t t e r p o s ; // i n v e r s e p u l s e l e n g h t f u n c t i o n f o r i f l o o p}
i f ( s h u t t e r p o s == h )// i f s h u t t e r p o s unchanged{i f ( j <100) // i f s h u t t e r p o s changed r e c e n t l y{
OCR1A = ( 3 * s h u t t e r p o s ) +1000;// s e t p u l s e l e n g h t , u n t i l news e r v o p o s i t i o n i s d r i v e n ( j =100 = 1 s , f o r 180
s e r v o ne e d s ˜ 0 .8
s , so i f f a s t s i g n a l −o f f u s e w i t h 90
s e t j =50 − b u t c h e c kaccurately ! )h = s h u t t e r p o s ; // i n v e r s e p u l s e l e n g h t f u n c t i o n f o r i f l o o p}
i f ( j >=100) // i f s h u t t e r p o s unchanged f o r l o n g e r time{
j =200;// s t a y i n t h i s mode u n t i l s h u t t e r p o s c h a ng e s
OCR1A = ICR1 ;//no pwm s i g n a l t o s e r v o , f o r a v o i d i n g v i b r a t i o n s
}
}
j ++;
SREG = stemp ;// l o a d i n g SREG73

C. Atomic beam shutter control

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}

//−−−−−−−−−−−−−−// i n i t i a l i s a t i o n//−−−−−−−−−−−−−−// inp u t −o u t p u t i n i t i a l i s a t i o nvoid i n i t i o ( void ){DDRA |= (1<<PA2) | (1<<PA4) | (1<<PA6) ;// l e d s s e t t o o u t p u t
PORTA |= (1<<PA0) | (1<<PA1) | (1<<PA3) | (1<<PA5) ; // a c t i v a t e p u l l −up @ t t l−p in and s w i t c h e s
DDRB |= (1<<PB5) ;// se r v o −p in s e t t o o u t p u t
PORTD |= (1<<PD0) ;// a c t i v a t e p u l l −up @ emergency s t o p
led all o n () ;delay ms (1000) ;l e d a l l o f f () ;alll e d s on f o r 1 s}// i n t e r r u p t i n i t i a l i s a t i o nvoid i n i t i n t ( void ){TCCR3B |= (1<<CS32 ) | (1<<CS30 ) ;// p r e s c a l e r = 1024 , normal o p e r a t i o nmode ( s e e t a b l e 61 i n d a t a s h e e t )OCR3A = ( i n t ) ( ( (XTAL/ 1 0 2 4 ) * 1 0 ) / 1 0 0 0 ) ;// compare : timer −i n t e r u p t e v e r y 10ms
, t a k e c a r e on t h e b r a k e t s and c a l c u l a t i o n o r d e r : c r u c i a l ! OCR3A=f ( c l k )/( p r e s c a l e r * f (OCR3A) )ETIMSK = (1<<OCIE3A ) ;// timer3 −compare−i n t e r r u p t −e n a b l e}// p u l s e w i d t h m o d u l a t i o n i n i t i a l i s a t i o nvoid i n i t p wm ( void ){TCCR1A = (1<<COM1A1) | (1<<WGM11) ; // n o n i n v e r t i n g f a s t pwm, TOP i s ICR1 (mode 1 4 , s e e t a b l e 61 i n d a t a s h e e t )TCCR1B = (1<<WGM13) | (1<<WGM12) | (1<<CS11 ) ; // f a s t pwm w i t h p r e s c a l e r 8 (r e s o l u t i o n maximal )ICR1 = 3 6 8 6 5 ; //TOP \ e q u i v 20ms ( @ p r e s c a l e r 8) −> 50Hz p u l s e [ ICR1=( f ( c l k ) /(p r e s c a l e r * f (pwm) ) ) ] −−> OCR1A= 3 6 8 7 , . . . , 1 8 4 3}// a na l o g t o d i g i t a l c o n v e r t i o n i n i t i a l i s a t i o nvoid i n i t a d c ( void ){ADMUX |= (1<<REFS0) ;// r e f e r e n c e v o l t a g e i s AVCC
ADCSRA |= (1<<ADEN) | (1<<ADPS2) | (1<<ADPS1) | (1<<ADPS0) ; // a c t i v a t e ADC,
p r e s c a l e r = 128 (−> ADC f r e q u e n c y = 115 kHz )

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ADCSRA |= (1<<ADSC) ;// s t a r t dummy r e a d o u twhile ( ADCSRA & (1<<ADSC) ){ ; } // w a i t f o r end o f c o n v e r s i o nbeam unshut = ADCW;// r e a d ADCW t o g e t r e s u l t o f t h e n e x t measurement i n
this variable

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// d e f a u l t l e d c h e c k @ i n i t i a l i s a t i o n :measure poti1 () ;settings
measure poti2 () ;// measure t h e p o t i sfors e l e c t i n g the recent se t}//−−−−−−−−−// f u n c t i o n s//−−−−−−−−−// v o l t a g e measurement @ p o t e n t i o m e t e r #1

74

C. Atomic beam shutter control

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void m e a s u r e p o t i 1 ( void ){ADMUX &= ˜(1<<MUX1) ;beam unshut = 0 ;// s e t c h a nne l z e r o , c h o s e c h a nne l ADC0 ( d e f a u l t )f o r ( k =0; k <32; k++) // measure k+1 t im e s and a v e r a g e , c h o s e k as 2ˆn f o r
faster calculation{
ADCSRA |= (1<<ADSC) ;// s i n g l e c o n v e r s i o nwhile ( ADCSRA & (1<<ADSC) ){;}beam unshut += ADCW;}
beam unshut /= ( k+1) ;}// v o l t a g e measurement @ p o t e n t i o m e t e r #2
void m e a s u r e p o t i 2 ( void ){ADMUX &= ˜(1<<MUX1) ;// s e t c h a nne l z e r o
ADMUX |= (1<<MUX1) ;// c h o s e c h a nne l ADC2
beam shut = 0 ;f o r ( k =0; k <32; k++)// measure k+1 t im e s and a v e r a g e{
ADCSRA |= (1<<ADSC) ;// s i n g l e c o n v e r s i o nwhile ( ADCSRA & (1<<ADSC) ){;}beam shut += ADCW;}
beam shut /= ( k+1) ;}// f l a s h i n g l e d s @ emergency b l o c kvoid l e d f l a s h ( void ){i f ((0 <b && b <20000) ){led a ll on () ;}i f ((10000 < b && b <40000) ){l e d a l l o f f () ;}i f ( b>=40000)
{
b=0;
}
b++;
}

// s e t s t h e s h u t t e r p o s i t i o n=BEAM UNSHUT]− s w i t c hvoid m a n u a l c o n t r o l ( void ){i = PINA ;i &= (1<<PA3) ;i /= 8 ;a c c o r d i n g t o t h e [SHUTTERPOS=BEAM SHUT <−> SHUTTERPOS

i f ( i ==1)// s w i t c h [SHUTTERPOS=BEAM SHUT <−> SHUTTERPOS=BEAM UNSHUT] ==SHUTTERPOS=BEAM UNSHUT{s h u t t e r p o s = beam unshut ;l e d a l l o f f () ;led g on () ;}75

C. Atomic beam shutter control

239

else

240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267

{

// s w i t c h [SHUTTERPOS=BEAM SHUT <−> SHUTTERPOS=BEAM UNSHUT] ==SHUTTERPOS=BEAM SHUTs h u t t e r p o s = beam shut ;l e d a l l o f f () ;led r on () ;}}// s e t s t h e s h u t t e r p o s i t i o nvoid p c c o n t r o l ( void ){t t l = PINA ;t t l &= (1<<PA0) ;a c c o r d i n g t o t h e TTL s i g n a l from t h e PC ( i n v e r t e d ! )i f ( t t l ==1){
s h u t t e r p o s = beam shut ;l e d a l l o f f () ;led r on () ;}else{s h u t t e r p o s = beam unshut ;l e d a l l o f f () ;led g on () ;}}Listing C.2: Header of the source code.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36

/ * ***********************************
atom beam−s h u t t e r c o n t r o l l e r − h e a d e r************************************ /// c o n s t a n t s#d ef i n e XTAL ( double ) 1 4 7 4 5 6 0 0// q u a r z f r e q u e n c y , ( d o u b l e ) t o fo r m a t −> h e l p swith c a l c u l a t i o n s#d ef i n e F CPU 1 4 7 4 5 6 0 0UL// cpu f r e q u e n c y d e f i n e d f o r d e l a y . h// macros#d ef i n e#d ef i n e#d ef i n e#d ef i n e#d ef i n e#d ef i n e#d ef i n e#d ef i n e

led b on ()led b o ff ()led g on ()l ed g o ff ()led r on ()l e d r o f f ()led a ll on ()l e d a l l o f f ()PORTA |= (1<<PA2)
PORTA &= ˜(1<<PA2)
PORTA |= (1<<PA4)
PORTA &= ˜(1<<PA4)
PORTA |= (1<<PA6)
PORTA &= ˜(1<<PA6)
PORTA |= (1<<PA2) | (1<<PA4) | (1<<PA6)
PORTA &= ˜((1<<PA2) | (1<<PA4) | (1<<PA6) )// v a r i a b l e s
unsigned
unsigned
unsigned
unsigned
unsigned
unsigned
unsigned
unsigned
unsigned
unsignedvolatilechar e ;// f o r emergeny s t o pchar i ;// f o r s w i t c h SHUTTERPOS=BEAM SHUT <−> SHUTTERPOS=BEAM UNSHUT
char l ;// f o r s w i t c h MANUAL CONTROL <−> PC CONTROL
char m;// f o r s w i t c h POSITIONING <−> OPERATING
char t t l ;// f o r TTL s i g n a lchar j =0;// f o r c o u n t e r o f t im e r i n t e r r u p t s
i n t h =0;// f o r i n t e r r u p t i n t e r m e d i a t e memory @ i f l o o p s
int k ;// f o r c o u n t e r o f m e a s u r e p o t i# mean−l o o p
i n t b =0;// f o r c o u n t e r o f f u n c t i o n f l a s h
i n t stemp ; // f o r b a c k s a v i n g SREG when i n t e r r u p t i s performed
unsigned i n t s h u t t e r p o s ;// v o l a t i l e , s i n c e used f o r timer −i n t e r r u p t

76

C. Atomic beam shutter control

37
38
39
40
41
42
43
44
45
46
47
48
49
50
51

unsigned i n t beam unshut ;unsigned i n t beam shut ;// f u n c t i o n s
void
void
void
void
void
void
void
void
void

i n i t i o ( void ) ;i n i t i n t ( void ) ;i n i t p wm ( void ) ;i n i t a d c ( void ) ;m e a s u r e p o t i 2 ( void ) ;m e a s u r e p o t i 1 ( void ) ;m a n u a l c o n t r o l ( void ) ;p c c o n t r o l ( void ) ;l e d f l a s h ( void ) ;77Appendix D

Calibrations
D.1

Laser frequency

To calibrate the laser frequency in the scanning region, we use a wavemeter.
It measures the wavelength of the non-frequency-doubled 802 nm light from thetest output of the laser system. Since the light is transported with a long fiber
to the wavemeter, the measurement is vulnerable to temperature fluctuationsand vibrations. Also the switcher box that is used to share the wavemeter withother experiments reduces the accuracy and time resolution if operated in switch
mode. Therefore, this method is not suitable for absolute frequency measurements. However, for relative frequency measurements with time averaged values,
the precision is sufficient. A long-term record from the wavemeter gives the maximum and minimum frequencies of the scan. To obtain the real maximum andminimum wavelength values, it is important to average the recorded values overlong times and then choose the absolute maxima and minima. Figure D.1 showssuch a record of the wavelength as a function of the time. The amplitudes do
not correspond to the real amplitudes, as we can see by the interference patternof the data points. Since the sampling rate of the wavemeter is too small toallow smooth sampling, we observe interference with the scan rate of the laser.
To convert the time axis of the measurements at the oscilloscope to a frequency
axis, we determine the frequency change per time. We measure the scan rate of
the laser with an oscilloscope and combine this with the absolute maxima andminima of the frequencies to obtain the frequency change per unit time of thescan. We scale the time scale of the oscilloscope with this value and obtain afrequency axis, which we normalize to the 166 Er absorption peak and that thus
shows the relative detuning.

78

D. Calibrations

Figure D.1: Interference pattern of the laser scan rate and the sampling rate of thewavemeter. The amplitude response does not correspond to the real amplitudes since
the sampling rate is too small.

Figure D.2: Brightness as a function of position along one pixel row of an image of anruler. One peak spacing corresponds to 1 mm what determines the scaling factor.

79

D. Calibrations

D.2

CCD camera

To calibrate the pixel size of the CCD images, we focus the camera lens to a ruler
at equal distance as the center of the chamber. The profile along one pixel row of
the resulting image, as in Fig. D.2, shows distinct peaks with a spacing of 1 mm.
This determines the scaling factor to convert pixel to mm.
The exposure time of the camera needs to be short to avoid saturation of
the CCD chip. As well, it needs to be long to detect very low fluorescence lightintensities. To find the optimum value, we measured the waist of an imaged
atomic cloud as a function of the exposure time. A measurement-set at TEC =1350 ◦ C and THL = 1450 ◦ C gives the upper bound, another set at TEC = 1250 ◦ C
and THL = 950 ◦ C gives the lower bound. As we see in Fig. D.3, for exposure
times below 100 ms, the low temperature cloud cannot be detected properly. For
exposure times above 250 ms, the waist of the high-temperature cloud is no longer
constant, but it depends linearly on the exposure time. It seems likely that thisis a smear effect, where at the readout of the chip, charges from the overexposed
pixels swap to neighboring pixels by mistake and broaden the bright region. Thismeasurement was made at collimation setup 1 and leads to an optimal exposure
time of 100 ms.

Figure D.3: The waist of an imaged atomic cloud in setup 1 for two different temperature settings. For too short or too long exposure times, the waist is no longer constant.

80

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87

List of Symbols andAbbreviations
Abbreviation

Description

2-LS
A
a
a
a.u.
add
a0
ADC
α
amu
b
BEC
c
C
CCD
d
D
DDI
∆ν
E
|ei
EC
EOM
f
F
FWHM
g

two level systemarea
distance between two apertures
scattering length
arbitrary units
dipole-dipole characteristic radius
Bohr radiusanalog to digital conversion
angle of emergence relative to the z-axis from the ovenatomic mass unit
inner diameter of aperture
Bose-Einstein condensate
speed of lightnormalisation constantcharge-coupled device
atomic beam diameterln (10)× optical density
dipole-dipole interaction
linewidthenergyexcited state
effusion cellelectro-optic modulator
collimation ratio
quantum number of the hyperfine splitting
full width half maximum
Landé-g factor
88List of Symbols and Abbreviations

Abbreviation

Description

|ei
Γ
h
~
HCL
HL
I
I
Isat
IC
j
J
k
kB
l
L
λ
λmf
λ/2
LED
LO
m
mJ

ground state
spontaneous decay rate
Planck constant
reduced Planck constanthollow cathode lamp
hot lip
intensity
total nuclear spin quantum number
saturation intensity
integrated circuit
light-atom interaction length
total angular momentum quantum number
photon momentum
Boltzmann constantdistance from aperture 2
total orbital angular momentum quantum number
wavelengthmean free pathhalf-wave plate
light emitting diodelocal oscillator
mass
projection of the total angular momentum quantum - number to the quantization axis
magneto-optical trap
magnetic momentmirco controller
magnetic constant
Bohr magneton
densityfrequency
resonance frequency
National Institute of Standards and Technology
optical density
optical dipole trap
solid angle
polarizing beam splitter
photo diodeflux
proportional integral derivative

MOT
µ
µC
µ0
µB
n
ν
ν0
NIST
OD
ODT
ω
PBS
PD
Θ
PID

89

List of Symbols and Abbreviations

Abbreviation

Description

PWM
r
S
σat
σ0
smsf
T
t
τ
TC
TTL
UHV
UPS
v
V
ZS

pulse width modulation
absolute distancetotal spin quantum number
atom-atom cross-section
light-atom cross-section
single-mode single-frequency
temperature
time
lifetimetransversal coolingtransistor-transistor logic
ultra high vacuum
uninterrupted power supply
velocity
volumeZeeman slower

90Merci!
First, I would like to thank my supervisor Francesca Ferlaino for giving me theopportunity to participate in setting up this new experiment. Especially from her,I also learnt things that are not directly connected to physics, such as presenting
and writing. In moments when we underestimated the power of Hofstadter's law,
our team play was exceptionally good – thanks. Großer Dank geht auch an Rudi
Grimm; dafür, in seiner Arbeitsgruppe mitarbeiten zu können, für seine weisen
physikalischen Ratschläge, als auch für die Möglichkeit an der EuroQUAM unddem netten Waldrast-Retreat teilnehmen zu können.
I thank our continuously growing erbium team for the great team work.
Besonders von Alberts schier grenzenlosen Technik Know-How konnte ich mir
so manches abschauen. Danke für die vielen feinen gemeinsamen Laborstunden.
I also want to mention Kiyotaka, with whom I shared some inspiring discussions
on easy, but amazingly complicated atomic beam physics.
The whole group offered a very pleasant and supporting working atmospherewith tasty 'cakes at 4' and many answers to my questions – thanks to all of you.
Besonderen Dank an Simon – meinen 'Postdoc' – der mir viel bei Belangen rundums blaue Licht half and also to Matteo for his supporting smile. Im weiteren
danke ich unseren Werkstattmitarbeitern für die technische Unterstützung, dievor allem beim Aufbau eines neuen Experiments nötig ist. Besonders Helmut
brachte mir mit seiner aufgeweckten Art die Bedienung vieler Maschinen bei.
Seit Begin meines Studiums begleitete mich und viele andere Studenten
Sabine Schindler als Studienbeauftragte bei allem Offiziellem höchst unbürokratisch, geduldig und fair – vielen Dank. Von Peter Zollers fast schon legendären
Vorlesungen konnte ich sehr viel lernen, und im Nachhinein diese auch genießen.
Danke auch an Alexander Glätzle, welcher mir hierbei als Tutor zur Seite standund uns die Türen öffnete, um den Viktor Franz Hess Südpfeiler zu erklettern.
Ohne den tollen und bergbegeisterten Studienkollegen hätten diese 6 Jahre
nicht halb so viel Spaß gemacht. Mit Roland und Ben teilte ich Biwakschachteln
und Lerngruppen, mit Flo eine wahnsinns WG und viele Flaschen Wein. Adam,
Andi und ich haben während der intensiven Diplomzeit viel zusammengearbeitet
und uns zudem einige belebende Auszeiten erlaubt: Nachtklettern an der Mar-91

tinswand, frühmorgentliche Gratüberschreitungen, Rennrad-Konferenzpausen,
Feierabend-Saunen und natürlich unsere tägliche, obligate Kaffepause. Besten
Dank. Auch meinem Bürokollegen Mohamed danke ich für erfrischende Schreibpausen mit Bürotennis und seine Hilfe bei unserem Umzug nur eine Woche vor
Abgabe dieser Arbeit.
Hans Strack-Zimmermann möchte ich als meinen langjährigen Berater im Hintergrund danken. Meinen Eltern Lisa und Wolfgang danke ich über alles für ihre
positive, vertrauensvolle Einstellung und die vielen Freiheiten die sie mir gaben.
Ihre Großzügigkeit hat es mir ermöglicht hier in Innsbruck das zu studieren,
was ich wollte. Schließlich möchte ich noch meiner wundervollen Freundin Chris
danken, die mich besonders im letzten Jahr auf jede mögliche Weise unterstützt
hat und somit auch einen Beitrag zu dieser Arbeit geleistet hat.
Merci!

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