PHYSICAL REVIEW A 84, 063420 (2011)

Low-temperature high-density magneto-optical trapping of potassium using theopen 4S → 5 P transition at 405 nm
D. C. McKay,1,* D. Jervis,1 D. J. Fine,1 J. W. Simpson-Porco,1 G. J. A. Edge,1 and J. H. Thywissen1,2
1

Department of Physics, CQIQC, and Institute for Optical Sciences, University of Toronto, M5S1A7 Canada
2
Canadian Institute for Advanced Research, Toronto, Ontario, M5G 1Z8 Canada(Received 16 October 2011; published 21 December 2011)

We report the laser cooling and trapping of neutral potassium on an open transition. Fermionic 40 K is captured
using a magneto-optical trap (MOT) on the closed 4S1/2 → 4P3/2 transition at 767 nm and then transferred,with high efficiency, to a MOT on the open 4S1/2 → 5P3/2 transition at 405 nm. Because the 5P3/2 state hasa smaller linewidth than the 4P3/2 state, the Doppler limit is reduced from 145 μK to 24 μK, and we observe
temperatures as low as 63(6) μK. The density of trapped atoms also increases, due to reduced temperatureand reduced expulsive light forces. We measure a two-body loss coefficient of β = 1.4(1) × 10−10 cm3 /s nearsaturation intensity, and estimate an upper bound of 8 × 10−18 cm2 for the ionization cross section of the 5P state
at 405 nm. The combined temperature and density improvement in the 405 nm MOT is a twenty-fold increasein phase-space density over our 767 nm MOT, showing enhanced precooling for quantum gas experiments. A
qualitatively similar enhancement is observed in a 405 nm MOT of bosonic 41 K.
DOI: 10.1103/PhysRevA.84.063420

PACS number(s): 37.10.De, 67.85.Lm, 32.80.−t, 34.50.Rk

I. INTRODUCTION

Magneto-optical trapping is a widely applied techniquefor creating cold, dense samples of neutral atoms. Ultracoldgas experiments typically use a MOT for accumulation andprecooling, although laser cooling alone has been unable tocreate a quantum degenerate sample without a subsequentevaporative cooling step. Density in laser cooling is limited
by repulsive radiation pressure due to reabsorption [1] andby collisional loss processes [2]. The temperature limit, inthe simplest two-level theory, is the Doppler temperature,kB TD = h̄/2, where  is the linewidth of the excited state [3].
Fortuitously, the multilevel structure of ground states can allow
for sub-Doppler temperatures [4,5], but these effects are notseen in all atomic species. Particularly, sub-Doppler cooling isnonexistent in 6 Li [6] and weak [7] or difficult to observe [8] in
40
K. Since these are the only two stable fermionic alkali-metal
isotopes, and thus commonly used for the study of quantum
degenerate Fermi gases, new cooling techniques would be
beneficial.
Laser cooling on narrower lines can achieve lower temperatures, as has been demonstrated with alkaline-earth metals.
In the case of 88 Sr [9], the broad 30 MHz cycling transition(1S0 → 1P1 ) at 461 nm is used to capture atoms, followed bycooling on the narrow 7.5 kHz forbidden transition (1S0 → 3P1 )at 689 nm. This two-step process combines a large capture rateduring the first stage with the low Doppler temperature of thesecond stage.
Alkali metals do not have forbidden cycling transitions;however, higher excited states do have smaller linewidths. In*
Current address: Department of Physics, University of Illinois,
Urbana, Illinois 61801, USA.

Published by the American Physical Society under the terms of theCreative Commons Attribution 3.0 License. Further distribution ofthis work must maintain attribution to the author(s) and the publishedarticle’s title, journal citation, and DOI.
1050-2947/2011/84(6)/063420(8)this work we excite potassium to the 5P state, which has alinewidth of 1.19 MHz, roughly five times smaller than the
6.04 MHz linewidth of the 4P state that has been used in
all potassium laser-cooling experiments to date. In addition
to reduced Doppler temperatures, higher-state transitions may
provide other advantages: multiphoton decay channels allow
for background-free detection, and the smaller transition
wavelength reduces the diffraction limit of imaging andmanipulation. A specific advantage of the potassium 4S → 5P
transition near 405 nm is the availability of inexpensive GaN
diode lasers in the 395–410 nm range. One disadvantage ofhigher-state transitions in alkali metals is that they are opentransitions. After excitation from the 4S1/2 ,F = 9/2 groundstate to the 5P3/2 ,F  = 11/2 excited state, 40 K can decay via
a three-photon cascade to the F = 7/2 ground state, whichcannot be excited by the same laser-cooling light. Furthermore,
the cascade decay acts to depolarize the atomic gas. Both ofthese effects can interrupt laser-cooling mechanisms.
It has been shown in a variety of systems that laser coolingis possible both with cascading and with open transitions.
Examples include metastable noble gases [10], lanthanides[11], excited-state alkali metals [12], ground-state alkali metals[13], and molecules [14]. Similar to our work, the cooling ofHe∗ [10] and 6 Li [13] use the transition from the nS groundstate to the (n + 1)P excited state. In the case of He∗ , a MOT
on the 2S → 3P transition at 389 nm, which is cascading
but closed, was shown to have a lower two-body loss rate β,lower reabsorption rates, and a larger cooling force per recoil,resulting in increased density. No reduction in temperature wasseen since the He∗ 2P and 3P excited states have the same
lifetime. In the case of 6 Li, a MOT on the open 2S → 3P
transition at 323 nm did have a reduced temperature, but not
an increased density. Unlike lithium and metastable helium,
potassium has a D-state decay channel that could perturb laser
cooling more significantly (see Fig. 1).
In this work, we explore cooling and trapping on the “blue”
4S1/2 → 5P3/2 transition of 40 K at 405 nm. Atoms are firstaccumulated in a standard MOT on the “D2” 4S1/2 → 4P3/2

063420-1

Published by the American Physical Society

D. C. MCKAY et al.

PHYSICAL REVIEW A 84, 063420 (2011)

741.09112(15)THz
404.52847(8)nm

5P3/2
4.6

740.52880(15)THz
404.83565(8)nm

0.15

F=5/2
F=7/2

-0.72(9) MHz

F=9/2

TABLE I. Key excitation properties of the 4S1/2 → 5P3/2 transition, with the 4S1/2 → 4P3/2 transition shown for comparison. Where
relevant, the drive is assumed to be σ + polarized. Saturation intensity
is defined as the drive strength at which 25% of the population is in
the excited state. “Steady-state polarization” is the fraction of atoms
in F = 9/2 that are in the mF = +9/2 sublevel, with a drive at
Isat . “Depumping probability” is the percent decay from |11/2,11/2
to the F = 7/2 manifold, through a multiphoton cascade. “Doppler
temperature” is the steady-state temperature in the low-intensity limit
and includes open-transition effects for 5P3/2 .

-14.99(13) MHz F=11/2

1.4

5P1/2

17.8(2) MHz
10.01(9) MHz

A=1.16µ s-14.5645.66265(15)THz

3D3/2

645.59346(15)THz

3D5/2

1.5

1.07

25.9

630.36014(15)THz

5S1/2

Linewidth [/(2π )]Branching ratio
Cross section (σ )Saturation intensity (Isat )Steady-state polarization
Depumping probability
Doppler temperature

22391.01629605(9)THz
766.7006747(2)nm

4P3/2

5P3/2

6.04(1) MHz
Cycling0.28 μm2
1.752(3) mW/cm2
100%0%145.0(3) μK

1.19(2) MHz
1/6.4(7)0.010(1) μm2
23(2) mW/cm2
61(1)%
18(2)%
23.5(7) μK

4.34
15.6
7.9

55.20(9) MHz F=5/2
31.02(4) MHz F=7/2-2.29(4) MHz F=9/2

4P3/2-46.37(6)MHz

389.28618436(6)THz
770.1081365(1)nm

4P1/2

F=11/237.97(7)37.47(7)

0THz

4S1/2

714.327(5) MHz

F=7/2-571.462(5)-14.98(13) MHz
MHz

F=9/2

FIG. 1. (Color online) Level diagram including all the possible
decay channels of the 4S → 5P transition in 40 K. Transition
probabilities are from [15] and listed as A = 1/τ in units of μs−1 .
Except for 4P → 4S (from [16]), the uncertainties in transition
probability rates are not shown explicitly. The uncertainties in the
5P → 4S rates are less than 8%, but all other rates are estimatedto have uncertainties between 25% and 50%. The total measured
lifetime from all decay channels is 134(2) ns for 5P3/2 [17] and137.6(1.3) ns for 5P1/2 [18]. Level energies E referenced from the 4S
state are from [15] and presented in both frequency units (as E/ h)and wavelength units (in italics, as hc/E). Hyperfine splittings E
referenced to the level energies are from [19] for 4S1/2 and 5P3/2 ,from [15] for 4P3/2 , and given in frequency units (as E/ h). The
solid blue and dashed red arrows indicate the cooling and repump
hyperfine transitions, respectively, used for laser cooling.

transition at 767 nm, for which the capture rate is high. The
cloud is then transferred to a blue MOT, where we observea three-fold reduction in temperature and a ten-fold increasein density. Although the capture velocity and beam size ofthe blue MOT are small, we observe almost perfect transfer
between MOTs. We find that loss rates in the blue MOTfrom two-body loss and photoionization are higher than in theD2 MOT, but these processes play little role on the sub-100 ms
timescale that we observe is necessary for equilibration.
II. 4S1/2 → 5 P3/2 TRANSITION: THEORY ANDBACKGROUND

Figure 1 shows a level diagram of potassium including
all possible decay paths from the 5P3/2 state. The transition
probability for 4S1/2 → 5P3/2 is 2π × 185 kHz, thirty times
weaker than the 2π × 6.04 MHz D2 transition. However, theexcited state is broadened to  = 2π × 1.19 MHz by otherdecay channels: five out of six times the 5P3/2 state decays

via a three-photon cascade instead of emitting a single blue
photon.
We calculate excitation properties and cooling rates of the
4S → 5P transition by finding the steady-state solution of
the optical Bloch equation (OBE) that includes all relevant
levels. Because the transition is not closed, continual excitation
requires a repumping beam. As in the experiment, atoms are repumped on the 4S1/2 ,F = 7/2 → 4P3/2 ,F = 9/2 transition,
whose strength is chosen here to be powerful enough that it is
not the limiting timescale.
Table I summarizes key steady-state properties of excitation
to the 4P and 5P states. Unlike in a cycling transition, thepossibility of a multiphoton cascade prevents complete opticalpumping. However, the depolarization effect is not quite as
bad as Fig. 1 might suggest: 61% of atoms in the F = 9/2
manifold are in the doubly polarized |9/2,9/2 state. The
resonant scattering cross-section is nearly thirty times smaller
than the D2 transition due to a narrow linewidth and smaller
wavelength. This could be an advantage for cooling trapped ordense clouds since optical density is reduced. However, for thesame reasons, the saturation intensity is an order-of-magnitude
higher, increasing optical power requirements.
Laser cooling and trapping performance on the 4S → 5P
transition is estimated by including either Doppler or Zeeman
shifts in the OBE calculation. The force on the atom is h̄k times
the calculated scattering rate, where k is the wave vector ofeach cooling beam. Close to zero velocity and position, atomic
motion can be described as a simple harmonic oscillator, withoscillation frequency ω0 and damping rate γ , plus a momentum
diffusion term from recoil heating. Momentum diffusion is due
to both absorption and emission along one of several possible
decay paths. For each transition from state i to state j , theenergy increase is (h̄kij )2 /(2M), where kij = Eij /(h̄c) andEij is the energy difference between the states and M is themass of 40 K. The total heating rate Ė gives rise to a steady-state
temperature Ė/(γ kB ).
At comparable scaled detunings and saturations, Fig. 2(a)shows that the blue transition can achieve a higher cooling rate
than the D2 transition. However, the maximum force and the063420-2

LOW-TEMPERATURE HIGH-DENSITY MAGNETO-OPTICAL . . .

PHYSICAL REVIEW A 84, 063420 (2011)

By contrast, the 4P state requires photons with a wavelength
less than 455 nm, which is not provided by the D2 MOT. The
405 nm trap light may also ionize any state during the radiative
cascade, and the 767 nm repump can only ionize the 5P state.

units of(a)III. LASER AND MOT SETUP

units of(b)

FIG. 2. (Color online) Blue cooling and trapping. Calculated
force (in units of Mg, where g is gravitational acceleration) versus(a) velocity (at zero displacement) or (b) position (at zero velocity)
for a 10 G/cm MOT at 767 nm (red dashed line) and 405 nm (bluedashed line). Both are calculated for counterpropagating beams at−/2 detuning from resonance and with intensity per beam of Isat /5
where Isat is indicated in Table I. For the 405 nm data there isa 767 nm repump beam on resonance with the 4S1/2 ,F = 7/2 →4P3/2 ,F  = 9/2 transition with 10% of the 405 nm beam intensity.
Near zero velocity, the damping rate is γ = 1.8 × 104 s−1 for the
red and γ = 6.9 × 104 s−1 for the blue. Near zero displacement,
the spring constant corresponds to an undamped trap frequency
ωosc /(2π ) = 730 Hz for the red and ωosc /(2π ) = 650 Hz for theblue.

capture range are greatly reduced. Figure 2(b) shows that the
spring constant is comparable for the two transitions, but thattrapping volume is larger for the red MOT. These calculations
support the strategy of loading atoms using the 767 nm
transition and then transferring later to the 405 nm MOT for
additional cooling and compression. We find a steady-state
temperature of 24 μK for the blue transition, which is indeed
smaller than the Doppler temperature of the D2 transition. In
fact, this steady-state temperature in the low-intensity limit
is slightly (∼18%) less than the h̄/(2kB ) expected in the
two-level Doppler cooling, because the multiphoton cascadecauses slower momentum diffusion than single-photon kicks
with the same total energy.
Another difference between laser cooling with blue insteadof infrared light is the possibility of photoionization. The
ionization energy of potassium is h × 1049.567 82( 2) THz[15], so the 5P state can be ionized by the 405 nm MOT
light, or by any photon with a wavelength less than 972 nm.

The 4S → 5P transition is in a wavelength band coveredby GaN diode lasers, which have become readily available
due to recent commercial interest in optical storage media.
These sources have been exploited to perform 4S → 5P
spectroscopy of naturally abundant potassium [18,20–23] andenriched 40 K [24], and here we use them for laser cooling ofenriched 40 K.
Our 405 nm master is a grating-stabilized diode laser
with 10 mW output. Half of this power is injected [25] into
a 100 mW diode laser (“slave” laser). At room temperature
and without injection, the slave diode spectrum is nearly
1 nm wide and centered at 407 nm. The poor current andtemperature tuning characteristics of the diode, approximately+0.02 nm/mA and +0.05 nm/◦ C, respectively, necessitate
cooling the diode to −20 ◦ C. Without injection, the FabryPerot spectrum of the slave is featureless, but a single strong
peak is evident when successfully injected. The output of theslave, typically run at 60 mW, is passed through a single-mode
optical fiber before being used for the MOT (see Fig. 3).
The remaining 5 mW of master light is used for modulationtransfer spectroscopy using a natural-abundance potassium
cell heated to 140 ◦ C. The elevated temperature is necessary
because the absorption of light at the 4S → 5P resonanceby the Doppler-broadened vapor is two orders of magnitude
weaker than at the D2 transition. We lock to the 4S1/2 ,F =1 → 5P3/2 transition in 39 K (with unresolved excited states)that is the closest spectral feature to the 4S1/2 ,F = 9/2 →5P3/2 ,F  = 11/2 transition of 40 K. The additional 0.5 GHz
shift is performed with acousto-optic modulators.
The D2 MOT uses retroreflected beams along three axes,
limited by the cell windows to be 4.4 cm diameter in thehorizontal axes and 3.8 cm diameter in the vertical axis.
A background potassium vapor is created from enricheddispensers (5% 40 K) and collected in the trap using the strong
4S1/2 → 4P3/2 transition. During this phase, there are twooverlapping 767 nm beams: a trap with 200 mW total power
detuned by  = −35 MHz from the F = 9/2 → F  = 11/2
transition, and a repump with 150 mW total power detuned by−25 MHz from the F = 7/2 → F  = 9/2 transition. After
10 s, the blue MOT is turned on, with up to 30 mW total
power. As shown in Fig. 3, the smaller (10 mm diameter) blue
beams are mixed with the infrared beams on dichroic mirrors.
There is a short time (3 ms) when both MOTs are on before
the D2 trap light is turned off (see timing diagram of Fig. 3),
while the D2 repump beam is left on at reduced intensity.
Blue laser cooling is applied typically for 30 ms.
Laser-cooled atoms are characterized using absorption
imaging on the 4S → 4P transition. Temperature is measured
after ballistic expansion, with a Gaussian fit to the density
distribution imaged at various free-flight times, 1.5–10 ms after
the magnetic field and laser beams have been extinguished.

063420-3

D. C. MCKAY et al.
DWPs

PHYSICAL REVIEW A 84, 063420 (2011)
DWPs

QP

BBM

2.5

(a)
DM

405 Trap

2.0

K

(b)

1.0

767
Trap

405
TOF
molasses

Optical Density

405
MOT

1 mm

767
MOT

1.5

767
Repump0.5
767 Repump

405
Trap

0.0
2000
3ms

1800
~10s

Blue MOT 0-10ms 1.5-10ms
Time

FIG. 3. (Color online) The optical configuration of the magnetooptical trap includes 767 nm trapping and repump beams (bothshown with red dashed outlines) and a 405 nm trapping beam(shown in solid blue). The two colors are mixed on a dichroic
mirror (DM), manipulated with dichroic quarter-wave plates (DWPs),
and retroreflected off a broadband mirror (BBM). Each DWP has aquarter-wave retardation at one wavelength and no retardation at theother wavelength. Only one MOT direction has been shown for clarity,
but there is an identical beam path in three orthogonal directions. The
magnetic quadrupole (QP) coils typically apply 10 G/cm along theirstrong axis. The potassium (K) cloud is imaged in absorption witha probe beam (not shown). Inset: Timing diagram of laser beam
intensities (top three lines) and magnetic field strength. After a 10 s
accumulation, the 767 nm trap is extinguished, the 767 nm repump
intensity is reduced, and the 405 nm trap is turned on for a variable
hold time. The molasses phase is only used in Sec. V. An absorption
image is taken after a variable-length time of flight (TOF).
IV. 4S → 5 P MOT OF 40 K

We observe that atoms are held by the blue MOT. A typicalabsorption image of the D2 MOT and the blue MOT are
shown in Fig. 4. Compression occurs across a broad rangeof parameters, which is a first indication of cooling (see below
for further discussion). Figure 4(c) shows that cloud sizes
in the blue MOT equilibrate with a 1/e relaxation time of
2–4 ms. In a damped oscillator model of atomic motion ina MOT, where γωosc , the atomic position damps with2
a time γ /ωosc∼ 4 ms [using the typical force curves ofFig. 2(b)]—which is comparable to what we measure. Atomic
velocities would damp in a much faster time γ −1 ∼ 15 μs so,after the spatial compression shown in Fig. 4(c), blue laser
cooling is complete.
Figure 5 shows the capture fraction and gravitational sag
as a function of blue trap intensity and D2 repump intensity.
In both cases, providing the saturation intensity (see Table I)
is sufficient for complete transfer into a strong trap.1 From

1

(c)

Time

For low intensities, the measured sag values are roughly ten-times
larger than the sag one would expect from our simple model. Also note

Width ( m)

QP Field

767 Trap

1600
1400
1200
1000
800
600
0

5

10

15

20

Blue MOT Time (ms)FIG. 4. (Color online) Trapped cloud measurements. Typicalabsorption images of (a) a 767 nm MOT with detuning  = −35 MHz
and intensity I ≈ 16 mW/cm2 and (b) a 405 nm MOT, for  =−1 MHz, I ≈ 90 mW/cm2 . In both images, pixel darkness denotes
optical density. Images were taken shortly (1.5 ms) after releasefrom the trap, such that clouds are little changed from their insitu distributions. Atom number is 108 , but the cloud in (b) isclearly compressed. (c) Cooling dynamics are observed in images
similar to (b) but with various hold times in a blue MOT; here with
 = −2 MHz and I ≈ 50 mW/cm2 . The rms width is shown forboth the vertical (open red circles) and horizontal (black squares)
directions. Simple exponential fits are shown as solid lines, with a
1/e time of 1.8 ms for the vertical width and 4 ms for the horizontal
width.

exponential fits, the transfer efficiency is 90% for 5.5 mW/cm2of blue trap intensity and for 0.21 mW/cm2 of D2 repump
intensity. The 26:1 ratio between these follows approximately
the ratio of saturation intensities of each transition.
Since the capture rate of a MOT from background vapor
is proportional to  4 d 4 for small beam sizes d, one would
expect a 106 reduction in steady-state number in going from the
767 nm trap to the 405 nm trap. Accordingly, a measurement ofthat the displacement switches sign for intermediate repump intensity,
which would not be the case if the spring constant were monotonic in
intensity. It may be that optical pumping is not correctly functioning
in a MOT at intensities far below saturation.

063420-4

LOW-TEMPERATURE HIGH-DENSITY MAGNETO-OPTICAL . . .

PHYSICAL REVIEW A 84, 063420 (2011)(a)FIG. 6. Lifetime. Atom number is shown versus hold time in theblue MOT. The data are fit to exponential decays in different regions
as a guide to the eye. Top inset: Peak density for short hold times
is approximately constant. Bottom inset: The one-body-lifetime fit atlong hold times decreases at higher 405 nm trap intensity.

(b)FIG. 5. (Color online) Intensity requirements. A threshold forproper trap function is observed by measuring the capture fraction(black squares, scale on left) and vertical displacement of the cloudfrom trap center (open red circles, “MOT sag” scale on right) as afunction of the six-beam intensity of (a) trap beams and (b) repump
beams. Lines are exponential fits to guide the eye. The blue-MOT
time was 30 ms for (a) and 20 ms for (b), both at −2 MHz detuning.
In both sets of data, the trap movement in the direction orthogonal togravity was less than 100 μm.

atom number versus time (Fig. 6) shows no sign of saturation
after a hundred-fold reduction in number. We can then use sucha measurement as a clean measure of loss processes, ignoring
additional capture.
We also note that, since we are not loading atoms fromvapor into the blue MOT, we can choose small beam sizes andreduce the 405-nm power requirement. In our configuration,
the total power required at saturation intensity is roughly
2.5 mW, which our laser system can easily provide.
The loss data in Fig. 6 fit well to two exponential timescales, indicative of two-body losses at high density andone-body losses (collisions with background atoms plus
photoionization) at low density. The loss rate from a MOT
is [2]
dN
N
=− −β
dt
τ


n(r )2 d 3 r,(1)where τ is the one-body lifetime, β is the two-body loss
coefficient, n is the atomic number density, and the integral isover three-dimensional space. To find τ , we fit the data at longhold times (t > 2 s, N < 5 × 106 ) where the atom number
is strongly reduced and two-body losses can be neglected.
The lifetime versus 405 nm intensity is shown as the bottom
inset to Fig. 6. The decrease in lifetime versus intensity
could be evidence of ionization losses. The line is a fit toa model that includes the intensity dependence of both theionization rate and the excited-state fraction. A separate studyof MOT fluorescence versus laser power, comparing D2 andblue MOTs, was used to calibrate excited state fraction versus
intensity. Together, we find an ionization cross section of
8 × 10−18 cm2 for the 5P3/2 state at 405 nm. We report thisvalue as an upper bound since the ionizing beams are also thetrap beams, and we cannot rule out other trap loss processes.2
There are no measured cross sections for the ionizationof the 5P states of potassium—only for the equivalent state,
6P , of rubidium [26–28]. These rates may be comparable
since the ionization cross section from the potassium 4P states[29,30] is within a factor of three of the 5P cross section for
rubidium [31]. Indeed, our upper bound is similar in magnitude
to the 2 × 10−18 cm2 cross section for the 6P state of rubidium
from [26] measured at λ = 350 nm.
To measure the two-body loss rate, we assume the MOT
density distribution is Gaussian, which is supported byabsorption images of the cloud. From the top inset in Fig. 6 we

2

From similar measurements of lifetime versus repump intensity,
we constrain the effect of repump ionization to be negligible. One
would guess a 15 s ionization time for I767 = 1 mW/cm2 using therubidium ionization cross section of σ = 1.5 × 10−17 cm2 measured
at 690 nm by [26]063420-5

D. C. MCKAY et al.

PHYSICAL REVIEW A 84, 063420 (2011)

in the potassium nS-(n + 1)P MOT, unlike metastable helium[10], are not smaller than in the nS-nP MOT. However, forthe short timescales (tens of milliseconds) required to decrease
temperatures and increase density, these loss rates are still
negligible.
A primary motivation for cooling on a narrow transition
is to achieve a lower asymptotic temperature. Figure 7 shows
how the temperature and peak density of the blue MOT changewith detuning, at various quadrupole gradients. A minimum
temperature of 63(6) μK is seen for a 5 G/cm magnetic
quadrupole gradient. Operating the MOT with higher gradients
increases both the temperature and density. In all cases, theminimum temperature and maximum density are found near/  ≈ −1.
We attribute the increase in density to three factors. First, thetemperature in the MOT is lower. Second, expulsive forces due
to reabsorption are reduced, because the same spring constantis achieved with a scattering rate that is six times smaller. The
open transition may further reduce reabsorption by pumping
to the F = 7/2 ground states. Third, the optical density seen
by both the incident and the scattered blue photons is reduced
by a factor of nearly thirty.
In comparison, our D2 MOT density is typically n0 =2 × 109 cm−3 and the temperature is typically T = 180 μK.
Since phase-space density scales as n0 T −3/2 , the combined
75 μK and n0 = 1.2 × 1010 cm−3 (achieved with a blue MOT
at 7.5 G/cm and −1.5 MHz detuning) realizes a twenty-foldenhancement in phase-space density.

(a)

(b)

FIG. 7. (Color online) Performance of a magneto-optical trap at
405 nm. Both (a) temperature and (b) peak density are shown versus
detuning from resonance, for several magnetic quadrupole gradients:
5 G/cm (black squares), 7.5 G/cm (red circles), and 10 G/cm (bluetriangles). Temperature is shown along a weak axis of the quadrupole;temperatures along the strong axis (along gravity) were 1.82(15) times
higher.

see that the peak density n0 at short times is roughly constant,so the number decays as [2]  
1 n0 βt .
N (t) = N0 exp −
+ √
τ
8

(2)

We then fit the data at short hold times (t < 300 ms) to an
exponential decay and use τ (from our previous measurement)
and n0 to find β. At  = −2 MHz, we find β = 2.0 (1) ×
10−10 cm3 /s for I ≈ 75 mW/cm2 , and β = 1.4(1) ×
10−10 cm3 /s for I ≈ 20 mW/cm2 . These are relatively hightwo-body loss rates compared to 40 K MOTs on the D2
transition, which are typically in the range of 10−12 to10−10 cm3 /s [32–34]. Therefore, density-dependent loss rates

FIG. 8. Molasses cooling. Blue laser cooling is continued for
10 ms after the magnetic quadrupole field is extinguished, followed
by a TOF temperature measurement. The horizontal temperature
is shown versus detuning; vertical (along gravity) temperatures are
1.96(11) times higher. In addition to the statistical error bars shown,
there is a systematic 0.5 MHz uncertainty in the detuning. The solidline is an OBE calculation, but it is not a quantitative prediction: theapproach is constrained to intensities well below saturation (here,
Isat /50 per beam), whereas the data were taken with roughly Isat /2
per beam.

063420-6

LOW-TEMPERATURE HIGH-DENSITY MAGNETO-OPTICAL . . .
V. PROSPECTS AND CONCLUSIONS

Since the lowest observed MOT temperatures occur at low
gradients, one might expect continued improvement during an
optical molasses phase in which magnetic fields have been
extinguished (see Fig. 3 inset). Figure 8 shows that the minimum molasses temperature, roughly 85 μK, is comparable towhat is observed in the MOT, although optimized at a lower
detuning, /  = −0.6(2). These temperatures are still morethan three times the Doppler temperature calculated in Sec. II,
which may be due to a low cooling rate as compared to theshort molasses time available. Indeed, we observe that thetemperature asymmetry between the vertical and horizontal
axes in the MOT persists during the molasses phase, when no
gradient asymmetry remains. Even the asymptotic temperaturemight not be expected to reach the Doppler limit: while thecalculation in Sec. II includes multilevel effects, it neglects
three-dimensional effects, reabsorption, and heating due theintensity fluctuations. The latter effect has been shown by
Chanelière et al. to limit one-dimensional Doppler cooling toseveral times TD in Sr, when Sisyphus and other sub-Doppler
mechanisms are absent [35]. In the case of 4S → 5P coolingin 40 K, polarization gradient cooling may be interrupted by the
optical pumping and depolarization effects of the three-photon
cascade.
We have also observed laser cooling and trapping forbosonic 41 K on the 4S1/2 → 5P3/2 transition. A similar orderof-magnitude increase in MOT density was apparent, althoughfurther study is warranted. With any isotope of potassium,
additional improvements might be possible with more sophisticated timing sequences of detuning and/or intensity of coolinglight, which has been fruitful in narrow-line MOTs and in
sub-Doppler cooling of bosonic potassium [36].
The reduced wavelength of the 4S1/2 → 5P3/2 transition
may enable improved imaging or addressing resolution, forinstance in the context of strongly correlated lattices where the[1] T. Walker, D. Sesko, and C. Wieman, Phys. Rev. Lett. 64, 408(1990); K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev.
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PHYSICAL REVIEW A 84, 063420 (2011)

spacing is typically 0.5 μm [37]. However ionization will eventually limit the number of photons that can be scattered from anatom, and thus the fidelity of imaging. Using an objective with
0.6 numerical aperture, collection efficiency would be 10%
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ACKNOWLEDGMENTS

We thank K. Pilch, M. Schöll, and F. Stubenrauch for theirearly contributions, and B. DeMarco, P. Duarte, M. Greiner,
E. Hessels, R. Hulet, A. Steinberg, S. Trotzky, and D. Weissfor discussions. This work was supported by the DARPA OLE
program, ARO, AFOSR, CIfAR, CFI, and NSERC.

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