US 11,291,103 B2

5

Primary atoms 228 can include an atomic, atomic ion,
molecule, or molecular ion species in vapor form and
physically capable of being slowed and cooled using lasers
‘As used herein, physically capable of being slowed refers to
the internal level structure of primary atom 288 having
repeated scattering of photons from slowing light 262 and
trap light 240. Exemplary primary atoms 228 include alkali
atoms such as lithium, sodium, potassium, rubidium, cesium
and francium; alkaline earth atoms such as magnesium,
calcium, and strontium; select species of lathanides or
actenides such as dysprosium, erbium, and ytterbium: meta-
stable noble gasses such as helium, argon, and xenon;
alkaline-fluoride molecules such as magnesium fluoride,
calcium fluoride, strontium fluoride; and molecules such as
boron monohydride and the like. A velocity distribution of
primary atoms 228 can include a velocity component that
can be slowed by slowing light 262 and subsequently
trapped by trap light 240. A total flux of primary atoms 228
can be from 1 to 10°° s“!, A maximum angular distribution
of primary atoms 228 can be 4x steradians, specifically up
to the angular opening of the atomic transfer wall 218, and
more specifically to the maximum initial angle, dependent
on velocity, whose trajectory is slowed by slowing light 262
and trapped by trap light 240. In an embodiment, primary
atoms 228 includes alkali atoms communicated, with a
thermal velocity distribution, from an alkali metal effusive
source.

Decelerating atoms 230 include a subset of primary atoms
228 that are slowed by slower light 262. A flux of deceler-
ating atoms 230 can be from 1 to 107° s~!
1s to 10! s-!, and more specifically from 10° s~! to
10’? s"!. Inan embodiment, decelerating atoms 230 includes
a fraction of primary atoms 228 whose velocity is small
enough to be decelerated by slowing light 262.

Slowing light 262 can include a light source that slows 3

primary atoms 228 and can include single frequency laser
light, multiple-frequency laser light, white light, chirped
frequency laser light, and the like. Exemplary slowing lights
262 include laser light slightly detuned from an atomic
transition or laser light whose frequency is chirped to
maintain resonance with decelerating atoms 230. Moreover,
slowing light 262 can include a combination of types of light
in order to drive transitions in primary atoms 228. A
wavelength of slowing light 262 can be from 100 nm to
15000 nm, specifically from 350 nm to 2000 nm, and more
specifically from 350 nm to 1500 nm. A ratio of intensity to
the saturation intensity of the transition in primary atom 228
of slowing light 262 can be from 107° to 10°, specifically
from 10-* to 10°, and more specifically from 0.1 to 10
Intensity can refer to the amount of intensity in any fre-
quency component of slowing light 262 driving any transi-
tion in primary atom 228. A ratio of the frequency detuning
of any particular frequency component of slowing light 262
from its relevant transition in primary atom 228 to the
natural linewidth of the transition in primary atom 228 can
be from -100 to 100, more specifically from -10 to 10, and
more specifically from -2 to 0. In an embodiment, primary
atoms 228 include lithium atoms, and slowing light 262
includes a circularly polarized, single frequency laser light
that is red-detuned from a transition between 2S, ,(F=2) to
2P,,.(F'=3) to twice that of a natural linewidth of the 2P,,
state with an intensity twice that of the saturation intensity
of the 2P,,, state.

Slowed atoms 232 can include decelerated atoms 230 that
interact with trapping light 240 after traversing atom the
atom transfer aperture 240. Moreover, primary atoms that
are not slowed may not interact with the trapping light 240

. specifically from 3

0

0

40

&

0

6

and pass through the trapping region 244. A flux of slowed
atoms 232 can be from 1 to 10° s“', specifically from 1 s~
to 10! s~!, and more specifically from 10° s~! to 10!? s"!. A
velocity distribution of slowed atoms 232 can be such that
a fraction of slowed atoms, afier interacting with trapping
light 240, will become trapped atoms 234. In an embodi-
ment, slowed atoms 232 include decelerated atoms 230
traversing the atomic aperture 240.

Slower field 256 can include a magnetic or electric field,
oscillating or constant in time, or any combination thereof,
independently or in conjunction with slowing light 262 that
decelerates primary atom 228. Exemplary slower fields 256
include a time-constant magnetic field whose spatial shape
varies in proportion to the Vz, where z is the position along
the axis defined by the slowing light (Zeeman slower). This
exemplary field can maintain resonance between slower
light 262 and decelerating atoms 230 via the Zeeman effect,
delivering the maximum possible acceleration throughout
their trajectory. A maximum field strength of slower field
256 can be from 1 G to 10 T, specifically from 1 G to 10 kG,
and more specifically from 1 G to 200 G. In an embodiment,
slower field 256 includes a magnetic field that varies in
proportion to z, maintaining resonance with slowing light
262.

Decelerating atoms 230, slowing light 262, slowed atoms
232, and slower field 256 are disposed in atom slower 210.
Moreover, atom slower 210 can include slower member 258
interposed between atom source 226 and optical diffractor
212. Slower member 258 can include magnetic field coils
270, permanent magnet 274, voltage electrode, or a combi-
nation thereof. In an embodiment, with reference to FIG. 2
and FIG. 3, atom slower 210 is a Zeeman slower 266. Here,
slower member 258 is magnetic field coils 270 that produces
a spherical magnetic quadrupole field. It is contemplated
that magnetic field coils 270 are disposed in atom slower 210
and trapping region 244 to provide a continuous field
between atom slower 210 and trapping region 244. In an
embodiment, with reference to FIG. 5 and FIG. 6, uniaxial
counter-propagating monolaser atom trap 200 includes a
plurality of permanent magnet 274 disposed around atom
slower 210 and trapping region 244.

Magnetic field coils 270 can include electrical conductors
wound to produce or contribute to slower field 256 or
trapping field 254 upon application of electric current
Exemplary magnetic field coils 270 include wires wound
onto multiple circular forms, wires wound to form solenoids
or tapered solenoids, or copper conductors deposited onto
substrates and subsequently etched. Moreover, multiple
magnetic field coils 270 can be used in conjunction to
produce or contribute to slower field 256 or trapping field
254. Moreover, magnetic field coils 270 can include wiring
used to connect multiple circular forms or copper conduc-
tors. In an embodiment, with reference to FIG. 3, magnetic
field coils 270 includes twelve copper spirals with eight

5 turns and rectangular cross section 0.025 in. wide by 0.012

in. high, disposed on plate mount 270 and connected
together with copper wire and solder.

Permanent magnet 274 can include a material with a
permanent magnetization that can be positioned such that it
can produce or contribute to slower field 256 or trapping
field 254. Exemplary permanent magnets 274 include neo-
dymium-iron magnets. A field strength produced by perma-
nent magnet 274 can be from 1 G to 10 kG. In an embodi-
ment, permanent magnet 274 includes rectangular

5 parallelepiped neodymium-iron magnets with "x!" 14"

dimensions. In an embodiment, with reference to FIG. 7,
first permanent magnet 274.1 is interposed between optical


US 11,291,103 B2

Sheet 12 of 15

Mar. 29, 2022

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US 11,291,103 B2

13

beams. Further, using a single beam to generate both trap-
ping and slower with differential pumping across a flow tube
offers vacuum advantages such as separated a 2D MOT
loading a 3D MOT through a differential pumping tube and
significantly reduces power requirements. Further, com-
pared to conventional single-beam magneto-optical traps
like grating MOTs, pyramid MOTs, or the like, the uniaxial
counter-propagating monolaser atom trap 200 differential
pumping across flow tube 252 offers better vacuum proper-
ties. Further, conventional articles using single-beam traps
and differential pumping require more than one beam, which
is overcome by uniaxial counter-propagating monolaser
atom trap 200.

Moreover, uniaxial counter-propagating monolaser atom
trap 200 and processes herein have numerous advantageous
properties. In an aspect, embodiments with shutter 276 can
have significantly longer lifetimes compared conventional
apparatus by controlling the source of primary atoms 228.
Primary atoms 228 that are not slowed and trapped can
scatter with trapped atoms 234 and cause ejection of the
latter. This process can limit the lifetime of the atom traps of
conventional single-beam atom traps. Longer lifetimes in
uniaxial counter-propagating monolaser atom trap 200 is
advantageous for , inertial sensing, frequency or wavelength
standards, clocks, quantum information transmission, quan-
tum-enhanced sensing, and the like.

Uniaxial counter-propagating monolaser atom trap 200
and processes herein unexpectedly loads significantly more
atoms into the trap than conventional single beam traps

because the slower captures higher velocity and more abun- 3

dant primary atoms. Moreover, uniaxial counter-propagating
monolaser atom trap 200 provides extended interaction of
primary atoms with slower light, reducing saturation effects
from other beams, increasing the force, and further increas-

ing the maximum velocity of primary atoms that can be 35

trapped, relative to trapping in conventional articles where
all slowing force and trapping force are imparted via trap
light 240.

The articles and processes herein are illustrated further by
the following Example, which is non-limiting.

EXAMPLE

Single-Beam Zeeman Slower and Magneto-Optical Trap
Using a Nanofabricated Grating

We describe a compact (0.25 L) system for laser cooling
and trapping atoms from a heated dispenser source. The
system includes a nanofabricated diffraction grating to gen-
erate a magneto-optical trap (MOT) using a single input
laser beam. An aperture in the grating allows atoms from the
dispenser to be loaded from behind the chip, increasing the
interaction distance of atoms with the cooling light. To take
full advantage of this increased distance, we extend the
magnetic field gradient of the MOT to create a Zeeman
slower. The MOT traps approximately 10° Li atoms emitted
from an effusive source with loading rates greater than
10° s“!. Our design is portable to a variety of atomic and
molecular species and could be a principal component of
miniaturized cold-atom-based technologies.

Miniaturized cold-atom systems may form the basis of a
host of emerging quantum technologies, from quantum
repeaters to clocks. Such miniaturized systems will likely
employ a magneto-optical trap (MOT) for initial cooling and
trapping of atoms. Conventional MOTs confine an atomic
gas near the center of a quadrupole magnetic field in the
overlap region of three pairs of counterpropagating laser
beams. Due to the number of laser beams, MOTs typically

14

have expansive optical layouts with a large number of
mechanical degrees of freedom. Even mobile experiments
that incorporate MOTs have a size on the order of 1 m. To
fully realize the potential of cold-atom-based quantum tech-
nologies beyond the laboratory environment, the size and
robustness of MOTs need to be improved.

Previous research on MOT miniaturization has focused on
elements that can be trapped from a room-temperature
background vapor, namely Cs or Rb. However, many other
elements can be laser cooled and each have advantages for
various quantum technologies. For example. Sr or Yb can be
used as a highly accurate clock. Lithium, due to its low mass,
has been identified as a possible sensor atom for primary
vacuum gauges and, given its large recoil energy, could find
use in cold-atom gravity gradiometers. Most atoms, includ-
ing Li, do not have an appreciable vapor pressure at room
temperature and thus are typically loaded from a heated
dispenser. Here, we present the design of a compact laser
cooling and trapping apparatus for Li that integrates a MOT
with a Zeeman slower and includes a single input laser
beam. FIG. 9 shows the apparatus.

FIG. 9 shows the experimental apparatus. Straight arrows
indicate the input and diffracted laser beams. Curved arrows
wrapping each laser beam indicate circular polarization. The
copper rings represent electromagnets and the attached black
arrows show the direction of current flow. The two MOT
coils form a quadrupole magnetic field, while the Zeeman
coil increases the magnetic field behind the diffraction
grating. Lithium atoms that leave the heated dispenser are
slowed by the single laser beam behind the grating and then
captured by the MOT. The second dispenser in the back-
ground illustrates a side-loading configuration. The axes of
ensuing figures refer to the coordinate system shown here.
The gravitational force is antiparallel to the Z axis.

MOT miniaturization is based on early experiments using
pyramidal retroreflectors or tetrahedral laser-beam arrange-
ments, These pyramidal and tetrahedral MOT configurations
allow the formation of a MOT using a single external laser
beam and a compound reflective optic. In the tetrahedral
geometry, the compound optic can be fully planarized by
replacing the reflectors with diffraction gratings (see FIG. 9)
Both grating and pyramidal MOTs have been demonstrated
to trap large numbers of atoms and cool them below the
Doppler limit. Pyramidal MOTs have been made into single-
beam atom interferometers. Grating MOTs have found use
as magnetometers and electron-beam sources. The optics for
both MOT types are amenable to nanofabrication. Nanofab-
ricated pyramidal MOTs are inferior to grating MOTs in two
key areas. First, grating MOTs form above the nanofabri-
cated grating chip, making the laser-cooled atoms easier to
manipulate and detect. Second, the fabricated optics of a
grating MOT are planar, making grating MOTs fully com-
patible with atom chips and photonics.

The atom loading rate R of a MOT depends strongly on
the capture velocity vc. Namely, Re(v/v,)*, where the
constant of proportionality depends on the total flux from the
source and v,=V2k,T7m is the most probable thermal veloc-
ity of particles with temperature T and mass m (ky is
Boltzmann’s constant). While difficult to calculate a priori,
a reasonable upper limit on ve is given by the maximum
atomic velocity that can be stopped in a distance ds (typi-
cally the radius rb of a MOT laser beam) by the radiation
force, i.e., v.<VdikT'/m, where k=2z/A is the wave number
of the cooling light with wavelength 2, I’ is the decay rate
of the excited state, and fi is the reduced Planck constant.
The corresponding figure of merit for R is then (d,ikT'/


U.S. Patent Mar. 29,2022 Sheet 3 of 15 US 11,291,103 B2

Support
brackets

A

“+; Substrate
: for magnetic
field coils

Support
tubes

support.

Figure 3


US 11,291,103 B2

7

diffractor 212 and light source 260 and provides an axial
magnetic field directed along the light primary direction
248; and second permanent magnet 274.2 is interposed
between optical diffractor 212 and light source 260 and
provides a two-dimensional magnetic field gradient along
light primary direction 248. It is contemplated that first
permanent magnet 274.1 also can be interposed between
optical diffractor 212 and atom source 226 and can provide
an axial magnetic field directed along the light primary
direction 248.

Magnet mount 304 can be any mechanically rigid system
that mechanically mounts permanent magnets 274. In an
embodiment, with respect to FIG. 6, magnet mount 304 is a
3D-printed polylactic acid form that holds six ¥4"x!4x1 14"
magnets in a hexagonal configuration.

The voltage electrode can include a conductivity plate,
wire, tube or the like positioned either in free space or on a
substrate to produce an electric field that assists in trapping,
by exerting a force on primary atom 228 or by providing a
Stark shift in primary atom 228 that provide laser cooling
with slowing light 262 or trap light 240. Exemplary voltage
electrodes include four parallel copper tubes positioned
rectangularly in free space. Moreover, the electric field
produced by the voltage electrode can be constant in time or
oscillating. A field strength produced by the voltage elec-
trode can be from 0 V/cm to 1 kV/cm, and specifically from
10 V/cm to 500 V/cm.

With reference to FIG. 3, slower member 258, e.g.,
magnetic field coils 270, permanent magnet 274, or voltage

electrodes, can be mechanically supported by mounting 3

plate 278 disposed on plate mount 280 and spaced apart by
spacer 282. Mounting plate 278 can be a compatible sub-
strate capable of hold magnetic field coils 250, permanent
magnet 274 or voltage electrodes and can be aluminum

nitride, sapphire, or other metal substrate and can be any 3

shape. Moreover, mounting plates have sufficient thermal
stability and conduct away heat dissipated by elements
attached. In an embodiment, mounting plate 278 includes
circular aluminum nitride boards with a center cut-out for
primary light 236 to pass and mounting holes spaced along
its outer circumference. Plate mount 280 can include a
metallic or insulating material to mechanically attach and
space mounting plates 278. Exemplary plate mounts include
copper or aluminum flats with mounting holes. Moreover,
the thermal conductivity of plate mount 280 can be equal to
or greater than that of mounting plate 278 to provide
dissipation of heat. In an embodiment, plate mount 280
includes toroidal sections with square cross sections with
vertically passing through holes, allowing for mechanical
connection to mounting plate 278 using machine screws and
nuts. Spacer 282 can include a tube or rod with a cross
section for mechanically attaching and spacing mounting
plates 278. Exemplary spacers include copper tubes and
aluminum rods. Moreover, the thermal conductivity of
spacer 282 can be equal to or greater than that of mounting
plate 278 to assist with the dissipation of heat. In an
embodiment, spacer 282 includes copper tubes with outer
diameter 7.62 mm and inner diameter 4.5 mm and with
various lengths to allow appropriate spacing of mounting
plates 278.

In an embodiment, with reference to FIG. 4, uniaxial
counter-propagating monolaser atom trap 200 includes opti-
cal fiber 284 through which primary light 236 is communi-
cated. Optical manipulation of primary light 236 is accom-
plished by communicating primary light 236 through optical
fiber 284 and optical coupler 286 that forms divergent beam
288 for primary light 236 with subsequent communication

2

40

&

60

8

of primary light 236 through lens 290 and waveplate 292 to
form primary light 236 that is collimated or polarized-
selected.

Uniaxial counter-propagating monolaser atom trap 200
can include vacuum chamber 296 that includes viewport 294
to receive and communicate primary light 236 to trapping
region 244. vacuum chamber 296 can be in communication
with vacuum pump 298 via vacuum connection 300 to
achieve a selected pressure in vacuum chamber 296. As a
base pressure, the pressure in vacuum chamber 296 can be
from 10~'* torr to 10-7 torr, specifically from 107'* torr to
10-7 torr, and more specifically from 10-!? torr to 10-* torr
in an absence of primary atoms 228, slowed atoms 232, or
trapped atoms 234. It is contemplated that the pressure in

s vacuum chamber 296 can be from 10-'* torr to 10~ torr,

specifically from 107!° torr to 10-* torr in presence of
primary atoms 228, slowed atoms 232, or trapped atoms
234. Further, atom slower 210 and trapping region 244 can
be subject to differential pumping through atom transfer
aperture 220. It is contemplated that flow tube 252 is
disposed on slower surface 216 and opposing atom source
226. In this manner, flow tube 252 can receive slowed atoms
232 from atom slower 210 and communicates slowed atoms
232 from atom slower 210 to trapping region 244 through
atom transfer aperture 220. Flow tube 252 can include a
tube, aperture, pinhole, or an opening to constrict flow of gas
in a molecular flow regime between atom slower 210 and
trapping region 244. A length of flow tube 252 along light
primary direction 248 can be from infinitesimally small to
the length of atom slower 210. The opening of flow tube can
be from 10 um to 10 mm, specifically between 1 mm and 5
mm. Moreover, flow tube 252 can be constructed in such a
way to allow for mechanical mounting of optical diffractor
212, with reference to FIG. 6. In an embodiment, flow tube
252 includes an aluminum right cylinder of dimensions that
include 18.69 mm outer diameter and 28.15 mm long with
a 3 mm diameter through hole and mounting hardware to
mechanically secure optical diffractor 212.

Optical diffractor 212 can include a chip, plate, or wafer
that can be etched or formed to create a reflective diffraction
grating 222 and can be a silicon, glass, and the like.
Exemplary optical diffractors 212 include nanofabricated
silicon chips, individual gratings on glass substrates cut and
glued together. Moreover, optical diffractor 212 can contain
atom transfer wall 218 bounding the atom transfer aperture
220. A thickness relative to light primary direction 248 of
optical diffractor 212 can be from 100 um to 5 mm,
specifically from 400 um to 2 mm, and more specifically
from 450 ym to 550 pm. In an embodiment, optical diffractor
212 includes a nanofabricated silicon chip, wherein multiple
diffraction gratings 222 and atom transfer wall 218 are
formed by chemical etching of the silicon chip and subse-
quently finished by depositing metal. Chemical etching
could include plasma reactive ion etching, inductively

5 coupled reactive ion etching, wet etching, and the like.

Diffraction grating 222 can include a reflective periodic
structure to create one or more beams upon reflection of
primary light 236. Exemplary diffraction gratings 222
include ruled, linear gratings, holographic gratings, or grat
ings made from the periodic arrangement of more compli-
cated shapes. Moreover, diffraction grating 222 minimizes
zero-order or retro-reflection. The bounding region of dif-
fraction grating 222 on optical diffractor 212 can be a
selected, arbitrary shape. In an embodiment, diffraction

grating 222 can be bound by a circle of radius 11 mm. A ratio

of the spacing of periodic structures and the average wave-
length of primary light 226 can be from 1 to 50, specifically


US 11,291,103 B2

19
limit at B'=5.5 mT/em and B,,,,,=13 mT (see FIG. 13). With
this correction, the loading rate, evaluated numerically,
scales roughly as R«B,,..° in our region of experimental
interest.

‘A source that is misaligned with respect to the slowing
laser beam was considered. FIG. 14 shows several such
trajectories, which start at x=5 mm with various emission
angles. Simulations of these off-axis trajectories indicate
that atoms starting outside the slowing laser beam can still
be captured provided that they enter the Zeeman slower at a
position ze such that v,(z,)>Vo and subsequently clear the
aperture. We use these two conditions to calculate the
scaling of the loading rate for each B', shown in FIG. 13 as
the solid curves. The model suggests that the vast majority
of the flux is being emitted from the source approximately
2.5 mm outside of the slowing laser beam, a slight misalign-
ment.

FIG. 14 shows off-axis trajectories of atoms, wherein total
saturation parameter of all lasers is s,,,,/3 stream lines show
magnetic field lines, with a larger magnetic field magnitude
being darker. Certain trajectories are trapped trajectories
from a source placed behind (to the side of) the chip, starting
at 0.7¥,, (0.25 v,); other trajectories are untrapped. The width
of the trajectory curves indicates the magnitude of the
velocity.

The device can be modified by moving the source further
from the MOT while maintaining alignment with the slow-
ing laser beam. Consider a fixed magnetic field gradient B'
throughout all space and a movable source with position z,.

The capture velocity for atoms traveling along the Z axis is 3

v.=v'z,. As the source moves away from the MOT, the
capture velocity increases because v,.~z,, but 6. decreases as
tan 6,=1/(z,-2,) for small v. and as tan 0,=1,v'/[volog(z,/
2,)| for velocities vysv'z,. To understand the competition

between ve and 6c, we numerically evaluate Eq. (2) as a 3

function of z,. We find that R is roughly constant for z,/z,,<3
and becomes R2(z,/z,)°” for zJz,>10. Therefore, placing
the source farther behind the chip is optimal, provided that
optical alignment can be maintained, the inequality in Eq.
(3) is always satisfied, and the magnetic field gradient can be
extended to continue the Zeeman slower.

Loading from behind the chip can outperform loading
from the side, given that v, and 6, are roughly equivalent for
a source at z,=z, and a source placed to the side (see FIG.
9). However, outperforming side loading places additional
restrictions on the size of the apparatus (z/z,>3), beam
alignments, and source placement. As an example, a source
placed to the side might have performed equally well in the
device presented here. We simulated several side-loaded
trajectories, shown in green in FIG. 14, and found that the
side-loaded capture velocity is roughly 25% that of the best
on-axis capture velocity. The reduction in capture velocity is
compensated by the increase in @,, causing R to be
unchanged. Moving our source forward to the position of the
peak magnetic field (i.e., Z,=Zpo.) would be sufficient for
back loading to be faster than side loading.

The single-beam slowing and trapping apparatus for Li
atoms traps more than 10° atoms with loading rates exceed-
ing 10° s~!. The integrated Zeeman slower behind the chip
is effective in increasing the captured flux by over a factor
of 3. The source placement prevents unwanted metal depo-
sition on the grating and allows for future vacuum improve-
ments via differential pumping.

The design can easily be adapted to serve as a cold gas
source for a variety of applications. By implementing dif-
ferential pumping or using a low-outgassing atom source
(rather than a dispenser), the device can be used as a primary

S

2

40

20

vacuum gauge. The diffraction grating period and etch depth
can be altered to optimize trapping of other elements, such
as Rb, Cs, Ca, Sr, or Yb. The trapping of alkaline-earth
atoms using our apparatus would allow the development of
portable optical frequency standards, which could be used
for geodesy or space-based gravitational wave detection and
can be used for redefinition of the SI second. A multiple-
length Z-wire magnetic trap could be patterned onto the
back of our grating chip, permitting atoms to be pulled
closer to the chip surface for chip-scale atom interferometers
or quantum memories. The tetrahedral MOT configuration
can provide “type-II” MOTs, which are used to laser cool
and trap molecules. The device can trap molecules from a
buffer-gas beam source for a deployable device using laser-
cooled molecules.

The dispenser can mode match the slowing laser beam
and be placed close to the maximum of the magnetic field
The Zeeman slower can be shortened by increasing the
magnetic field gradient. Differential pumping decreases loss
rate t and increases an equilibrium number of atoms in the
MOT.

While one or more embodiments have been shown and
described, modifications and substitutions may be made
thereto without departing from the spirit and scope of the
invention. Accordingly, it is to be understood that the present
invention has been described by way of illustrations and not
limitation. Embodiments herein can be used independently
or can be combined.

All ranges disclosed herein are inclusive of the endpoints,
and the endpoints are independently combinable with each
other. The ranges are continuous and thus contain every
value and subset thereof in the range. Unless otherwise
stated or contextually inapplicable, all percentages, when
expressing a quantity, are weight percentages. The
suffix “(s)” as used herein is intended to include both the
singular and the plural of the term that it modifies, thereby
including at least one of that term (e.g., the colorant(s)
includes at least one colorants). “Optional” or “optionally”
means that the subsequently described event or circumstance
can or cannot occur, and that the description includes
instances where the event occurs and instances where it does
not. As used herein, “combination” is inclusive of blends,
mixtures, alloys, reaction products, and the like.

As used herein, “a combination thereof” refers to a
combination comprising at least one of the named constitu-
ents, components, compounds, or elements, optionally
together with one or more of the same class of constituents,
components, compounds, or elements.

All references are incorporated herein by reference.

The use of the terms “a” and “an” and “the” and similar
referents in the context of describing the invention (espe-
cially in the context of the following claims) are to be
construed to cover both the singular and the plural, unless
otherwise indicated herein or clearly contradicted by con-
text. “Or” means “and/or.” It should further be noted that the
terms “first.” “second,” “primary,” “secondary,” and the like
herein do not denote any order, quantity, or importance, but
rather are used to distinguish one element from another. The
modifier “about” used in connection with a quantity is
inclusive of the stated value and has the meaning dictated by
the context (e.g., it includes the degree of error associated
with measurement of the particular quantity). The conjunc-
tion “or” is used to link objects of a list or alternatives and
is not disjunctive; rather the elements can be used separately
or can be combined together under appropriate circum-
stances.


US 11,291,103 B2

11

includes a laser beam with two frequency components with
frequencies 12 MHz red-detuned from resonance with the
2S o(F=2) to 2P,,9(F'=3) cycling transition and the 2S,,>
(F=1) to 2P5,.(F"=2) repump transition. Both components
are circularly polarized and have an intensity equal to twice
that of the saturation intensity of the transition.

Light source 260 produces primary light 236 and can
include lasers, fibers, white-light sources, and other com-
patible components that produce primary light 236 with
frequencies, polarizations, and powers. Exemplary light
sources 260 include diode lasers. Moreover, depending on
application, the light source can be made of combinations of
lasers and other devices such as acousto-optic modulators,
electro-optic modulators, and the like. In an embodiment,
light source 260 includes 671 nm diode lasers and Ti:
Sapphire lasers with acousto-optic modulators and spectros-
copy cells to produce primary light 262 and its necessary
frequency components. In an embodiment, with reference to
FIG. 8, light source 260 produces a first primary light 236.1
and second primary light 236.2 that are combined into
primary light 236, wherein second primary light 236.2
includes a frequency that is chirped for slowing primary
atoms 228. Here, first primary light 236.1 and second
primary light 236.2 are combined by beam combiner 306.

Further, vacuum pump 298 sustains the base vacuum
levels described above. Exemplar vacuum pumps include
turbomolecular pumps, ion pumps, Ti:sublimation pumps,
or non-evaporable getter pumps. In an embodiment, with

respect to FIG. 6, vacuum pump 298 connected to the atom 3

slower is a 400 L/s non-evaporable getter pump.

Uniaxial counter-propagating monolaser atom trap 200
can be made in various ways. In an embodiment, a process
for making uniaxial counter-propagating monolaser atom

trap 200 includes: forming optical diffractor 212; disposing 3

optical diffractor 212 in vacuum chamber 296; disposing
atom source 226 on vacuum chamber 296; and aligning light
source 260 so that primary light 236 propagates along light
primary direction 248 such that light primary direction 248
is normal to optical diffractor 212.

In an embodiment, a process for making optical diffractor
212 includes providing a substrate, e.g., a silicon wafer;
forming a photomask of a pattern for diffraction grating 222
with direct laser writing or electron beam lithography; spin
coating and baking a photoresist on the substrate; exposing
the substrate to light through the photomask to cross-link a
resist in specific positions provided by photomask locations;
developing the resist; transferring the photoresist pattern
onto the substrate via reactive ion plasma etching; dissolving
the photoresist; forming atom transfer aperture 220 atomic
aperture by lithography followed by deep silicon reactive
etch; and optionally sputtering a thin layer of metal, e.g.,
aluminum on the substrate to form optical diffractor 212.
Optical diffractor 212 can include that has greater than
10,000 etched triangles spaced approximately 1 micrometer
(um) apart with 0.5 um width and a triangular atom transfer
aperture 220 centrally disposed on slower surface 216. The
etch depth of the grating can be, e.g., about 168 nm to reduce
zero-order reflection. It is contemplated that the metal coat-
ing can be, e.g., 100 nm thick.

The process for making uniaxial counter-propagating
monolaser atom trap 200 also can include disposing flow
tube 252 and separating vacuum chamber 296 into separate
regions connected through flow tube 252, disposing a
vacuum connection 300 and vacuum pump 298 onto both
vacuum regions, and establishing independent vacuum
pumping in atom slower 210 and trapping region 244.

S

2

60

12

Uniaxial counter-propagating monolaser atom trap 200
has numerous advantageous and unexpected benefits and
uses. In an embodiment, a process for cooling and trapping
atoms with the uniaxial counter-propagating monolaser
atom trap 200 includes: providing primary atoms 228 from
atom source 226, such that primary atoms 228 move in atom
primary direction 246; producing, by light source 260,
primary light 236, primary light 236 propagating in light
primary direction 248, light primary direction 248 opposing
atom primary direction 246; counter-propagating primary
light 236 relative to primary atoms 228; receiving, by atom
slower 210, primary atoms 228 from atom source 226;
communicating primary light 236 to atom slower 210 from
trapping region 244; receiving, by atom slower 210, primary

5. light 236 as slowing light 262; subjecting primary atoms 228

to slowing light 262; slowing primary atoms 228 by slowing
light 262; forming slowed atoms 232 from primary atoms
228 in response to interaction of primary atoms 228 with
slowing light 262, slowed atoms 232 moving in atom
primary direction 246; communicating, by atom transfer
aperture 220, slowed atoms 232 to trapping region 244 from
atom slower 210 receiving, by first diffraction grating 222.1,
primary light 236 from light source 260; producing, by first
diffraction grating 222.1, first reflected light 238.1 from

s primary light 236, first reflected light 238.1 moving in first

light reflection direction 250.1; receiving, by second diffrac-
tion grating 222.2, primary light 236 from light source 260;
producing, by second diffraction grating 222.2, second
reflected light 238.2 from primary light 236, second
reflected light 238.2 moving in second light reflection direc-
tion 250.2; receiving, by third diffraction grating 222.3,
primary light 236 from light source 260; producing, by third
diffraction grating 222.3, third reflected light 238.3 from
primary light 236, third reflected light 238.3 moving in third
light reflection direction 250.3; receiving, by trapping region
244, first reflected light 238.1, second reflected light 238.2,
and third reflected light 238.3; intersecting first reflected
light 238.1, second reflected light 238.2, and third reflected
light 238.3 in reflected light intersection volume 224 in
trapping region 244; forming trap light 240 from first
reflected light 238.1, second reflected light 238.2, the third
reflected light 238.3: receiving slowed atoms 232 in trap
light 240; and subjecting slowed atoms 232 to trap light 240
to produce trapped atoms 234 from slowed atoms 232

In an embodiment, the process can include producing
slower field 256, wherein trapping field 254 is in commu-
nication with Zeeman atom slower 210. A magnetic field
gradient of trapping field 254 extends into atom slower 210
by magnetic field coils 270. Zeeman atom slower 210
includes slower field 256 that is a magnetic field that scales
as a square root of position to maximize efficiency in
slowing primary atoms 228 and production of slowed atoms
232, wherein a magnetic field profile is selectively tailored
to change smoothly from a linear magnetic field to a

5. square-root magnetic field. According to an embodiment, the

magnetic field is produced, e.g.. in-vacuum by copper coils
directly bonded to aluminum-nitride substrates.

Uniaxial counter-propagating monolaser atom trap 200
and processes disclosed herein have numerous beneficial
uses, including measurement of vacuum pressure, inertial
sensing, frequency or wavelength standards, clocks, quan-
tum information transmission, quantum-enhanced sensing,
and the like. Advantageously, uniaxial counter-propagating
monolaser atom trap 200 overcomes limitations of technical

3 deficiencies of conventional articles such as standard six

beam atom traps, which occupy large volumes, involve more
laser power, and are more sensitive to misalignments of laser


US 11,291,103 B2

1
UNIAXIAL COUNTER-PROPAGATING
MONOLASER ATOM TRAP

CROSS REFERENCE TO RELATED
APPLICATIONS

The application claims priority to U.S. Provisional Patent
Application Ser. No. 62/744,385 filed Oct. 11, 2018, the
disclosure of which is incorporated herein by reference in its
entirety.

STATEMENT REGARDING FEDERALLY
SPONSORED RESEARCH

This invention was made with United States Government
support from the National Institute of Standards and Tech-
nology (NIST), an agency of the United States Department
of Commerce. The Government has certain rights in the
invention. Licensing inquiries may be directed to the Tech-
nology Partnerships Office, NIST, Gaithersburg, Md.,
20899; voice (301) 301-975-2573; email tpo@nist.gov; ref-
erence NIST Docket Number 18-050US1

BRIEF DESCRIPTION

Disclosed is a uniaxial counter-propagating monolaser
atom trap for cooling and trapping atoms with a single a
laser beam, the uniaxial counter-propagating monolaser
atom trap comprising: an atom source that provides primary

atoms, such that the primary atoms move in an atom primary 3

direction; a light source opposing the atom source and that
produces primary light, the primary light propagating in a
light primary direction, the light primary direction opposing
the atom primary direction such that the primary light

counter-propagates relative to the primary atoms; an atom 3

slower interposed between the atom source and the light
source and that: receives the primary atoms from the atom
source; receives the primary light as slowing light; subjects
the primary atoms to the slowing light; and slows the
primary atoms to form slowed atoms from the primary
atoms in response to interaction of the primary atoms with
the slowing light, the slowed atoms moving in the atom
primary direction; an optical diffractor interposed between
the atom slower and the light source and comprising: a
diffraction surface opposing the light source; a slower sur-
face opposing the atom source; an atom transfer wall that
bounds an atom transfer aperture: the atom transfer aperture
that communicates the slowed atoms to a trapping region
from the atom slower and communicates the primary light to
the atom slower from the trapping region; a plurality of
diffraction gratings disposed on the diffraction surface and
comprising: a first diffraction grating that receives the pri-
mary light from the light source and produces first reflected
light from the primary light, the first reflected light moving
in a first light reflection direction; a second diffraction
grating that receives the primary light from the light source
and produces second reflected light from the primary light,
the second reflected light moving in a second light reflection
direction; and a third diffraction grating that receives the
primary light from the light source and produces third
reflected light from the primary light, the third reflected light
moving in a third light reflection direction; the trapping
region interposed between the optical diffractor and the light
source and that: receives the first reflected light, the second
reflected light, and the third reflected light such that the first
reflected light, the second reflected light, and the third
reflected light intersect in a reflected light intersection

40

&

2

volume in the trapping region to form trap light from the first
reflected light, the second reflected light, and the third
reflected light; receives the slowed atoms in the trap light;
and produces trapped atoms from the slowed atoms in
response to subjecting the slowed atoms to the trap light

Disclosed is an optical diffractor for cooling and trapping
atoms with a single a laser beam, the optical diffractor
comprising: a diffraction surface; a slower surface ona side
of the optical diffractor opposite the diffraction surface; an
atom transfer wall that bounds an atom transfer aperture; the
atom transfer aperture that communicates slowed atoms to a
trapping region from an atom slower and communicates
primary light to the atom slower from the trapping region; a
plurality of diffraction gratings disposed on the diffraction
surface and comprising: a first diffraction grating that
receives the primary light from a light source and produces
first reflected light from the primary light, the first reflected
light moving in a first light reflection direction; a second
diffraction grating that receives the primary light from the
light source and produces second reflected light from the
primary light, the second reflected light moving in a second
light reflection direction; and a third diffraction grating that
receives the primary light from the light source and produces
third reflected light from the primary light, the third reflected
light moving in a third light reflection direction, wherein the
diffraction gratings reflects the primary light as the first
reflected light, the second reflected light, and the third
reflected light respectively along the first light reflection
direction, the second light reflection direction, and the third
light reflection direction into the trapping region so that the
first reflected light, the second reflected light, and the third
reflected light intersect in a reflected light intersection
volume in the trapping region and form trap light that traps
the slowed atoms to form trapped atoms from the slowed
atoms.

Disclosed is a process for cooling and trapping atoms with
the uniaxial counter-propagating monolaser atom trap, the
process comprising: providing primary atoms from the atom
source, such that the primary atoms move in the atom
primary direction; producing, by the light source, primary
light, the primary light propagating in the light primary
direction, the light primary direction opposing the atom
primary direction; counter-propagating the primary light
relative to the primary atoms; receiving, by the atom slower,
the primary atoms from the atom source; communicating the
primary light to the atom slower from the trapping region;
receiving, by the atom slower, the primary light as slowing
light; subjecting the primary atoms to the slowing light;
slowing the primary atoms by the slowing light; forming the
slowed atoms from the primary atoms in response to inter-
action of the primary atoms with the slowing light, the
slowed atoms moving in the atom primary direction; com-
municating, by the atom transfer aperture, the slowed atoms
to the trapping region from the atom slower receiving, by the

5 first diffraction grating, the primary light from the light

source; producing, by the first diffraction grating, the first
reflected light from the primary light, the first reflected light
moving in a first light reflection direction: receiving, by the
second diffraction grating, the primary light from the light
source; producing, by the second diffraction grating, the
second reflected light from the primary light, the second
reflected light moving in a second light reflection direction;
receiving, by the third diffraction grating, the primary light
from the light source; producing, by the third diffraction

5 grating, the third reflected light from the primary light, the

third reflected light moving in a third light reflection direc-
tion; receiving, by the trapping region, the first reflected


U.S. Patent Mar. 29,2022 Sheet 8 of 15 US 11,291,103 B2

292

292-——

38 TM

S

288
SY 270
[en
238
212 ~ 1
(el GH
270
+ 262
226

Figure 8


U.S. Patent Mar. 29,2022 Sheet 5 of 15 US 11,291,103 B2

Ue 38

2381
21d :

of Ika Poo Y
i, Fr pl 274 id 274

ph 300

302 (:/)

274

Figure 5


U.S. Patent Mar. 29,2022 Sheet 4 of 15 US 11,291,103 B2

290

———
I J 296
[t <I It

238
a tT 270
238+
Lp 270)
ion i
238+
. fb 294
212,14 1 =
ao Coo
|; 270
of 7 270
} LI
296 p> 300

Figure 4


US 11,291,103 B2

3

light, the second reflected light, and the third reflected light;
intersecting the first reflected light, the second reflected
light, and the third reflected light in a reflected light inter-
section volume in the trapping region; forming trap light
from the first reflected light, the second reflected light, and
the third reflected light; receiving the slowed atoms in the
trap light; and subjecting the slowed atoms to the trap light
to produce trapped atoms from the slowed atoms.

BRIEF DESCRIPTION OF THE DRAWINGS

‘The following description should not be considered lim-
iting in any way. With reference to the accompanying
drawings, like elements are numbered alike.

FIG. 1 shows a uniaxial counter-propagating monolaser
atom trap;

FIG. 2 shows a uniaxial counter-propagating monolaser
atom trap;

FIG. 3 shows a uniaxial counter-propagating monolaser
atom trap;

FIG. 4 shows a uniaxial counter-propagating monolaser
atom trap;

FIG. 5 shows a uniaxial counter-propagating monolaser
atom trap;

FIG. 6 shows a uniaxial counter-propagating monolaser
atom trap;

FIG. 7 shows a uniaxial counter-propagating monolaser
atom trap;

FIG. 8 shows a uniaxial counter-propagating monolaser
atom trap;

FIG. 9 shows a uniaxial counter-propagating monolaser
atom trap;

FIG. 10 shows a uniaxial counter-propagating monolaser
atom trap in panel A, an optical diffractor in panel B, a

cross-section through the optical diffractor in panel C, anda 3

diffraction surface of the optical diffractor;

FIG. 11 shows a absorption images in panel A, a graph of
squared radii versus squared time in panel B, and a graph of
laser tuning versus intensity for steady-state atom numbers
in panel C;

FIG. 12 shows a graph of velocity versus position;

FIG. 13 shows a graph of frequency versus magnetic field
strength;

FIG. 14 shows a graph of lateral position versus axial
position for trajectories of atoms; and

FIG. 15 shows exemplary shapes and patterns of elements
in diffraction gratings.

DETAILED DESCRIPTION

A detailed description of one or more embodiments is
presented herein by way of exemplification and not limita-
tion.

It has been discovered that uniaxial counter-propagating
monolaser atom trap 200 and processes herein provide
slowing, cooling, and trapping atoms with a single laser
beam. Atoms are slowed by a slower and trapped in the
intersection of optical beams produced by an optical dif-
fractor. In an embodiment, with reference to FIG. 1, FIG. 2,
FIG. 3, FIG. 4, FIG. 5, FIG. 6, FIG. 7, FIG. 8, and FIG. 9,
uniaxial counter-propagating monolaser atom trap 200
includes: atom source 226 that provides primary atoms 228,
such that primary atoms 228 move in atom primary direction
246; light source 260 opposing atom source 226 and that
produces primary light 236, primary light 236 propagating
in light primary direction 248, light primary direction 248
opposing atom primary direction 246 such that primary light

20

45

50

4

236 counter-propagates relative to primary atoms 228; atom
slower 210 interposed between atom source 226 and light
source 260 and that: receives primary atoms 228 from atom
source 226; receives primary light 236 as slowing light 262;
subjects primary atoms 228 to slowing light 262; and slows
primary atoms 228 to form slowed atoms 232 from primary
atoms 228 in response to interaction of primary atoms 228
with slowing light 262, slowed atoms 232 moving in atom
primary direction 246; optical diffractor 212 interposed
between atom slower 210 and light source 260 and includ-
ing: diffraction surface 214 opposing light source 260;
slower surface 216 opposing atom source 226; atom transfer
wall 218 that bounds atom transfer aperture 220; atom
transfer aperture 220 that communicates slowed atoms 232
to trapping region 244 from atom slower 210 and commu-
nicates primary light 236 to atom slower 210 from trapping
region 244; a plurality of diffraction gratings 222 disposed
on diffraction surface 214 and including: first diffraction
grating 222.1 that receives primary light 236 from light
source 260 and produces first reflected light 238.1 from
primary light 236, first reflected light 238.1 moving in first
light reflection direction 250.1; second diffraction grating
222.2 that receives primary light 236 from light source 260
and produces second reflected light 238.2 from primary light
236, second reflected light 238.2 moving in second light
reflection direction 250.2; and third diffraction grating 222.3
that receives primary light 236 from light source 260 and
produces third reflected light 238.3 from primary light 236,
third reflected light 238.3 moving in third light reflection
direction 250.3; trapping region 244 interposed between
optical diffractor 212 and light source 260 and that: receives
first reflected light 238.1, second reflected light 238.2, and
third reflected light 238.3 such that first reflected light 238.1,
second reflected light 238.2, and third reflected light 238.3
intersect in reflected light intersection volume 224 in trap-
ping region 244 to form trap light 240 from first reflected
light 238.1, second reflected light 238.2, and third reflected
light 238.3; receives slowed atoms 232 in trap light 240; and
produces trapped atoms 234 from slowed atoms 232 in
response to subjecting slowed atoms 232 to trap light 240.

Atom source 226 produces primary atoms 228. It is
contemplated that atom source 226 can include an oven,
heater, and the like to produce a vapor or increase a vapor
pressure of a selected atom, atomic ion, molecule, or
molecular ion. It should be appreciated that the phrase
“primary atom” includes the atom, atomic ion, molecule,
molecular ion, or combination thereof produced by atom
source 226. Atom source 226 can include a slit, nozzle, tube,
and the like to direct flow of the atom, atomic ion, molecule
or molecular ion. Moreover, the total flux of primary atoms
228 or other species can be less than an amount of flux such
that scattering of primary atoms 228 or other species causes
scattering of trapped atoms 234 that does not exceed the rate

5 of conversion of primary atoms 228 into trapped atoms 234

by slowing primary atoms 228. Exemplary atom sources 226
include metallic ovens, getter dispensers, metal dispensers,
and ablation sources. In an embodiment, atom source 226
includes a titanium-encased alkali metal dispenser. With
reference to FIG. 5, uniaxial counter-propagating monolaser
atom trap 200 can include shutter 276 interposed between
atom source 226 and trapping region 224 to interrupt com-
munication of primary atoms 228 from atom source 226 to
trapping region 224. Rotational actuator 302 can be in

5 communication with shutter 276 to position shutter 276 in or

out of the beam of primary light 236 or to completely isolate
atom source 226 from trapping region 224.


U.S. Patent Mar. 29,2022 Sheet 7 of 15 US 11,291,103 B2

274
274 274
212 222
{e) oO
274 274
[+] a [>]
229 ——_f P-220
(e) \ Oo
222
274 274
274
Side view Top view

Figure 7


US 11,291,103 B2

15

2k,T)*, assuming the same source output flux. Lithium’s
figure of merit is among the worst of all laser-coolable
atoms, with its red cooling wavelength of 4,,~671 nm, its
linewidth of I’, ~2x6 MHz, and its typical source operating
temperature T=700 K.

Lithium’s poor figure of merit is worsened when loading
a grating MOT directly from a dispenser. For simplicity, the
dispenser could be placed to the side to avoid blocking laser
beams (see FIG. 9). This placement results in d,sV2r, for a
conventional six-beam MOT, but only d,sr,/2 for a grating
MOT. Moreover, a dispenser placed to the side of a grating
MOT will tend to deposit metal on the grating, gradually
reducing its performance.

‘Another MOT performance metric is steady-state atom
number N,=Rr, where 7 is the trap lifetime. To achieve the
same output flux, different elements require different source
temperatures, T. Higher-temperature sources outgas unde-
sired species at a rate that is exponential in T. These
undesired species can collide with trapped atoms, reducing
t

The device herein integrated a tetrahedral MOT configu-
ration with a Zeeman slower by etching an aperture in the
grating and loading the atoms from behind. Light passing
through the aperture in the chip can interact with the
counterpropagating atoms for a greater distance, increasing
ds (see FIG. 9). By tailoring the magnetic field behind the
chip, we make a Zeeman slower to capture atoms with
higher initial velocity. The aperture can also limit gas flow,
allowing for differential pumping that mitigates the effects
of dispenser outgassing.

Ananofabricated silicon diffraction grating chip forms the
core of the device, as shown in FIG. 2(a). The grating chip,
fabricated using photolithography at the National Institute of
Standards and Technology in the Center for Nanoscale

Science and Technology (CNST) NanoFab cleanroom facil- 3

ity, includes three one-dimensional diffraction gratings,
which are arranged so that their grooves form concentric
equilateral triangles [see FIG. 10(5) and (c)]. Each grating
has a period p=1.00(5)um and a 500(10) nm trench width
[see FIG. 10(d)]. The gratings are cropped by an outer circle
with a diameter of 22 mm. The diffraction gratings have a
first-order diffraction angle 642° at 2,,. The grating
trenches are etched to a depth of 168(2) nm (approximately
2/4). chosen to minimize zero-order reflections. A 100(5)
nm layer of aluminum is deposited on the chip surface via
sputtering. The thickness of the aluminum coating was
selected to yield, at 2.,,, the optimum first-order diffraction
efficiency of 33% for a triangular-grating MOT; we measure
37(1)%. Higher-order diffraction is suppressed because
p<2h,,. For normally incident, circularly polarized light, the
normalized Stokes parameters of the first-order diffracted
beam are Q=0.03(1), U=0.13(1), V=0.84(1). A triangular
aperture, defined by an inscribed circle of radius 1.5 mm,
allows both light and atoms to pass through the chip.

With regard to FIG. 10, cooling and trapping apparatus for
Li is shown, wherein a picture of the full device including
compensation coils, MOT coils, and Zeeman coils. The atom
dispenser is concealed by the Zeeman coils, but its approxi-
mate position is shown in FIG. 9. Panel shows the 27
mmx35 mm diffraction-grating chip. Panel (c) shows a
scanning-electron-microscope (SEM) image of the diffrac-
tion grating near a vertex of the triangular aperture. Panel (d)
shows an edge-on SEM image with critical dimensions.

Three sets of electromagnets produce magnetic fields [see
FIG. 10(a)]. Set (2) is an anti-Helmholtz pair that produces
the magnetic field gradient needed for the MOT. Set (3)
extends the range of the magnetic field beyond the chip and

S

20

2

40

&

16

adapts it into the square-root profile ofa Zeeman slower. The
antisymmetric set prevents the field from set (3) from
shifting the MOT axially. All sets were made from direct
bond copper on an aluminum-nitride substrate.

A Li dispenser included a stainless-steel tube filled with
15 mg of unenriched Li. The dispenser emits atoms through
a 5 mmx0.1 mm rectangular slit. Assuming an operating
temperature of 375° C., the dispenser can operate continu-
ously for approximately 200 days before exhausting its Li
supply. The trapping system can include a three-dimension-
ally printed titanium dispenser that can hold more than 100
mg of Li [40], allowing at least 500 days of continuous
operation.

The full 0.25-L assembly was constructed on a vacuum
flange and inserted into a vacuum chamber pumped by a 50
L/s ion pump. The vacuum chamber has a base pressure of
3(1)x10-* Pa. Outgassing from the Li source causes the
pressure to increase to approximately 10~° Pa

The single intensity-stabilized laser beam strikes the
grating normally. It has a 1/e? radius of 20(1) mm; an iris
stops the beam to fit the grating. The center frequency of the
laser is detuned relative to the 2S,,,(F=2) to 2P,,9(F'=3)
cycling transition, which has a saturation intensity of
Toae2.54 mW/cm?. An electro-optic modulator adds side-
bands at approximately 813 MHz; the +1 sideband is equally
detuned from the 28,(F=1) to 2P,,(F*=2) repump transi-
tion. Because the MOT magnetic field gradient continuously
deforms into the magnetic field of the Zeeman slower, an
additional slowing laser would not improve atom capture.
The intensities 1 reported herein are the carrier intensity at
the center of the incident beam. Fluorescence from the MOT
is continuously monitored by a camera along an axis
orthogonal to the cooling beam. The same camera also
records absorption images to more accurately measure the
number of trapped atoms.

FIG. 11(a) shows images of the cloud of 7Li atoms
trapped in the MOT after various expansion times t. The
diffraction grating was not visible in the images, as the MOT
formed approximately 4 mm from the chip. The fitted 1/e
radii of the cloud, shown in FIG. 11(5), followed w?(t)}=wo?+
(2ksT orm), where Tyo, is the temperature of the
trapped cloud and wo is the initial radius. The measured
temperatures are 900(50) jK in the radial direction and

5 590(30) LK in the axial direction. For the data in FIG. 11(a)

and (6), the laser detuning is A/T,,=-2.0, the saturation
parameter is s,=I/l,,,-3.6. the carrier-to-repump power ratio
is about 3:2, the magnetic field gradient at the center of the
MOT is B'=4.5 mT/cm, and the peak magnetic field of the
Zeeman slower is B,,.~12 mT. These trapping parameters
and the extracted temperatures are similar to those of
“compressed” Li MOTs.

With reference to FIG. 11, panel (a) shows absorption
images of optical density (OD) of the Li cloud at three

‘5. different expansion times t. Panel (b) shows fitted x and z

squared I/e radii w,...? of the cloud versus ? (most error
bars are smaller than the data points). Panel (c) steady-state
atom number N, versus the laser detuning and intensity, in
units of I’, and I,,,. respectively. Here, panel (c) provides
equilibrium atom number NS in the MOT as a function of
the detuning and intensity of the laser beam. The magnetic
field gradient, the peak field of the Zeeman slower, and the
carrier-to-repump ratio are the same as in FIG. 11(a) and (6).
The captured atom number increases with the laser intensity

5 and begins to saturate at I/I,, 2.5. We find that the maxi-

mum atom number occurs near a detuning of A/T,=-2.5.
Varying the carrier-to-repump power ratio between 1:1 and


a2 United States Patent

US011291103B2

(10) Patent No.: US 11,291,103 B2

Eckel et al. (45) Date of Patent: Mar. 29, 2022
(54) UNIAXIAL COUNTER-PROPAGATING (52) U.S. Ch
MONOLASER ATOM TRAP CPC veesssecse HOSH 3/02 (2013.01); HOLT 37/075
(71) Apeticas: Goverment ofthe Uli Sats of (2013.01; ond 3708 2013.01, 028 272
America, as represented by the 4
Secretary of Commerce, Gaithersburg, (58) _ Field of Classification Seareh
MD (US) None
See application file for complete search history.
(72) Inventors: Stephen Paul Eckel, Rockville, MD
(US); Daniel Schaeder Barker, (56) References Cited
Berwyn Heights, MD (US); James
Anthony Fedchak, Washington, DC U.S. PATENT DOCUMENTS
(US); Julia Kay Schersehligt,
Montgomery Village, MD Ss Erie S710428 BL A214 Loftus et al
Burton Norrgard, Silver Spring, MD ee NS
(US); Nikolai Nikolaevich Klimov, (Continued)
Ellicott City, MD (US)
OTHER PUBLICATIONS
(73) Assignee: GOVERNMENT OF THE UNITED
STATES OF AMERICA, AS Nshii, C.C., et al., “A surfaced-patterned chip as a strong source of
REPRESENTED BY THE ultracold atoms for quantum technologies”, Nature Nanotechnol-
SECRETARY OF COMMERCE, ogy, 2013, p. 321-324, vol. 8.
Gaithersburg, MD (US) (Continued)
*) Notice: — Subject to any disclaimer, the term of this 7 +
o patent is extended of adjusted under 35. Primary Examiner — James Choi ae
U.S.C. 154(b) by 103 days. (74) Attorney, Agent, or Firm — Office of Chief Counsel
for National Institute of Standards and Technology
(21) Appl. No.: 16/598,144
(57) ABSTRACT
(22) Filed: Oct. 10, 2019 A uniaxial counter-propagating monolaser atom trap cools
+ eae and traps atoms with a single a laser beam and includes: an
(65) Prior Publication Data atom slower that slows atoms to form slowed atoms; an
US 2020/0120785 Al Apr. 16, 2020 optical diffractor including: a first diffraction grating that
receives primary light and produces first reflected light; a
Related U.S. Application Data second diffraction grating that receives primary light and
(60) Provisional application No. 62/744,385, filed on Oct. produces second reflected light; and a third diffraction
11, 2018. grating that receives the primary light and produces third
reflected light; and a trapping region that forms trap light
(51) Int. Ch from the reflected lights and receives slowed atoms to
HOSH 3/02 (2006.01) produce trapped atoms from the slowed atoms that interact
HOLI 37/075 (2006.01) with the trap light.
HOLJ 37/08 (2006.01)
G02B 27/42 (2006.01) 18 Claims, 15 Drawing Sheets
S50
\
210

soon


U.S. Patent Mar. 29,2022 Sheet 10 of 15 US 11,291,103 B2

Figure 10


U.S. Patent Mar. 29,2022 Sheet 9 of 15 US 11,291,103 B2

236

Dispenser

Figure 9


US 11,291,103 B2

Sheet 6 of 15

Mar. 29, 2022

U.S. Patent

9g amnsty



US 11,291,103 B2

9

from 1.001 to 10, and more specifically from 1.01 to 2, the
latter resulting in diffraction angles from 80° to 45°. A
diffraction efficiency can be engineered by choosing a
reflective material to provide a correct amount of power in
reflected light 238 after reflection of primary light 236. The
diffraction efficiency can be unbalanced between positive
and negative orders by using a blazed or otherwise asym-
metric grating. In an embodiment, diffraction grating 222
includes an 100 nm aluminum-coated, linear grating with
square-wave cross section with period 1000 nm, 50% duty
cycle, and depth 168 nm, resulting in diffraction angles of 42
degrees, no second order diffraction, and minimum zero
order diffraction with average wavelength 671 nm primary
light 236.

With reference to FIG. 9 and FIG. 10, first diffraction
grating 222.1 can include a first set of linear grating lines
268.1; the second diffraction grating 222.2 comprises a
second set of linear grating lines 268.2; and the third
diffraction grating 222.3 comprises a third set of linear
grating lines 268.3. According to an embodiment, the first
set of linear grating lines 268.1, the second set of linear
grating lines 268.2, and the third set of linear grating lines
268.3 are arranged on diffraction surface 214 in three
truncated triangles, wherein atom transfer aperture 220 is
centrally disposed among the three truncated triangles. In an
embodiment, with reference to FIG. 7, optical diffractor 212
further includes fourth diffraction grating 222.4 that receives
primary light 236 from light source 260 and produces fourth
reflected light 238.4 from primary light 236, fourth reflected

light 238.4 moving in fourth light reflection direction 250.4, 3

and has a rectangle or square shape.

With reference to FIG. 15, diffraction gratings of two-
dimensional periodic structures can be used as diffraction
gratings 222. In an embodiment with respect to FIG. 15(A)

and FIG. 15(B), four beams are made from the single 3

diffraction grating. In an embodiment with respect to FIG.
15(C) and FIG. 15(D), six beams are made. Here, the
diffraction grating is made by forming (e.g., by etching)
periodic patterns of certain shapes (e.g., polygons, squares
(panel A), circles (panel B), triangles (panel C), circles
(panel D), and the like) in selected regions of a substrate
FIG. 15 shows such diffraction gratings, wherein black
regions are etched regions of the substrate; white space is
exposed substrate; and dashed lines are for reference to
show periodocity.

Reflected light 238 is derived from primary light 236
reflected by diffraction grating 222 and can include polar-
ization rotations, intensity changes and beam shaping
required by trap light 240. Moreover, reflected light 238 has
the same wavelength spectrum as primary light 236 and can
include a wavelength spectrum of trap light 240. The force
at zero magnetic or electric field and for a trapped atom 234
with zero velocity exerted by all reflected lights 238 and in
the direction of light primary direction 248 balances an
opposing force exerted by primary light 236 over the entire
trapping region 244. This condition is met if Njn=1, where
N, is the number of reflected light beams and y is the
diffraction efficiency of diffraction grating 222, and assum-
ing a flat-top input beam profile for primary light 236. The
product of N,n of reflected light 238 in the trapping region
244 can be from 0.5 to 1.5, specifically from 0.75 to 1.25. In
an embodiment, reflected light 238 includes spectral com-
ponents of primary light 236, with opposite circular polar-
ization, and an intensity specified by a diffraction efficiency
of 9=0.38, with N,=3.

Reflected light intersection volume 224 includes the vol-
ume formed by the intersection of all reflected beams 238

S

2

40

45

g

6:

10

whose directions, in the plane orthogonal to the axis defined
by light primary direction 248, oppose one another. A
volume of reflected light intersection volume 224 can be
from 10 to 10° mm*, specifically from 100 to 5000 mm’,
and more specifically from 1000 to 2000 mm*. Moreover,
the volume is dependent on the number of reflected light
beams and their specific geometry.

Trapping region 244 is disposed in reflected light inter-
section volume 224. Trapping region 244 also can include
magneto-optical trap 264. Magneto-optical trap 264 uses a
spherical quadrupole trapping field 254 in combination with
circularly-polarized trap light 240 which together form a
trap for the trapped atoms 234.

Trap light 240 is formed in reflected light intersection
volume 224 and includes reflected beams 238 within the
intersection region whose directions 250 oppose one another
along with primary light 236. Together, the beams exert
forces on the atoms along the three spatial dimensions
Moreover, the trap light has the appropriate wavelength or
frequency and polarization for the type of trap being created.
In an embodiment, with respect to FIG. 2, FIG. 3, FIG. 4,
FIG. 5, FIG. 6, trap light 240 is light whose frequency is
slightly smaller than that of the internal transition of the

5 ttapped atoms 234 and are circularly polarized.

Trapped atoms 234 can include the subset of primary
atoms from the atom source that have been decelerated,
traversed the atom transfer aperture 220, and trapped in the
trap light 240. A number of trapped atoms 234 can be from
1 to 10", specifically from 10* to 10°, and more specifically
from 10° to 10°. A velocity distribution of trapped atoms 234
can be thermal, with the ultimate temperature is limited by
the properties of the trapping field 254 and trap light 240. A
temperature of trapped atoms 234 can be from 1 1K to 100
mK, specifically from 10 1K to 10 mK. In an embodiment,
trapped atoms 234 includes laser-cooled atoms held in a
magneto-optical trap at temperatures of the order of 100 1K.

‘Trapping field 254 can include any magnetic field, that in
conjunction with or independently of trapping light 240 is
capable of trapping the atoms. Exemplary trapping fields
254 that work in conjunction with trapping light include
spherical quadrupole fields where

where z is the axial position from the center of the trap, and
x and y are the orthogonal in-plane positions, and B' is the
magnetic field gradient. A field gradient B' of a spherical
quadrupole trapping field 254 can be from 5 G/em to 500
Gicm, specifically from 10 G/em to 50 G/em, and more
specifically from 15 G/em to 45 G/cm. Exemplary trapping
field 254 that work independently of trapping light include

5 magnetic bottle trap fields given by B=B'(xx-yy)+(Bo+

B,z7/2). Moreover, the fields generated may vary in time
and switch between those that work in conjunction and
independently with trapping light 240. In an embodiment,
with reference to FIG. 2, FIG. 3, FIG. 4, FIG. 5, and FIG.
6, trapping field 254 includes a spherical quadrupole trap
with B'=45 G/cm. In an embodiment with respect to FIG. 7,
trapping field 254 includes a magnetic bottle trap with
B,=50 G, B'=100 Gem, and B,=100 G/em?.

Primary light 236 is formed in light source 260 and
includes frequency components, powers, and polarizations
of trap light 240 and slowing light 262. In an embodiment
using lithium atoms as primary atom 228, primary light 236


US 11,291,103 B2

21

What is claimed is:

1. A uniaxial counter-propagating monolaser atom trap for

cooling and trapping atoms with a single a laser beam, the
uniaxial counter-propagating monolaser atom trap compris-
ing:

an atom source that provides primary atoms, such that the
primary atoms move in an atom primary direction;

a light source opposing the atom source and that produces
primary light, the primary light propagating in a light
primary direction, the light primary direction opposing
the atom primary direction such that the primary light
counter-propagates relative to the primary atoms;

an atom slower interposed between the atom source and
the light source and that:
receives the primary atoms from the atom source;
receives the primary light as slowing light;
subjects the primary atoms to the slowing light; and
slows the primary atoms to form slowed atoms from the

primary atoms in response to interaction of the
primary atoms with the slowing light, the slowed
atoms moving in the atom primary direction;

an optical diffractor interposed between the atom slower
and the light source and comprising:

a diffraction surface opposing the light source:

a slower surface opposing the atom source;

an atom transfer wall that bounds an atom transfer
aperture:

the atom transfer aperture that communicates the

slowed atoms to a trapping region from the atom 3

slower and communicates the primary light to the
atom slower from the trapping region;

a plurality of diffraction gratings disposed on the dif-
fraction surface and comprising:

a first diffraction grating that receives the primary 3

light from the light source and produces first
reflected light from the primary light, the first
reflected light moving in a first light reflection
direction;

a second diffraction grating that receives the primary
light from the light source and produces second
reflected light from the primary light, the second
reflected light moving in a second light reflection
direction; and

a third diffraction grating that receives the primary
light from the light source and produces third
reflected light from the primary light, the third
reflected light moving in a third light reflection
direction;

the trapping region interposed between the optical dif-
fractor and the light source and that:
receives the first reflected light, the second reflected
light, and the third reflected light such that the first
reflected light, the second reflected light, and the
third reflected light intersect in a reflected light
intersection volume in the trapping region to form
trap light from the first reflected light, the second
reflected light, and the third reflected light;
receives the slowed atoms in the trap light; and
produces trapped atoms from the slowed atoms in
response to subjecting the slowed atoms to the trap
light.
2. The uniaxial counter-propagating monolaser atom trap
of claim 1, further comprising:
a flow tube disposed on the slower surface and opposing
the atom source and that receives the slowed atoms
from the atom slower and communicates the slowed

S

2

40

22

atoms from the atom slower to the trapping region
through the atom transfer aperture.

3. The uniaxial counter-propagating monolaser atom trap
of claim wherein the trapping region further comprises a
magneto-optical trap.

4. The uniaxial counter-propagating monolaser atom trap
of claim 1, wherein the atom slower comprises a Zeeman
slower.

5. The uniaxial counter-propagating monolaser atom trap
of claim 1, wherein the atom slower comprises a slower
member interposed between the atom source and the optical
diffractor.

6. The uniaxial counter-propagating monolaser atom trap
of claim 5, wherein the slower member comprises magnetic
field coils, a permanent magnet, a voltage electrode, or a
combination comprising at least one of the foregoing slower
members.

7. The uniaxial counter-propagating monolaser atom trap
of claim 6, wherein the slower member is the magnetic field
cons that produces a spherical magnetic quadrupole field.

8. The uniaxial counter-propagating monolaser atom trap
of claim 1, wherein the first diffraction grating comprises a
first set of linear grating lines; the second diffraction grating

5 comprises a second set of linear grating lines; and the third

diffraction grating comprises a third set of linear grating
lines.

9. The uniaxial counter-propagating monolaser atom trap
of claim 8, wherein the first set of linear grating lines, the
second set of linear grating lines, and the third set of linear
grating lines are arranged on the diffraction surface in three
truncated triangles, wherein the atom transfer aperture is
centrally disposed among the three truncated triangles

10. The uniaxial counter-propagating monolayer atom
trap of claim 1, further comprising a shutter interposed
between the atom source and the atom slower and that
interrupts communication of the primary atoms from the
atom source to the atom slower.

11. The uniaxial counter-propagating monolayer atom
trap of claim 1, further comprising a vacuum chamber in
which are disposed the atom slower, the optical diffractor,
and the trapping region.

12. The uniaxial counter-propagating monolaser atom
trap of claim 1, further comprising:

a first permanent magnet interposed between the optical
diffractor and the light source and that provides an axial
magnetic field directed along the light primary direc-
tion; and

a second permanent magnet interposed between the opti-
cal diffractor and the light source and that provides a
two-dimensional magnetic field gradient along the light
primary direction.

13. The uniaxial counter-propagating monolaser atom
trap of claim 12, wherein the optical diffractor further
comprises a fourth diffraction grating that receives the
primary light from the light source and produces fourth
reflected light from the primary light, the fourth reflected
light moving in a fourth light reflection direction.

14. The uniaxial counter-propagating monolaser atom
trap of claim 1, wherein the light source produces a first
primary light and a second primary light that are combined
in primary light,

wherein the second primary light comprises a frequency
that is chirped for slowing the primary atoms.

15. An optical diffractor for cooling and trapping atoms

with a single a laser beam, the optical diffractor comprising:

a diffraction surface;


U.S. Patent Mar. 29,2022 Sheet 2 of 15 US 11,291,103 B2

200
236
238 238 270 238 238
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Figure 2


US 11,291,103 B2

Sheet 13 of 15

Mar. 29, 2022

U.S. Patent

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U.S. Patent Mar. 29,2022 Sheet 15 of 15 US 11,291,103 B2

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(A)

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US 11,291,103 B2

Sheet 1 of 15

Mar. 29, 2022

U.S. Patent

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98%



US 11,291,103 B2

17
2:1 does not qualitatively change the results in FIG. 11(c) or
substantially affect the maximum atom number.

There is not a distinct laser beam for the Zeeman slower
so the MOT loads atoms during operation. However, we can
shut off the current in the Zeeman and compensation coils
[see FIG. 9 and FIG. 10(a)] to reduce the MOT loading rate
The MOT population then exponentially decays to a lower
equilibrium atom number. Fitting the MOT decay curves
yields trap lifetimes t1 s for our operating conditions.

To quantitatively understand the loading of the MOT, we
calculate the average force f exerted on an atom by the input
beam, with wave vector k,, and its reflections, with wave
vector k, (=1,2.3), using

1
_ Sills Fi) o

To Sixt #457 [2

yard i

a as

= A= k= mipeB/h,

where we have assumed an S-to-P transition (ie., ignoring
fine and hyperfine structure). Here, s=1,1,,, is the saturation
parameter for beam i (with intensity I), 8,.../=28), A is the
detuning, v is the atom’s velocity, 1, is the Bohr magneton,
m,, 40 is the projection of the excited-state’s orbital angular
momentum onto the magnetic field, and y, is the angle
between the magnetic field B and the wave vector k,. The
polarization of beam i is denoted by €=#1, where +1 (-1)
represents right-handed (left-handed) circular polarization.
P is a Wigner d-matrix that determines the transition prob-
abilities to excited state m, and is given by P(m,'=-1. y,,
€=+1)=(Fcos y,)7/4, P(m,'=0, y,, €=#1)=sin?y/2, and
P(m,'=#1, y,, €=£1)=(1tc0s ¥,)°/4.

The calculated force along the % axis is shown in FIG. 12 3

for a magnetic field gradient of B'=4.5 mT/cm and a maxi-
mum magnetic field of B,,..~12 mT. For these values of BY
and B,,,,. the magnetic field behind the chip closely matches
the ideal BU) profile of a Zeeman slower. The input
laser beam (see FIG. 9) is resonant with the cycling transi-
tion along the bright yellow curve (ie, kv=-A+}1;B/f),
maximizing the slowing force f [see Eq. (1)]. The force is
reduced in the MOT region (the yellow curve darkens to pale
green) because the diffracted laser beams increase stotal (see
FIG. 14). The dispenser source is located at z,~54 mm,
beyond the maximum of the magnetic field at z,,,.~30 mm,
and about 10 times further from the MOT than the aperture
at z,=5 mm with characteristic radius r,=2 mm.

FIG. 12 shows forces on atoms in the Zeeman slower,
wherein an axial force on a 7Li atom versus position z and
axial velocity v for B'=4.5 mT/em and B,,,,=12 mT. The
vertical dashed lines denote the MOT region; the vertical
short-dashed line denotes the chip location. The atom source
is positioned at the left edge of the plot (z=z,~54 mm). The
solid curves show the trajectories of the slowest and fastest
captured velocities. The dashed white curves show the
trajectories for intermediate initial velocities.

Behind the aperture (see FIG. 9), atoms are slowed
similarly to an ideal Zeeman slower, where the velocity
follows v,(z)=11)B(z)iik. In this case, all initial velocities
Vo<V--HBmadfik should be slowed. FIG. 12 shows simu-
lated on-axis v(z) trajectories. Atoms emitted from the
source with v, receive a slowing impulse as they come into
resonance with the slowing laser beam in the region of
increasing magnetic field (2230 mm in FIG. 12), travel along
the Zeeman slower at nearly constant velocity, and then fall
onto the v,(z) curve.

20

3

40

18

We calculate the resulting loading rate by considering an
effusive source with surface area S. Each area element of the
source dS emits atoms per second per unit area per
steradian, according to a cosine distribution. Due to the size
of the chip aperture and MOT beams, only atoms emitted at
angles 6 (relative to the z axis) less than the capture angle
6. are captured by the MOT. Integrating over the full source
surface S leads to

0) 3 (2)
R= sv Goaas [ “coxa [* Reade

As a first approximation, we consider a point source at
x=0, take v, to be independent of 6, and define the capture
angle 6, through geometry, ie., tan 6.=r+,/(z,-z,). The
capture velocity then scales as v..~B,,,,, and thus the loading
rate R«B,,,,“. FIG. 13 shows the experimental efficacy of
our Zeeman slower for four different magnetic field gradi-
ents B'. At most, we observe a factor-of-4 increase in R for
a doubling of B,,... Suggesting a scaling closer to By, x.

FIG. 13 shows measured loading rate of the MOT with

AIT’ ,=-2.0 and s)=I/I, ,,-3.9 at four different magnetic field

S gradients B': 4 mT/cem, 4.5 mT/em, 5 mT/em, and 5.5

mT/cm. The curves are best fits.

The naive B,,..* scaling breaks down if the acceleration
required to keep an atom on the v,(z) curve (see FIG. 12)
exceeds the maximum possible acceleration from the slow-
ing laser beam. This condition is expressed as

dato Mol 50
"2 T¥ 59"

= Mahko

where the right-hand side of the inequality is the maximum
magnitude of f in the Zeeman slower [see Eq. (1)]. In the
present study, the largest Vp(Z,x120 m/s, defined by
Brax~13 mT. Combining this largest Vp(%pqx) With 55=3.9
and the largest B'=5.5 mT/cm from FIG. 13, we find that the
inequality in Eq. (3) is always fulfilled. Because dB(z)/dz<B'
in our apparatus, our calculation also demonstrates that
deviations from the ideal B(z)«Vz field in the Zeeman
slower cannot explain the observed scaling of R with B,,_,

Another potential deviation from R«B,,.:° is the assumed
independence of v, and 0,. Consider the on-axis atomic
trajectories in FIG. 14 with a nonzero initial angle with the
Z axis. These trajectories blossom: as the axial velocity
decreases, the initial transverse velocity causes the atom to
deviate farther off-axis. The blossoming effect reduces 0.
Neglecting the initial velocity change in the increasing
magnetic field region (230 mm in FIG. 12), an atom will
travel at its initial velocity vO until it intersects the universal
v,(z) curve. To illustrate the blossoming effect, we take
v,(2)=V'z so that the atom falls onto the universal trajectory
at Z,=Vv,/v', where v'=1,,B'/fik. Along the v,(z) trajectory, the
atom obeys z(t)=(vo/v')e~””. The angle 0, that just clears the
aperture can then be determined from the source-aperture
travel time tsa:

ersten, =< 2 ko re)
tants = FeNota = Te Zell =lopte eal”

where we have assumed that 0,<<I. For our device, the term
in braces reduces 6,, by approximately 70% of the geometric


US 11,291,103 B2
Page 2

(56) References Cited
U.S. PATENT DOCUMENTS

10,278,275 B2 4/2019 Imhof

2015/0200029 Al* 7/2015 Hughes G21K 1/006
250/251
2017/0359888 Al* 12/2017 Imhof G21K 1/006

2019/0200445 Al 6/2019 Imhof

OTHER PUBLICATIONS

McGilligan, .P, et al., “Phase-space properties of magneto-optical
traps utilising micro-fabricated gratings”, Optics Express, 2015, p.
8948-8959, vol. 23 No.7.

Cotter, J.P, et al., “Design and fabrication of diffractive atom chips
for laser cooling and trapping”, Applied Physics B, 2016, 172 p. 1-6,
vol. 122

Imhof, E., et al., “Two-dimensional grating magneto-optical trap”,
Physical Review A, 2017, p. 033636, vol. 96.

Lee, J., et al., “Sub-doppler cooling of neutral atoms in a grating
magneto-optical trap”, Journal of Optical Society of America, 2013,
Pp. 2869-2874, vol. 30 No. 11

Gustavson, TL., et al., ‘Rotation sensing with a dual atom-
interferometer Sagnac gyroscope”, Classical and Quantum Gravity,
2000, p. 2385-2398, vol. 17

Kasevich, M., et al, “Atomic Interferometry Using Stimulated
Raman Transitions”, Physical Review Letters, 1991, p. 181-184,
vol. 67 No.2

* cited by examiner


US 11,291,103 B2

23

aslower surface on a side of the optical diffractor opposite
the diffraction surface;

an atom transfer wall that bounds an atom transfer aper-
ture;

the atom transfer aperture that communicates slowed
atoms to a trapping region from an atom slower and
communicates primary light to the atom slower from
the trapping region;

a plurality of diffraction gratings disposed on the diffrac-
tion surface and comprising:

a first diffraction grating that receives the primary light
from a light source and produces first reflected light
from the primary light, the first reflected light mov-
ing in a first light reflection direction;

a second diffraction grating that receives the primary
light from the light source and produces second
reflected light from the primary light. the second
reflected light moving in a second light reflection
direction; and

a third diffraction grating that receives the primary light
from the light source and produces third reflected
light from the primary light, the third reflected light
moving in a third light reflection direction,

wherein the diffraction gratings reflects the primary light
as the first reflected light, the second reflected light, and
the third reflected light respectively along the first light
reflection direction, the second light reflection direc-
tion, and the third light reflection direction into the

trapping region so that the first reflected light, the ,

second reflected light, and the third reflected light
intersect in a reflected light intersection volume in the
trapping region and form trap light that traps the slowed
atoms to form trapped atoms from the slowed atoms.

16. The uniaxial counter-propagating monolaser atom ,

trap of claim 15, wherein the first diffraction grating com-
prises a first set of linear grating lines; the second diffraction
grating comprises a second set of linear grating lines; and the
third diffraction grating comprises a third set of linear
grating lines.

17. The uniaxial counter-propagating monolaser atom
trap of claim 16, wherein the first set of linear grating lines,
the second set of linear grating lines, and the third set of
linear grating lines are arranged on the diffraction surface in
three truncated triangles, wherein the atom transfer aperture
is centrally disposed among the three truncated triangles.

18. A process for cooling and trapping atoms with the
uniaxial counter-propagating monolaser atom trap of claim
1, the process comprising:

10

20

2

24

providing primary atoms from the atom source, such that
the primary atoms move in the atom primary direction;

producing, by the light source, primary light, the primary
light propagating in the light primary direction, the
light primary direction opposing the atom primary
direction;

counter-propagating the primary light relative to the pri-
mary atoms:

receiving, by the atom slower, the primary atoms from the
atom source;

communicating the primary light to the atom slower from.
the trapping region:

receiving, by the atom slower, the primary light as slow-
ing light;

subjecting the primary atoms to the slowing light;

slowing the primary atoms by the slowing light;

forming the slowed atoms from the primary atoms in
response to interaction of the primary atoms with the
slowing light, the slowed atoms moving in the atom
primary direction;

communicating, by the atom transfer aperture, the slowed
atoms to the trapping region from the atom slower

receiving, by the first diffraction grating, the primary light
from the light source;

producing, by the first diffraction grating, the first
reflected light from the primary light, the first reflected
light moving in a first light reflection direction;

receiving, by the second diffraction grating, the primary
light from the light source;

producing, by the second diffraction grating, the second
reflected light from the primary light, the second
reflected light moving in a second light reflection
direction;

receiving, by the third diffraction grating, the primary
light from the light source:

producing, by the third diffraction grating, the third
reflected light from the primary light, the third reflected
light moving in a third light reflection direction;

receiving, by the trapping region, the first reflected light,
the second reflected light, and the third reflected light;

intersecting the first reflected light, the second reflected
light, and the third reflected light in a reflected light
intersection volume in the trapping region;

forming trap light from the first reflected light, the second
reflected light, and the third reflected light;

receiving the slowed atoms in the trap light; and

subjecting the slowed atoms to the trap light to produce
trapped atoms from the slowed atoms.

+ * RR Oe


U.S. Patent Mar. 29,2022 Sheet 11 of 15 US 11,291,103 B2

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U.S. Patent Mar. 29,2022 Sheet 14 of 15 US 11,291,103 B2

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