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The Integration of Photonic Crystal Waveguides with Atom
Arrays in Optical Tweezers
Xingsheng Luan, Jean-Baptiste Béguin, Alex P. Burgers, Zhongzhong Qin, Su-Peng Yu,
and Harry J. Kimble*
Integrating nanophotonics and cold atoms has drawn increasing interest in
recent years due to diverse applications in quantum information science and
the exploration of quantum many-body physics. For example,
dispersion-engineered photonic crystal waveguides (PCWs) permit not only
stable trapping and probing of ultracold neutral atoms via interactions with
guided-mode light, but also the possibility to explore the physics of strong,
photon-mediated interactions between atoms, as well as atom-mediated
interactions between photons. While diverse theoretical opportunities
involving atoms and photons in 1D and 2D nanophotonic lattices have been
analyzed, a grand challenge remains the experimental integration of PCWs
with ultracold atoms. Here, an advanced apparatus that overcomes several
significant barriers to current experimental progress is described, with the
goal of achieving strong quantum interactions of light and matter by way of
single-atom tweezer arrays strongly coupled to photons in 1D and 2D PCWs.
Principal technical advances relate to efficient free-space coupling of light to
and from guided modes of PCWs, silicate bonding of silicon chips within
small glass vacuum cells, and deterministic, mechanical delivery of
single-atom tweezer arrays to the near fields of photonic crystal waveguides.
X. Luan, Dr. J.-B. Béguin, Dr. A. P. Burgers
[
+
]
, Dr. Z. Qin, Dr. S.-P. Yu
[
++
]
,
Prof.H.J.Kimble
Norman Bridge Laboratory of Physics
California Institute of Technology
Pasadena, CA 91125, USA
E-mail: hjkimble@caltech.edu
Dr. Z. Qin
State Key Laboratory of Quantum Optics and Quantum Optics Devices
Institute of Opto-Electronics
Shanxi University
Taiyuan 030006, China
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/qute.202000008
[
+
]
Present address: Department of Electrical Engineering, Princeton Uni-
versity, Princeton, NJ 08540, USA
[
++
]
Present address: Time and Frequency Division, NIST, 385 Broadway
Boulder, CO 80305, USA
© 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co.
KGaA, Weinheim. This is an open access article under the terms of the
Creative Commons Attribution-NonCommercial-NoDerivs License,
which permits use and distribution in any medium, provided the original
work is properly cited, the use is non-commercial and no modifications
or adaptations are made.
DOI: 10.1002/qute.202000008
1. Introduction
The research described in this manuscript
attempts to create novel paradigms for
strong quantum interactions of light and
matter by way of single atoms and photons
in nanoscopic dielectric lattices. Nanopho-
tonic structures offer the intriguing possi-
bility to control interactions between atoms
and photons by engineering the medium
properties through which they interact.
[1,2]
Opportunities beyond conventional quan-
tum optics thereby emerge for unconven-
tional quantum phases and phenomena for
atoms and photons in 1D and 2D nanopho-
tonic lattices.
[3–5]
The research is inher-
ently multidisciplinary, spanning across
nanophotonics, atomic physics, quantum
optics, and condensed matter physics.
Beyond the advances reported here, this
general area has diverse implementations
for Quantum Information Science, includ-
ing the realization of complex quantum
networks
[6]
and the exploration of quan-
tum many-body physics with atoms and
photons.
[7]
Further avenues of interest are the investiga-
tion of quantum metrology and long-distance quantum
communication
[8]
combined with the integrated functional-
ity of nanophotonics and atoms. As a comparison, solid-state
emitters coupled to nanophotonic structures
[9–11]
provide a
complementary route to some of the physics described here.
However, these systems exhibit inhomogeneous broadening
which can make the coupling of even two such emitters in a sin-
gle nanophotonic structure a challenging experimental task
[12]
and they are not, in their current form, designed to generate
controllable interactions across a large system of emitters as has
been demonstrated with numerous atomic physics platforms.
While exciting theoretical opportunities of atoms coupled to
nanophotonics have emerged, this research only moves forward
in the laboratory by advancing nanophotonic device fabrication
and by integrating these novel devices into the realm of ul-
tracold atoms. Important experimental milestones have been
reached,
[13–18]
but generally laboratory progress has lagged the-
ory in combining ultracold atoms and novel nanophotonic de-
vices. As illustrated in
Figure 1
, a grand challenge for experi-
ments in this new field is the realization of atomic arrays with
high fractional filling of single atoms into unit cells of 1D and
2D lattices.
[1,2]
In this paper, we describe an apparatus that
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Figure 1.
Schematic for building nanoscopic atomic arrays with one atom per unit cell in a) 1D alligator photonic crystal waveguide (APCW)
[15,19]
and
b) 2D honeycomb photonic crystal lattice,
[5]
respectively. In both cases, the silicon nitride structures (gray) are suspended above an underlying silicon
substrate (dark background). Green spheres represent the yet to be achieved single atoms trapped by optical forces within unit cells of the photonic
crystal structures.
[20,21]
Figure 2.
The old (a) and new (b,c) ways of integrating nanophotonic chips with cold-atom vacuum systems; a) scale for old system is set by 2.75
′′
flange to connect to conventional 6
′′
diameter vacuum chamber with chip (top of figure) then centered in chamber. (For more details, see Chapter 6 and
Figure 6.4 in ref. [27].) b) New system with silicon chip of 4 mm width mounted on a SiO
2
“optical table” of dimensions 5
×
11
×
2 mm. For more details,
refer to Section 2. c) The assembled system in a SiO
2
glass cell of internal dimension 1
×
1
×
4
.
5 cm (rectangular part), surrounded by two coupling
objectives (CO
1
and CO
2
with N
.
A
.
=
0
.
4) for free-space optical coupling to photonic crystal waveguides and two tweezer objectives (TO
1
and TO
2
with
N.A.
=
0
.
4) for generating optical tweezer traps and imaging. Reproduced with permission.
[28]
Copyright 2020, OSA Publishing.
provides several significant advances relative to prior technical
capabilities, that are summarized as follows:
1.1. Silicate Bonding
We have previously used large manipulators inside conven-
tional stainless steel chambers for mounting our silicon chips
illustrated in
Figure 2
a. This method posed several limitations
in our previous experiments,
[15,16,21]
including mechanical and
thermal instability, complexity in fiber alignment and assembly,
and limitations on baking temperature due to various epoxy
resins and bonding agents required for “gluing” optical fibers
to silicon chips and chips to vacuum mounting hardware. Fol-
lowing discussions with Jun Ye and John Hall at JILA, we have
developed a new platform to mount our chips in vacuum. As
shown in Figure 2b and also described in details in Section 2,
we now bond a Si chip to an SiO
2
substrate by way of silicate
bonding that we have developed in our group (with significant
input from a LIGO research team at Caltech). This bonding tech-
nique has extremely low out-gassing properties compared to our
previous chip mounting configurations and enables high tem-
perature baking of our vacuum cell for ultra-high vacuum (UHV)
operation.
1.2. A New Generation of PCWs
We have developed optical chips that eliminate fiber optics within
the vacuum chamber, achieve more efficient coupling of light
into and out of our PCWs, increase power handling capabilities
by 20-fold to facilitate long-lived guided-mode optical traps,
[20]
and enable high-temperature baking for improved atom trapping
times.
[22]
All of these goals have been met by way of the design
and fabrication of devices that utilize free-space optical coupling
whereby input laser light is coupled from outside the vacuum
chamberdirectlyintoindividualPCWs.AsdescribedinSection3,
we have removed the need for in-vacuum fibers by designing and
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fabricating a new Y-coupler at the terminating ends. The silicon
chip also has a significantly reduced footprint necessitated by
having the terminating Y-couplers much closer to the edges of
the silicon chip to allow free-space coupling for numerical aper-
tures (N.A.)
≈
0.1–0.2 of the new Y-couplers.
[22]
1.3. A New Laboratory
Free-space coupling and silicate bonding have enabled the con-
struction of a new laboratory in the Quantum Optics Group at
Caltech, which is built around a vacuum envelope reduced in
size by approximately a factor of 10
2
to reach a volume
≈
10 cm
3
with unprecedented optical access relative to our prior chambers,
as shown in Figure 2c. We aim to achieve nanoscopic lattices of
atoms that are assembled deterministically with arrays of single-
atom tweezers and that are coupled to guided modes (GMs) of
PCWs for efficient atom–photon coupling along the PCW and of
GM photons to and from free-space. As described in Section 4,
our experiment is in the spirit of recent worldwide advances with
free-space tweezer arrays
[23–26]
but adds the significant complex-
ity of assembling such atomic arrays near the surfaces of 1D and
2D PCWs.
A general summary of our advances is provided by Figure 2,
which shows our “old”
[22,27,29]
and “new”
[28]
systems side by side.
Of course, small glass cells with volume
≈
1cm
3
for various opti-
cal trapping schemes have been employed by various groups for
many years,
[30]
but to our knowledge, no group has succeeded to
implement a compact setup as in Figure 2b,c when the difficult
constraints of localization of atoms near PCWs have been part of
the setup.
[28]
2. Silicate Bonding
In previous atom–nanophotonic experiments
[15–17,21]
in the
Quantum Optics Group at Caltech, the nanophotonic chips were
held inside a stainless vacuum chamber by a long mechanic
manipulator (
≈
10 cm) with input-output fibers pre-aligned and
glued in the V-groove on chip,
[19]
asshowninFigure2a.This
posed three major limitations in our previous experiments: 1)
The long mechanical arm did not have sufficient mechanical sta-
bility, thereby limiting the ability for precise positioning of atoms
on nanophotonic structures and dissipation of guided mode heat-
ing power. 2) Fiber coupling of light into and out of the chip in-
volved cumbersome fiber pre-alignment and gluing outside the
vacuum chamber, and the number of devices (8 APCWs) that
could be coupled was limited by failure probability and the num-
ber of vacuum feedthroughs available (eight input plus eight out-
put fibers). Furthermore, once the chip was inside the vacuum
chamber, the coupling efficiency could not be further adjusted
or optimized. 3) The usage of UHV-compatible epoxy for glu-
ing fibers and the chip prohibited the possibility of significantly
baking the entire vacuum chamber. As a result, the typical life-
time for atoms trapped near (
≈
300 μm) the chip was limited to
be
≲
100 ms.
[16]
Here, by adapting the silicate bonding method
[31]
whose relia-
bility was demonstrated in NASA and ESA astronomical satellite
missions (e.g., Gravity Probe B and The LISA Pathfinder) and
current LIGO instruments, we are now able to overcome these
limitations by mounting the nanophotonic chip inside a glass cell
with small footprint that is compatible with free-space coupling
from microscope objectives outside the vacuum cell. This largely
eliminates the relative motion between chip and vacuum cham-
ber, and also the need of all optical fibers within the vacuum en-
velope.
The hydroxide catalysis bonding method of ref. [32] involves
strong chemical bonds between oxidizable materials such as
SiO
2
and silicon. Such chemical bonds can be formed at room-
temperature. Optically, silicate bonding provides a transparent
bond, the refractive index of which between two SiO
2
surfaces,
converges to the index of SiO
2
[33]
thereby minimizing Fresnel re-
flections from the bonded surfaces and allowing low-loss opti-
cal transmission through the bond. AR-coated glass surfaces can
also be silicate bonded if terminal layers of SiO
2
are deposited on
the surfaces to be bonded. Silicate bonding allows UHV opera-
tion, which is an important requirement for research involving
trapped cold atoms near surfaces inside a vacuum chamber. The
operating temperature for components secured by silicate bond-
ing ranges from cryogenic to beyond typical bake-out tempera-
tures for UHV chambers (i.e., 300–400 K). Because of the UHV
compatibility of silicate bonding and the small footprint of the
glass cell, a vacuum pressure of
≈
10
−
11
Torr is achieved after the
first baking of the entire vacuum setup, as compared to
≈
10
−
9
Torr in previous work.
Turning then to the steps for achieving a mounted silicon chip
by way of silicate bonding, we show in
Figures 3
and
4
pho-
tographs of various stages of the sequence. Figure 3a shows the
glass tables upon which 200 μm thick (4
×
9 mm) silicon chips
will be bonded via three effective contact surfaces, as in Fig-
ure 3b,c using rods and spheres as well as hemispheres in Fig-
ure3a.Here,weconsiderthecaseofhemispheresforwhichthree
SiO
2
hemispheres are first bonded onto a SiO
2
rectangular prism
table. The curved caps of the hemispheres are then flat polished
to better than
휆
∕
10 over a circular area of diameter
≈
0.8 mm,
defining a precision plane (to within 100 nm) for next bonding
the silicon chip to the flat tops of the polished hemispheres and
hence to the optical table. The table-chip assembly is then itself
bonded to the inner wall of a precision fused quartz glass cell fab-
ricated by Starna
[34]
shown in Figure 4e. It should be noted that
the rectangular prism table is AR-coated on its outer side (i.e.,
facing into the glass cell), while the glass cell is AR-coated on its
outer surface but not inner.
We recall that the nanophotonic structures are e-beam writ-
ten into a 200 nm sacrificial layer of silicon nitride deposited on
the 200 μm thin silicon substrate,
[19]
so that considerable care
is required to avoid damage to the surface containing the de-
vices. Without the use of additional optical elements, the bare di-
vergence angle of the light emerging from the nano-waveguides
(N.A.
≈
0
.
15, as in ref. [22]) requires elevating the chip base from
any surface and to position it in relation to the glass cell geometry
to avoid clipping loss.
3. The Y-Coupler Technology
In this section, we present a description of the new “Y-coupler”
design which provides efficient free-space coupling, minimal
light scattering, and better mechanical stability. This design
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Figure 3.
Photographs of a) SiO
2
polished rectangular tables (5
×
11
×
2 mm) with three SiO
2
hemispheres silicate-bonded onto the AR-coated table
surface. b) Three parallel SiO
2
cylindrical rods with diameter 1 mm and length 2 mm individually bonded on flat cross-section to an APCW Si chip.
c) Three SiO
2
spheres (diameter 1.5 mm) bonded to a blank 1
×
1 cm square silicon chip. d) SiO
2
glass chamber with external AR-coating on all five
surfaces of the rectangular glass cell with 1.25 mm wall thickness, internal square cross-section 1
×
1 cm, and length 4.5 cm; a Quartz to Pyrex graded
seal (internal diameter 2.54 cm) is fused via a cup (for coating protection) to the rectangular cell, for chamber bake-out temperatures up to 400 K.
Figure 4.
a) 3D model drawings of fused silica glass table assembly with silicon chip with three different perspective views. b–e) Photographs of table
assembly during construction and inside coated vacuum glass cell. b) The weight of the glass table with hemispheres is used during bonding to the
Si-chip frame. c) Example photograph of a window-less Si-chip bonded to the glass table. d,e) The small chip-table assembly is finally bonded onto one
inner wall of the rectangular glass cell.
extends the maximum power by roughly 20x beyond the failure
power for our previous fiber butt coupled devices,
[19]
which
was a major limitation in our previous atom–nanophotonic
experiments
[15,16,21]
for achieving long-lived guided-mode atom
trapping at magic wavelengths,
[20,35]
as previously demonstrated
in the optical nanofiber system.
[36,37]
The chip design in this work is an adaptation of the system
presented in ref. [19] to enable direct free-space coupling from
an objective into the waveguides. The devices are fabricated from
a 200 nm silicon nitride device layer, suspended from a 200 μm
silicon substrate. Precision grooves aligned to the waveguide de-
vice layer are etched into the substrate, to enable cleaving of the
chip for clearance for free-space beam inputs and outputs. The
absence of terminated optical fibers in the vicinity of the waveg-
uide input coupler widens the design space available for coupler
designs. Here, we present a Y-coupler design that simultane-
ously optimizes transmission, suppresses residual reflection,
and provides mechanical stability.
[22]
In order to mode-match
the guided mode of a photonic waveguide to a Gaussian beam,
we taper the waveguide width to
≃
130 nm, before terminating
the waveguide and launching the mode. The terminated end of
the suspended waveguide is affixed to the substrate through two
≤
100 nm wide tethers. Conventionally, the tethers are simply
arranged perpendicular to the waveguide,
[19]
asshowninthe
SEM image in
Figure 5
a(i). Two issues arise from such tethering
design. First, the tether pair is polarized by the guided mode
light, creating scattering and back-reflection that are undesirable.
Second, the tethers are perpendicular to the waveguide, therefore
releasing the tensile stress on the waveguide, potentially making
the tapered section of the waveguide mechanically pliable. At
high optical power, the waveguide-tether junction is observed
to produce fluctuating scattering intensity prior to mechanical
failure, which we attribute to thermally induced stress distribu-
tions causing physical movements of the junction. These pose a
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Figure 5.
a) SEM images of the coupler with conventional 90
◦
tether termination (i) and the Y-coupler (ii). b) Vectorial illustration of the polarizabilities
on tethers shows the working principle for the coupler with conventional tether termination (i) and the Y-coupler (ii). c) FDTD simulation of wave
propagation in Y coupler for an incident Gaussian beam propagating from the bottom to the top of the figure. Inset is an SEM image of device under
simulation with the Gaussian mode input indicated as a red arrow.
significant constraint for achieving guided-mode traps at magic
wavelengths for Cs with a typical power handling
≈
10 mW, well
beyond the
≈
0.5 mW limit found for conventional couplers in
refs. [19, 38].
To overcome this limitation, an unconventional Y-shaped ter-
mination of the free-standing end of the waveguide was designed
in joint consideration of mechanical and optical properties, as
shown in Figure 5a(ii). The termination ends of the suspended
waveguide need to be mechanically affixed to the substrate with
tethers. By tilting the tethers away from the tapered waveguide, a
controllable weak tensile stress can be maintained on the waveg-
uide and tethers to make them mechanically robust. Optically,
the tethers are tilted away from the electric field vector of the
incoming mode, reducing the polarizability of each tether. This
effect, in addition to the partial cancellation of the polarization
vectors of the two tethers, reduce the total polarizability of the
junction, therefore reducing the scattering loss due to the tethers,
as shown in Figures 5b(i) and 5b(ii) with vectorial illustrations
for conventional coupler with 90
◦
tethers and the Y-coupler, re-
spectively. In practice, a tilt angle of 60
◦
from perpendicular was
chosen from FDTD optimization.
[39]
The simulated field pattern
of a Gaussian beam incident on the junction frombelow is shown
in Figure 5c. Coupling efficiencies of a 1
∕
e
2
waist
w
0
≈
2
.
5μm
beam with different input polarizations to different couplers
are calculated from FDTD simulations and are summarized in
Table 1
. It suggests that the Y-coupler has a better performance
than conventional couplers in terms of Gaussian-beam-to-
waveguide transmission (87% vs conventional 79%) and
reflection (
<
0.1% vs conventional 2.7%) for input polarization
along
y
direction (TE), which is critical for quantum correla-
tion measurements in nanophotonics.
[15]
We have measured a
coupling efficiency up to 80
%
for TE input using the Y-coupler
design.
[28]
Table 1.
FDTD simulated transmission and reflection efficiencies for dif-
ferent couplers.
Type
TE
transmission
TM
transmission
TE
reflection
TM
reflection
With 90
◦
tethers
79%
65%
2.7%
0.6%
With Y-shape tethers
87%
56%
<
0.1%
<
0.1%
In
Figure 6
, we show measurement data asserting the power
handling capability of the devices with the free-space coupling
and Y-coupler design strategy. Figure 6a shows the optical power
transmitted by the device as a function of the input power for
light propagating in the TE mode with a magic wavelength for Cs
atoms at 935.7 nm. The new design allows a measured 20-fold
increase (from
≈
0.5 to
≈
10 mW) in the maximum optical light
power before breaking or irreversible damages as compared to
our previous devices with the butt-coupler design.
[19]
This should
enable long-lived guided-mode atom traps by way of higher inten-
sities required for larger atomic detunings, including for magic-
wavelength traps.
[20,35]
While the detailed physics of device failure and plastic defor-
mation is beyond the scope of this article, we show in Figure 6b
a measurement of the dependence of the mechanical frequency
of the fundamental differential in-plane mode of motion of the
APCW as a function of the output light power. Devices physi-
cally break at
P
out
≈
20 mW. At the very low powers, the quasi-
linear decrease in frequency is compatible with a simple model
of reversible thermal elongation of a highly stressed string. At the
highest powers before failure, the frequency shift would amount
to a relative physical elongation and equivalent strain of
≈
0.04,
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Figure 6.
a) Measured output light power
P
out
versus input light power
P
in
for optical light field propagating in the TE mode with vacuum wavelength
935.7 nm and chamber pressure of
≈
3
×
10
−
10
Torr. b) Fundamental mechanical frequency of the differential in-plane mechanical mode of APCW as a
function of output light power. Different colors correspond to different nanophotonic devices on the same chip.
compatible with typical ratios of the yield strength of silicon ni-
tride to its Young’s modulus.
4. Single Atom Trapping in a Tweezer Array Near
PCWs
One of the key challenges in atom–nanophotonic experiments
is to achieve efficient loading of atoms into guided mode traps
formed on the nanophotonic structures. Given the small guided-
mode trap volume and strong Casimir–Polder potential near the
dielectric surfaces, it was shown in refs. [15, 21] that direct load-
ing of background Cs atoms into the APCW guided mode traps is
very difficult. Trapping few atoms in a single trap
≈
130 nm above
the APCW surface is demonstrated in refs. [16, 17] by reflecting
awaist1
∕
e
2
w
0
≈
60 μm dipole trap beam (the so-called side-
illumination beam). However, the average trapped atom num-
bers
̄
N
is restricted to
≈
3 atoms and the trap size along the APCW
is
≈
10 μm (along the
x
direction as in Figure 1a), corresponding
to
≈
27 unit cells.
[16]
Therefore, it was not possible to have precise
positioning of individually trapped atoms and full control of their
photon-mediated interactions. By adapting techniques developed
in free-space 1D, 2D, and 3D atom assemblies in optical tweezer
arrays,
[25,26,40]
our goal here is to achieve efficient atom assem-
bly on the PCWs with each single atom precisely positioned with
respect to the nanophotonic structures as in Figure 1. In this sec-
tion, we present a description of the experimental protocol for
trapping single atoms in a 1D tweezer array near PCWs with our
advanced apparatus.
As shown in
Figure 7
, our apparatus consists of two vacuum
glass cells named source cell (top) and science cell (down) in a
top-down configuration which is parallel to the gravity direction.
The experiment cycle starts with the loading of a magneto-optical
trap (MOT) from background, room temperature Cs vapor in the
source cell for a duration
≈
1 s. With
≈
10
7
atoms loaded into the
≈
2 mm effective diameter MOT, we then perform a 10 ms polar-
ization gradient cooling (PGC)
[41]
to cool the dense atom cloud
to
≈
10 μK before transferring into a blue-detuned donut-shaped
dipole trap beam which guides falling cold atoms down into the
science cell. Due to the
≈
0.5 m separation between source cell
and science cell, it takes
≈
300 ms for cold atom freely falling from
Figure 7.
A simplified AutoCAD drawing of the experimental setup. The
source MOT and science PGC cloud positions are also indicated with red
circles. Falling atoms are delivered from source cell to science cell by the
guiding of a blue-detuned donut-shaped beam (not shown).
the source cell, with total delivery efficiency
≈
20%, which is lim-
ited by the lifetime of atoms in the blue dipole trap. In the science
cell, atoms are stopped and then cooled by PGC to a volume of
≈
(200
휇
m
)
3
with temperature
≃
20 μK.
Next, individual Cesium atoms from the PGC cloud are
loaded into a linear array of optical tweezers with trap depths
U
trap
∕
k
B
≈
1 mK at a Cs magic wavelength (935.7 nm). The
tweezer array is generated by sending the output of an acoustic-
optical deflector (AOD) with RF-controlled spacing into a tweezer
objective (N.A.
=
0
.
4), forming focal spots with 1
∕
e
2
waist
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Figure 8.
a) A typical histogram of fluorescence counts(green color) measured from a single site of the tweezer traps shows a discrete distribution of 0
and 1 atom loaded each time, as compared to the background (gray) with no loading (i). The vertical blue dashed line sets the threshold of detecting
1 atom. Inserts (ii) and (iii) indicate the typical image on EMCCD for “0” atom and “1” atom, respectively. Insert (iv) shows the extracted probability
of detecting 1 atom after different holding time of the tweezer without cooling. An exponential fit shows the average 1
∕
e
lifetime of an atom inside the
tweezer is 25 s for vacuum cell after baking. b)Image of scattered light from tweezer spots when aligned with the APCW, collected through the same
tweezer objective (i). ii) An SEM image of the APCW with red ellipses indicate the separation of two neighbour tweezer spots. The size of red ellipses
indicate the estimated confinement of an atom trapped with energy half the trap depth. iii) Free-space atomic fluorescence from loading of the six tweez
er
sites with a 1.26 μm beam waist for 150 experimental shots 3 mm away from the chip structure. iv) Free-space atomic fluorescence from loading of the
17 tweezer sites under same conditions in (iii).
w
0
≃
1
.
26
±
0
.
15 μm. After 30 ms of PGC and loading into the
tweezer array, we turn off the PGC beams for 50 ms to let back-
ground atoms drop away and then turn on the same PGC beams
(15 MHz red detuned from D2,
F
=
4
−
5
′
transition) to illumi-
nate the trapped atoms for 50 ms. As shown in
Figure 8
a(i–iii),
by binning fluorescence counts recorded on the EMCCD (Andor
Camera iXon 3) around each tweezer location, we demonstrate
that the distributions of fluorescence counts are well separated
due to discrete loading of either 0 or 1 atom into each tweezer
spot with approximately equal probability. This corresponds to
the “collisional blockade” for loading atoms into tightly focused
dipole traps.
[43,44]
To determine the lifetime of a trapped atom
in the optical tweezer, we measured the occurrence of “1 atom”
events after different holding times, with cooling light shut off by
an optical shutter. As shown in Figure 8a(iv), we measured
≃
25 s
for the first baked vacuum cell and 14 s for the unbaked vacuum
cell (not shown). To minimize the impact of light scattering from
the chip during trap loading and also the Cs atoms deposition on
PCWs from high Cs densities,
[29]
the tweezer array is loaded ap-
proximately 3 mm away from the surface of the silicon chip. Due
to the relatively long trap lifetime and flexibility afforded by ex-
ternal objective lenses, transport of atoms trapped in the tweezer
array to near the surface of the silicon chip along the PCW is
accomplished over a programmable interval 0
.
02
<
Δ
t
<
0
.
1sby
mounting the tweezer objective on a precision linear translation
stage (model Physik Instrumente V-522, 20 nm unidirectional re-
peatability) with motion along the
z
direction defined in Figure 7.
To investigate the efficiency for transport of single atoms in
a linear array of tweezer traps, we measured the conditional sur-
vival probability
P
s
by transporting single atoms from the loading
zone to a target position near the PCW (
Δ
t
≃
0
.
1 s), holding still
at target position for
≃
0.1 s, and then moving back (
Δ
t
≃
0
.
1s)to
the loading zone for a second fluorescence imaging. In this mea-
surement, a specific target position is chosen to be
≈
10 μm away
from the APCW (along
y
axis) and in the APCW’s
x
−
y
plane,
as indicated by the green dots in
Figure 9
a. Given an initial mea-
surement that verifies that a particular tweezer trap is loaded, we
find that
P
s
≃
0
.
90 for transport from the loading zone to a target
position and back to the loading zone for a second fluorescence
measurement. This observation suggests that the one-way suc-
cess probability for transport from loading zone to target position
is
≃
0
.
95 and the lifetime of trapped atoms at the target position
near the PCW is
≥
2s.
Examples of atom loading into 6 and 17 tweezer sites far from
the APCW are shown in Figure 8b(iii,iv). Figure 8b(i) displays the
reflection of multiple tweezer spots from the APCW with the tar-
get positions now being inside the gap of the APCW (i.e.,
y
=
0
and along the
x
-axis), albeit with no atom imaging. Beyond these
initial measurements, sub-micron waists are achievable with a
higher numerical aperture objective (N.A.
≈
0.7) and will be dis-
cussed in Section 5.
After transport of the 1D trapped atoms array to the target po-
sition
≈
10 μm from the PCW, the single atom 1D array will be
further transferred into reflective traps near the dielectric sur-
face of the PCW for strong atom-light interactions.
[13,21,45]
Here,
we numerically investigate a protocol for atom assembly on the
PCW inspired by refs. [13,25], now within the setting of the
APCW. As illustrated in Figure 9a, moving the entire tweezer ar-
ray vertically along the
y
direction is achieved by sweeping the
RF drive frequency for a second AOD with axis along
y
orthog-
onal to that of the first AOD forming the original tweezer array
along
x
. Figure 9b shows a typical atom trajectory (white curve)
from numerical simulation being successfully transferred into
the so-called
z
1
trap close to the upper surface of the APCW trap
with the largest coupling rate to TE mode of the APCW.
[16,17]
Here, the free-space initial position of the tweezer waist is located
at (
x, y, z
)
=
(0
,
−
2
.
5
,
−
1) μm with the atom initial temperature
≈
50 μK.
More generally, the probabilities of transferring into different
reflective trap sites {
z
i
} can be tuned by changing the initial
tweezer focus along the
z
direction. This is further quantified
by a Monte-Carlo simulation of atom trajectories as shown in
Figure 9c for tweezer waist
w
0
=
850 nm and atom initial temper-
ature 20 μK. The simulated probability of transferring into the
z
1
trap is peaked at
≈
100% between
z
=−
1μmand
z
=−
1
.
7μm,
which indicates a relatively large tolerance of tweezer focus
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2020
,
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, 2000008
2000008 (7 of 11)
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Figure 9.
a) An illustration of the scheme for transferring a free-space array of single atoms to reflective traps above PCWs. The red circles indicate
the size of a tweezer with radius equal to the waist
w
0
=
850 nm and green dots indicate the rms span sizes of
≈
100 μK trapped atoms in a 1 mK
tweezer trap. b) A COMSOL
[42]
simulation of the tweezer trap when aligned on PCWs with tweezer focus position at
z
=−
1 μm and polarization along
x
direction (out of page), with the closest three reflective traps labeled as ‘
z
1
,’ ‘
z
−
1
,’ and ‘
z
2
.’ The white curve shows a typical atom trajectory starting
at initial tweezer trap minimum (
x, y, z
)
=
(0
,
−
2
.
5
,
−
1) μm with initial temperature
≈
50 μK. c) Probability of transferring into different reflective traps at
different tweezer focus positions along
z
direction, with atom initial temperature
T
i
=
20 μK. d) Probability of transferring into
z
1
trap at different atom
initial temperatures at 1 mK tweezer trap.
positions along
z
. Our investigations of atom trajectories via
Monte-Carlo simulation show that achieving high probability
transfer with (
p
>
0
.
9) into the
z
1
trap also requires that the
atom starts initially with a temperature less than 60 μK, as
shown in Figure 9c for tweezer waist
w
0
=
850 nm, trap depth
U
∕
k
B
=
1 mK, and focus position
z
=−
1
.
5 μm. Absent the
difficulties brought by the dielectric boundary, this can be
achieved with PGC in the tweezer or Raman sideband cooling as
shown in refs. [23, 24]. Once atoms are transferred into
z
1
trap,
further transferring into the guided mode trap can be achieved
by adiabatically turning off tweezer traps and turning on suitable
guided mode traps.
[15,20,21,46]
For the APCW as well as more complicated structures such as
2D photonic crystals in Figure 1b, we have recently proposed a
quite different scheme for direct delivery with high efficiency of
single atoms from free-space tweezer traps into
z
1
traps at the
surfaces of nanophotonic structures.
[47]
In this work, we exploit
the rapid spatial variation of the Gouy phase for optical tweezers
formed by radial Laguerre–Gauss beams to reduce the trap size
in the axial direction.
5. Toward Higher Optical Resolution
Ourcurrentapparatuscanbeimprovedintermsofopticalresolu-
tion for both imaging and smaller trap volume. It can accommo-
date state-of-the-art long-working distance objective lenses with
N.A.
≈
0
.
7. To characterize the tweezer waist under different N.A.
objectives and filling ratio, we employed three different methods
for a cross-check: i) Imaging by a CCD camera and a telescope
system which consists of a N.A.
=
0
.
8 objective and 125 mm fo-
cal length lens. ii) A knife-edge experiment
[48]
with a razor blade
glued inside a fused silica cell with inner dimensions of 2 cm
×
1 cm. The objective is moved on a 2D motorized stage to scan
along and perpendicular to the light propagation direction. The
Rayleigh range and tweezer waist can be fitted from the transmit-
ted light after the glass cell. To investigate the effect of glass cell
bowing on tweezer waist, the measurement is performed when
the glass cell is either at atmospheric pressure or under vacuum
(below 10
−
4
Torr). iii) For tweezers inside the science glass cell,
the tweezer beam is scanned across a 500 nm wide and 200 nm
thick uniform waveguide region inside the glass cell, and the re-
flection and scattering are imaged by an EMCCD. The Rayleigh
range and tweezer waist can be obtained by fitting the images.
The tweezer waist measured from these three different methods
for the N.A.
=
0
.
4 objective are all around 1.25 μm and consistent
within 10%.
Table 2
shows the measured beam waist
w
0
(1
∕
e
2
radius for
intensity) with the razor blade method for three different NA
objectives (N.A.
=
0
.
4 Mitutoyo M Plan Apo NIR B 20X, N.A.
=
0
.
67 OptoSigma PAL-50-NIR-HR, compensated for glass thick-
ness 1.25 mm, and Mitutoyo G Plan Apo 100X, compensated for
glass thickness 1 mm). The tweezer waists can reach 1.02 μm
for N.A.
=
0
.
67 objective and sub-μm for N.A.
=
0
.
7 objective. It
shows that the differences for tweezer waists in air and under
vacuum are negligible for all three different NA objectives and
thus the bowing effect of the glass cell does not significantly con-
tribute to the tweezer aberration.
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Table 2.
Waist benchmark of higher N.A. objectives.
N.A.
f [mm]
W.D.
[mm]
Input waist
[mm]
Waist in
air [μm]
Waist in
vacuum [μm]
0.4
10
25
2.5
1.22
1.23
0.67
4
10.5
1.8
1.02
1.02
0.7
2
6
1.1
0.91
0.87
a)
f and W.D. mean focal length and working distance, respectively.
In
Figure 10
a, we show an image of the APCW inside a glass
cell imaged with N.A.
=
0
.
7 objective under broadband illumina-
tion at 532 nm. The high resolution of the N.A.
=
0
.
7 objective
allows us to resolve the gap of APCW and precise location of
tweezer spot, as shown in Figure 10a with the tweezer aligned on
one nanobeam of the APCW (white dashed circle). Further atom
trapping near PCWs in tweezer arrays focused by high resolution
objectives is a work under progress.
6. Summary and Outlook
We have presented an advanced apparatus for the integration
of atoms and nanophotonics with several significant advances,
including 1) efficient free-space coupling of light to and from
guided modes of PCWs with greatly improved power handling
capabilities relative to our previous work,
[15–17]
2) silicate bonding
of silicon chips within small glass vacuum cells thereby reducing
the volume of the (bake-able) vacuum envelope of our systems
from
≈
1 liter
[19,27]
to
≈
5cm
3
with an associated drop in pressure
>
100x, and 3) deterministic, mechanical delivery of 1D single-
atom tweezer arrays to near an APCW. Each of these advances
eliminates significant impediments present in prior experiments
in the Quantum Optics Group at Caltech as explained in previ-
ous sections.
The advanced atom-nanophotonic platform that we have de-
scribed can provide a foundation for realizing nanoscopic atomic
lattices in 1D and 2D as envisioned in Figure 1 and thereby for
experimental explorations of these systems involving strong in-
teractions between atoms and photons in nanophotonic struc-
tures as described in refs. [1, 2]. Deterministic atom arrays, in
the spirit of recent worldwide advances with free-space tweezer
arrays,
[23–26,40]
will allow us to probe the physics of strong,
photon-mediated interactions between many atoms, as well as
atom-mediated interactions between photons. The versatility
of dispersion-engineered nanostructures makes accessing these
physical regimes possible in a single cold-atom experiment by
changing the nanophotonic structures the atom interacts with.
Moreover, the compact nature of our system also lends it-
self to more easily deployable quantum technologies that are
of growing interest in the community. Possible applications of
these nanophotonic systems range from quantum communica-
tion using strong atom–photon interactions to probing uncon-
ventional quantum phase transitions and investigating quan-
tum metrology applications by combining the functionality of
nanophotonics and atoms. One example relates to ongoing in-
vestigations of the integration of nanophotonic systems such
as described here with on-chip frequency combs for a compact
atomic frequency standard.
[49,50]
The collective decay of
N
atoms
(known as Dicke superradiance) into PCWs demonstrated in
ref. [16] could provide a simple, deterministic, and scalable way
to generate Fock states with large and fixed photon numbers,
and enable quantum-enhanced metrology.
[51]
Apart from quan-
tum information science, an essential aspect of atom trapping
near nanophotonic structures is a quantitative understanding of
Casimir–Polder interactions between trapped atoms and the di-
electric boundaries.
[3,20]
We have taken a modest step toward this
end in recent work.
[21]
With a broad set of such objectives in mind, we have developed
the advanced apparatus described in this article. In terms of an
outlook for closing the aforementioned gap described in the in-
troduction between experiment and theory (e.g., ref. [1]), there
are two issues to address. The first is the development of an ap-
paratus suited to the laboratory realization of the current cartoon
depicted in Figure 1 for dense filling of 1D and 2D PCWs with
single atoms, which our advanced apparatus should be capable of
achieving. However, the second challenge is that the PCW should
excel beyond the current APCW in terms of coupling strength
between single atoms and photons within a guided mode of the
PCW. For a 1D PCW, the still current state-of-the-art is the exper-
iment in ref. [17].
This experiment and its possible improvements are reviewed
in ref. [52]. For previous experiments with the APCW,
[16,17]
the
ratio of the waveguide coupling rate
Γ
max
1
D
(
휈
1
) for an atom trapped
Figure 10.
a) A CCD image of APCW inside a glass cell with N.A.
=
0
.
7 objective under broadband illumination at 532 nm. The focused tweezer is at
852 nm with 1
∕
e
2
waist
w
0
≃
0
.
7 μm, indicated as white dashed circle with radius
=
0.7 μm. The junction between the nanobeam waveguide and the
APCW region is resolved. b) A SEM image of the part of APCW under image, corresponding to the red dashed box in (a).
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within the vacuum gap to the rate
Γ
′
of atomic spontaneous decay
to all other modes is
P
=Γ
max
1
D
(
휈
1
)
∕Γ
′
≃
1
.
4. Here, the notation is
as described in ref. [17], with
휈
1
a resonance frequency near the
dielectric band edge of the APCW. However, by moving from the
APCW to a more advanced PCW that has already been fabricated
and tested, namely the slot photonic crystal waveguide (SPCW)
described in ref. [22], we would have
P
=Γ
max
1
D
(
휈
1
)
∕Γ
′
≃
44. For
operation with the Cs frequency within the bandgap, the authors
of ref. [52] project the ratio
R
of coherent “spin” exchange
J
1
D
to
incoherent guided-mode loss
Γ
1
D
to be
R
=
J
1
D
∕Γ
1
D
≃
20 at a de-
tuning of 20 GHz from the band edge, with the possibility to ob-
serve coherent spin-exchange oscillations between two proximal
atoms trapped within the SPCW shown in Figure 6b in ref. [52].
To achieve such an advance would require a) the capabilities de-
scribed in this manuscript for placing two tweezer-trapped atoms
precisely along the SPCW, b) transfer from the tweezer traps to
GM traps within the vacuum gap for 5
×
increased coupling rate,
and c) a next-generation PCW such as the SPCW.
Apart from improved coupling in 1D PCWs, switching to 2D
nanophotonic structures offers many new opportunities such
as anisotropic emissions,
[5,53]
Markovian and non-Markovian
dynamics,
[54]
and topological quantum optics.
[55]
An example
of a basic experiment can involve only a pair of atoms in two
tweezer traps near the surface of the 2D photonic crystals. The
anisotropic character of 2D photonic bands for photonic crystal
structures described in ref. [5] could be mapped by exciting one
“emitter” atom and monitoring the fluorescence counts from
another neighbour “probe” atom. By varying the relative angle
and distance between the “emitter” and “probe” atoms, we could
measure the anisotropic emission of “emitter” atom and from
that infer the spatial information of the 2D Green function as
described in ref. [52].
Supporting Information
Supporting Information is available from the Wiley Online Library or from
the author.
Acknowledgements
The authors thank John Hall and Jun Ye (JILA), Julien Laurat (Sor-
bonne University), Norma Robertson (Caltech), Keith Hulme (Starna),
Jeff Gabriel (PI), and Craig Goldberg (Newport) for important discus-
sions. The authors acknowledge the support from the following grants
and organizations: ONR (Grant No. N000141612399), ONR MURI Quan-
tum Opto-Mechanics with Atoms and Nanostructured Diamond (Grant
No. N000141512761), AFOSR MURI Photonic Quantum Matter (Grant
No. FA95501610323), and NSF (Grant No. PHY 1205729), as well as the
Caltech KNI.
Conflict of Interest
The authors declare no conflict of interest.
Keywords
atoms and nanophotonics, quantum dielectrics, quantum information sci-
ence, quantum simulation
Received: January 10, 2020
Revised: February 27, 2020
Published online: April 24, 2020
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