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The integration of photonic crystal waveguides with atom arrays in optical tweezers
Xingsheng Luan,
1
Jean-Baptiste B ́eguin,
1
Alex P. Burgers,
1, 2
Zhongzhong Qin,
1, 3
Su-Peng Yu,
1, 4
and H. J. Kimble
1, 5
1)
Norman Bridge Laboratory of Physics, California Institute of Technology,
Pasadena, California 91125, USA
2)
Present Address: Department of Electrical Engineering, Princeton University,
Princeton, New Jersey 08540, USA
3)
State Key Laboratory of Quantum Optics and Quantum Optics Devices,
Institute of Opto-Electronics, Shanxi University, 030006 Taiyuan,
China
4)
Present Address: Time and Frequency Division, NIST, 385 Broadway, Boulder,
Colorado 80305, USA
5)
Corresponding author: hjkimble@caltech.edu
(Dated: 4 March 2020)
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 crys-
tal waveguides (PCWs) permit not only stable trapping and probing of ultracold
neutral atoms via interactions with guided-mode light, but also the possibility to ex-
plore 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 1-D and 2-D nanophotonic lattices have been ana-
lyzed, a grand challenge remains the experimental integration of PCWs with ultracold
atoms. Here we describe an advanced apparatus that overcomes several significant
barriers to current experimental progress with the goal of achieving strong quantum
interactions of light and matter by way of single-atom tweezer arrays strongly cou-
pled to photons in 1-D and 2-D 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.
1
arXiv:2003.01236v1 [physics.optics] 2 Mar 2020
I. 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. Nanophotonic structures offer the intriguing possibility to control inter-
actions between atoms and photons by engineering the medium properties through which
they interact
1,2
. Opportunities beyond conventional Quantum Optics thereby emerge for
unconventional quantum phases and phenomena for atoms and photons in one and two-
dimensional nanophotonic lattices
3–5
. The research is inherently 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, including the realization of complex quantum networks
6
and
the exploration of quantum many-body physics with atoms and photons
7
. Further av-
enues of interest are the investigation of quantum metrology and long distance quantum
communication
8
combined with the integrated functionality of nanophotonics and atoms.
As a comparison, solid-state emitters coupled to nanophotonic structures
9–11
provide a com-
plementary 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
single 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 fabri-
cation and by integrating these novel devices into the realm of ultracold atoms. Important
experimental milestones have been reached
13–18
, but generally laboratory progress has lagged
theory in combining ultracold atoms and novel nanophotonic devices. As illustrated in Fig-
ure 1, a grand challenge for experiments 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
manuscript we describe an apparatus that provides several significant advances relative to
prior technical capabilities, that are summarized as follows:
1. Silicate bonding – We have previously used large manipulators inside conventional
stainless steel chambers for mounting our Silicon chips illustrated in Figure 2a. This method
2
FIG. 1. Schematic for building nanoscopic atomic arrays with one atom per unit cell in (a)
1-D alligator photonic crystal waveguide (APCW)
15,19
and (b) 2-D honeycomb lattice PCW
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
posed several limitations in our previous experiments
15,16,21
, including mechanical and ther-
mal instability, complexity in fiber alignment and assembly, and limitations on baking tem-
perature and out-gasing due to various epoxy resins and bonding agents used for “gluing”
optical fibers to Silicon chips and chips to vacuum mounting hardware. Following discus-
sions 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 II, 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
technique has extremely low out-gassing properties compared to our previous chip mount-
ing configurations and enables high temperature baking of our vacuum cell for ultra-high
vacuum (UHV) operation.
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 twenty fold to facilitate long-lived
guided-mode optical traps
20
, and enable high-temperature baking for improved atom trap-
ping 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 chamber directly into individual PCWs. As described in Section III, we have re-
moved the need for in-vacuum fibers by designing and 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 apertures (N.A.)
0
.
1
0
.
2 of the new Y-couplers
22
.
3
FIG. 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 II. (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
28
.
3. A new laboratory – Free-space coupling and silicate bounding 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 IV, our experiment is in the spirit of recent worldwide advances with
free-space tweezer arrays
23–26
but adds the significant complexity 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
4
and ‘new’
28
systems side by side. Of course, small glass cells with volume
1 cm
3
for
various optical 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
2(b, c) when the difficult constraints of localization of atoms near PCWs have been part of
the setup
28
.
II. SILICATE BONDING
FIG. 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 5 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.
In previous atom-nanophotonic experiments
15–17,21
in the Quantum Optics Group at Cal-
tech, 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
, as shown in Figure 2a. This posed three major limitations in our previous exper-
iments: 1) The long mechanical arm did not have sufficient mechanical stability, thereby
5
limiting the ability for precise positioning of atoms on nanophotonic structures and dissi-
pation of guided mode heating power. 2) Fiber coupling of light into and out of the chip
involved 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 number of vacuum feedthroughs available (8 input plus 8 output 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 gluing fibers and the chip
prohibited the possibility of significantly baking the entire vacuum chamber. As a result,
the typical lifetime for atoms trapped near (
300
μ
m) the chip was limited to be
.
100
ms
16
.
Here, by adapting the silicate bonding method
31
whose reliability 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 chamber, and also the need of all
optical fibers within the vacuum envelope.
The hydroxide catalysis bonding method of Ref. 32 involves strong chemical bonds be-
tween 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 minimiz-
ing Fresnel reflections from the bonded surfaces and allowing low-loss optical 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 operation,
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
bonding ranges from cryogenic to beyond typical bake-out temperatures 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 photographs of various stages of the sequence. Figure 3a shows
6
FIG. 4. (a) 3D model drawings of Fused Silica glass table assembly with Silicon chip with three
different perspective views. (b,c,d,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.
the glass tables upon which 200
μ
m thick (4
×
9 mm) Silicon chips will be bonded via three
effective contact surfaces as in (b-c) using rods and spheres as well as hemispheres in (a).
Here we consider the case of hemispheres for which three 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
λ/
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 fabricated by Starna
34
shown in Figure
4(e). 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 written into a 200 nm sacrificial
layer of Silicon Nitride deposited on the 200
μ
m thin Silicon substrate
19
, so that considerable
care is required to avoid damage to the surface containing the devices. Without the use of
additional optical elements, the bare divergence angle of the light emerging from the nano-
7
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.
III. THE Y-COUPLER TECHNOLOGY
In this section, we present a description of the new “Y-coupler” design which pro-
vides efficient free-space coupling, minimal light scattering and better mechanical stabil-
ity. This design 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
μ
m Silicon substrate. Pre-
cision grooves aligned to the waveguide device 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 waveguide input coupler widens the design
space available for coupler designs. Here, we present a Y-coupler design that simultaneously
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 perpendic-
ular to the waveguide
19
, as shown in the SEM image in Figure 5a (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 perpen-
dicular 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 distributions causing
physical movements of the junction. These pose a significant constraint for achieving guided
mode traps at magic wavelengths for Cs with a typical power handling
10 mW, well
8
beyond the
0.5 mW limit found for conventional couplers in Refs. 19 and 38.
FIG. 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. Insert is a SEM image of device under simulation with the Gaussian mode
input indicated as a red arrow.
To overcome this limitation, an unconventional Y-shaped termination 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 waveguide
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
9
loss due to the tethers, as shown in Figure 5b (i) and (ii) with vectorial illustrations for
conventional coupler with 90
tethers and the Y-coupler, respectively. 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 from below is shown in Figure 5c.
Coupling efficiencies of a 1
/e
2
waist
w
0
2
.
5
μ
m beam with different input polarizations to
different couplers are calculated from FDTD simulations and are summarized in Table I. 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 correlation measurements in nanophotonics
15
. In experiment, we have
measured a coupling efficiency up to 80% for TE input using the Y-coupler design
28
.
TABLE I.
FDTD simulated transmission and reflection efficiencies for different 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 mW 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 intensities required for larger atomic detunings, including for magic-wavelength
traps
20,35
.
While the detailed physics of device failure and plastic deformation 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 physically 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, compatible
10
0
3
6
9
12
P
in
[
mW
]
0
2
4
6
8
P
out
[
mW
]
(a)
0
5
10
15
20
25
P
out
[
mW
]
2
.
32
2
.
34
2
.
36
2
.
38
2
.
40
F
[
MHz
]
(b)
FIG. 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.
with typical ratios of the yield strength of Silicon Nitride to its Young’s modulus.
IV. 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 Ref. 15 and 21 that direct loading 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 and 17 by reflecting a waist 1
/e
2
w
0
60
μ
m dipole trap beam (the so-called side-illumination beam). However, the average trapped
atom numbers
̄
N
is restricted to
3 atoms and the trap size along the APCW is
10
μ
m
(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
11
FIG. 7. A simplified AutoCAD
R
©
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).
atom assembly on the PCWs with each single atom precisely positioned with respect to
the nanophotonic structures as in Figure 1. In this section, 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
polarization gradient cooling (PGC)
41
to cool the dense atom cloud to
10
μ
K 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 the source cell, with total
12
delivery efficiency
20% which is limited 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
μm
)
3
with temperature
'
20
μ
K.
FIG. 8. (a) (i) 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. The vertical blue dashed line sets the threshold of
detecting 1 atom. Inserted (ii) and (iii) indicate the typical image on EMCCD for ‘0’ atom and ‘1’
atom, respectively. Inserted (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 a
atom inside the tweezer is 25 s for vacuum cell after baking. (b) (i) Image of scattered light from
tweezer spots when aligned with the APCW, collected through the same tweezer objective. (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 tweezer sites with a 1.26
μ
m 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).
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
w
0
'
1
.
26
±
0
.
15
μ
m. After 30 ms of PGC and loading into the tweezer array, we
turn off the PGC beams for 50ms to let background atoms drop away and then turn on the
13
same PGC beams (15 MHz red detuned from D2,
F
= 4
5
transition) to illuminate the
trapped atoms for 50 ms. As shown in Figure 8a (i), (ii) and (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
FIG. 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
μ
K trapped atoms
in a 1 mK tweezer trap. (b) A COMSOL
R
©
42
simulation of the tweezer trap when aligned on
PCWs with tweezer focus position at
z
=
1
μ
m 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)
μ
m with
initial temperature
50
μ
K. (c) Probability of transferring into different reflective traps at different
tweezer focus positions along z direction, with atom initial temperature
T
i
= 20
μ
K. (d) Probability
of transferring into
z
1
trap at different atom initial temperatures at 1 mK tweezer trap.
14
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 approximately 3 mm away from
the surface of the Silicon chip. Due to the relatively long trap lifetime and flexibility afforded
by external 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
<
t <
0
.
1 s by mounting the tweezer objective on a precision linear translation stage
(model Physik Instrumente V-522, 20 nm unidirectional repeatability) 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 survival probability
P
s
by transporting single atoms from the
loading zone to a target position near the PCW (∆
t
'
0
.
1 s), holding still at target position
for
'
0
.
1 s, and then moving back (∆
t
'
0
.
1 s) to the loading zone for a second fluorescence
imaging. In this measurement, a specific target position is chosen to be
10
μ
m away from
the APCW (along
y
axis) and in the APCW’s
x
y
plane, as indicated by the green dots
in Figure 9a. Given an initial measurement 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 success 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
2 s.
Examples of atom loading into 6 and 17 tweezer sites far from the APCW are shown in
Figure 8b (iii) and (iv). Figure 8b (i) displays the reflection of multiple tweezer spots from
the APCW with the target 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 discussed in Section V.
After transport of the 1D trapped atoms array to the target position
10
μ
m from the
15
PCW, the single atom 1D array will be further transferred into reflective traps near the
dielectric surface 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 and 25, now
within the setting of the APCW. As illustrated in Figure 9a, moving the entire tweezer array
vertically along the
y
direction is achieved by sweeping the RF drive frequency for a second
AOD with axis along
y
orthogonal 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)
μ
m with
the atom initial temperature
50
μ
K.
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 temperature 20
μ
K. The simulated probability of transferring
into the
z
1
trap is peaked at
100% between
z
=
1
μ
m and
z
=
1
.
7
μ
m which indicates
a relatively large tolerance of tweezer focus 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
μ
K, 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
μ
m. 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 and 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.
16
V. TOWARDS HIGHER OPTICAL RESOLUTION
TABLE II.
Waist benchmark of higher N.A. objectives.
f and W.D. mean focal length and
working distance, respectively.
N.A.
f
W.D. Input waist Waist in air Waist in vacuum
(mm) (mm)
(mm)
(
μ
m)
(
μ
m)
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
Our current apparatus can be improved in terms of optical resolution for both imaging and
smaller trap volume. It can accommodate 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
focal length lens. (ii) A knife-edge experiment
48
with a razor blade glued inside a fused silica
cell with inner dimensions of 2 cm by 1 cm. The objective is moved on a two-dimensional
motorized stage to scan along and perpendicular to the light propagation direction. The
Rayleigh range and tweezer waist can be fitted from the transmitted 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 reflection 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
μ
m and consistent within 10%.
Table II 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 thickness 1.25 mm
and Mitutoyo G Plan Apo 100X, compensated for glass thickness 1 mm). The tweezer waists
can reach 1.02
μ
m for
N.A.
= 0
.
67 objective and sub-
μ
m for
N.A.
= 0
.
7 objective. It shows
that the differences for tweezer waists in air and under vacuum are negligible for all three
17
FIG. 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
μ
m, indicated
as white dashed circle with radius = 0.7
μ
m. 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).
different NA objectives and thus the bowing effect of the glass cell does not significantly
contribute to the tweezer aberration.
In Figure 10a, we show an image of the APCW inside a glass cell imaged with
N.A.
= 0
.
7
objective under broadband illumination 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.
VI. 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
5 cm
3
with an associated drop in pressure
>
100x, and 3) deterministic,
mechanical delivery of 1
D
single-atom tweezer arrays to near an APCW. Each of these
18
advances eliminates significant impediments present in prior experiments in the Quantum
Optics Group at Caltech as explained in previous sections.
The advanced atom-nanophotonic platform that we have described can provide a foun-
dation for realizing nanoscopic atomic lattices in 1
D
and 2
D
as envisioned in Figure 1 and
thereby for experimental explorations of these systems involving
strong interactions between
atoms and photons
in nanophotonic structures as described in Ref. 1 and 2. Attaining de-
terministic 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 be-
tween 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 itself to more easily deployable
quantum technologies that are of growing interest in the community. Possible applications of
these nanophotonic systems range from quantum communication using strong atom-photon
interactions to probing unconventional quantum phase transitions and investigating quan-
tum metrology applications by combining the functionality of nanophotonics and atoms. One
example relates to ongoing investigations 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, 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 dielectric 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 manuscript. In terms of an outlook for closing the aforementioned gap
described in the introduction between experiment and theory (e.g., Ref. 1), there are two
issues to address. The first is the development of an apparatus 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
19
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 experiment 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
(
ν
1
) for an
atom trapped within the vacuum gap to the rate Γ
of atomic spontaneous decay to all
other modes is
P
= Γ
max
1
D
(
ν
1
)
/
Γ
'
1
.
4. Here the notation is as described in Ref. 17, with
ν
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
(
ν
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 detuning of 20 GHz from the band edge, with
the possibility to observe 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 described in this manuscript for placing two tweezer-trapped atoms
precisely along the SPCW, 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 of-
fers 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.
ADDITIONAL ACKNOWLEDGEMENTS
The authors thank John Hall and Jun Ye (JILA), Julien Laurat (Sorbonne University),
Norma Robertson (Caltech), Keith Hulme (Starna), Jeff Gabriel (PI) and Craig Goldberg
(Newport) for important discussions.
20