of 11
Superradiance for atoms trapped along a photonic crystal waveguide
A. Goban
1
,
2
,
, C.-L. Hung
1
,
2
,
,
, J. D. Hood
1
,
2
,
, S.-P. Yu
1
,
2
,
,
J. A. Muniz
1
,
2
, O. Painter
2
,
3
, and H. J. Kimble
1
,
2
,
1
Norman Bridge Laboratory of Physics 12-33
2
Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, USA and
3
Thomas J. Watson, Sr., Laboratory of Applied Physics 128-95
(Dated: March 17, 2015)
We report observations of superradiance for atoms trapped in the near field of a photonic crystal waveguide
(PCW). By fabricating the PCW with a band edge near the D
1
transition of atomic cesium, strong interaction
is achieved between trapped atoms and guided-mode photons. Following short-pulse excitation, we record the
decay of guided-mode emission and find a superradiant emission rate scaling as
̄
Γ
SR
̄
N
·
Γ
1D
for average
atom number
0
.
19
.
̄
N
.
2
.
6
atoms, where
Γ
1D
/
Γ
0
= 1
.
1
±
0
.
1
is the peak single-atom radiative decay rate
into the PCW guided mode and
Γ
0
is the Einstein-
A
coefficient for free space. These advances provide new
tools for investigations of photon-mediated atom-atom interactions in the many-body regime.
Interfacing light with atoms localized near nanophotonic
structures has attracted increasing attention in recent years.
Exemplary experimental platforms include nanofibers [1, 2],
photonic crystal cavities [3] and waveguides [4, 5]. Owing
to their small optical loss and tight field confinement, these
nanoscale dielectric devices are capable of mediating long-
range atom-atom interactions using photons propagating in
their guided modes. This new paradigm for strong interac-
tion of atoms and optical photons offers new tools for scalable
quantum networks [6], quantum phases of light and matter
[7, 8], and quantum metrology [9].
In particular, powerful capabilities for dispersion and
modal engineering in nanoscopic photonic crystal waveguides
(PCWs) provide opportunities beyond conventional settings
in AMO physics within the new field of
waveguide QED
[1, 2, 5, 10–12]. For example, the edge of a photonic band gap
aligned near an atomic transition strongly enhances single-
atom emission into the one-dimensional (1D) PCW due to a
van-Hove singularity at the band edge (i.e., a ‘slow-light’ ef-
fect [13–15]). Because the Bloch function for a guided mode
near the band edge approaches a standing-wave, symmet-
ric optical excitations can be induced in an array of trapped
atoms, resulting in superradiant emission [16, 17] into the
PCW. Superradiance has important applications for realizing
quantum memories [18–22], single photon sources [23, 24],
laser cooling by way of cooperative emission [25, 26], and
narrow linewidth lasers [27].
Related cooperative effects
are predicted in nano-photonic waveguides absent an exter-
nal cavity [28], including atomic Bragg mirrors [29] and self-
organizing crystals of atoms and light [30–32].
Complimentary to superradiant emission is the collective
Lamb shift induced by proximal atoms virtually exchanging
These authors contributed equally to this research.
Present address: Purdue University, West Lafayette, IN 47906,
USA
Correspondence and requests for materials should be addressed to
HJK (hjkimble@caltech.edu.)
off-resonant photons [33–36]. With the atomic transition fre-
quency placed in a photonic band gap of a PCW, real photon
emission is largely suppressed. Coherent atom-atom interac-
tions then emerge as a dominant effect for QED with atoms in
bandgap materials [37–42]. Both the strength and length scale
of the interaction can be ‘engineered’ by suitable band shap-
ing of the PCW, as well as dynamically controlled by external
lasers [41, 42]. Exploration of many-body physics with tun-
able and strong long-range atom-atom interactions are thereby
enabled [41, 42].
In this Letter, we present an important advance for the field
of waveguide QED. We describe an experiment that cools, sta-
bly traps, and interfaces multiple cold atoms along a quasi
one-dimensional PCW. Through precise band edge alignment
and guided-mode (GM) design, we achieve strong radiative
coupling of one trapped atom and a GM of the PCW, such
that the inferred single-atom emission rate into the GM is
Γ
1D
/
Γ
0
= 1
.
1
±
0
.
1
, where
Γ
1D
is the peak single-atom ra-
diative decay rate into the PCW guided mode and
Γ
0
is the
Einstein-
A
coefficient for free space. With multiple atoms, we
observe superradiant emission in both time and frequency do-
mains with measurements of transient decay following pulsed
excitation and steady-state transmission spectra, respectively.
We infer cooperative, superradiant coupling with rate
̄
Γ
SR
that
scales with the mean atom number
̄
N
as
̄
Γ
SR
=
η
̄
N
·
Γ
1D
over
the range
0
.
19
.
̄
N
.
2
.
6
atoms, where
η
= 0
.
34
±
0
.
06
.
Our experimental platform is based on trapped cesium
atoms near a 1D alligator photonic crystal waveguide
(APCW) [4, 5]. The APCW is formed by two parallel SiN
nanobeams separated by 238 nm with periodic corrugations
at the outer edges (Fig. 1(a)). The APCW consists of
150
identical unit cells with lattice constant
a
= 371
nm (length
L
'
55
.
7
μ
m) and is terminated at either end by
30
tapered
cells for mode matching to parallel nanobeams without cor-
rugation. Photons can be coupled into and out of the APCW
from conventional cleaved-fibers at either end of the structure.
Design principles, fabrication methods, and device character-
ization of the APCW can be found in Refs. [4, 5, 44].
For the APCW used here, we align the band edge of
the fundamental guided mode (electric field predominantly
arXiv:1503.04503v1 [physics.optics] 16 Mar 2015
2
transverse-electric (TE) polarized in the plane of the waveg-
uide) near the cesium D
1
line at 894.6 nm, with a mode-
matched TE input field
E
in
tuned around the
6
S
1
/
2
, F
=
3
6
P
1
/
2
, F
= 4
transition. Near the band edge, the atom-
photon coupling rate is significantly enhanced by the group in-
dex
n
g
, as well as by reflections from the tapering regions that
surround the APCW. From the measured transmission spec-
trum of the device absent atoms, we estimate a group index
n
g
'
11
and an intensity enhancement
E
I
6
from the taper
reflections [44].
To trap atoms along the APCW, we create tight optical po-
tentials using the interference pattern of a side-illumination
(SI) beam and its reflection from the surface of the APCW
[3, 44]. The polarization of the SI beam is aligned paral-
lel to the
x
-axis of the 1D waveguide to maximize the re-
flected field. Figure 1(b) shows the calculated near-field in-
tensity distribution in the
y
-
z
plane [45]. With a red-detuned
SI beam, cold atoms can be localized to intensity maxima
(e.g., positions
z
1
,z
1
,z
2
in Fig. 1(b)). However, because
of the exponential falloff of the GM intensity, only those
atoms sufficiently close to the APCW can interact strongly
with guided-mode photons of the input field
E
in
, Fig. 1(c).
y
(
μ
m
)
z
(
μ
m
)
1
0
1
1
0
1
10
-3
10
-2
10
-1
1
10
1
0
1
1
0
1
0.2
0.4
0.6
0.8
1
0
y
(
μ
m
)
z
(
μ
m
)
SI
E
in
rE
in
tE
in
APCW
(a)
(b)
(c)
z
1
z
2
z
-1
1D
x
500 nm
0
x
y
z
FIG. 1: Trapping and interfacing atoms with a 1D photonic crys-
tal waveguide. (a) A side-illumination (SI) beam is reflected from
an ‘alligator’ photonic crystal waveguide (APCW) to form a dipole
trap to localize atoms near the APCW (gray shaded structure). The
red shaded region represents trapped atoms along the APCW. An in-
cident field
E
in
excites the TE-like fundamental mode and thereby
trapped atoms couple to this guided mode (GM). The transmitted
tE
in
and reflected field
rE
in
are recorded. The inset shows an SEM
image of the APCW and corresponding single-atom coupling rate
Γ
1D
along the
x
axis at the center of the gap (
y
= 0
). (b) Normal-
ized intensity cross section of the total intensity
I
tot
resulting from
the SI beam and its reflection, which form an optical dipole trap.
Trap locations along the
z
axis at
y
= 0
are marked by
z
i
. Masked
gray areas represent the APCW. (c) The single-atom coupling rate
into the TE guided mode
Γ
1D
(0
,y,z
)
normalized to the free-space
decay rate
Γ
0
for the cesium D
1
line.
0
20
40
60
80 100
0.0
0.2
0.4
0.6
0.8
1.0
0
20
40
60
80
0.7
0.8
0.9
1.0
(a)
(b)
FIG. 2: Lifetime of trapped atoms near the APCW. (a)
1
/e
-lifetime
of
τ
fs
= 54
±
5
ms is determined using free-space absorption imaging
of the trapped atom cloud. (b)
1
/e
-lifetime of
τ
GM
= 28
±
2
ms is
observed from the normalized transmission
T/T
0
of resonant GM
probe pulses.
The trap site with the strongest atom-photon coupling is lo-
cated at
(
y
1
,z
1
) = (0
,
220)
nm, closest to the center of the
unit cell and
z
120
nm from the plane of the upper sur-
faces of the APCW. Other locations are calculated to have
coupling to the fundamental TE-like mode less than
1%
of
that for site
z
1
(e.g., the sites at
z
1
,z
2
have intensity ratios
I
(
z
1
)
/I
(
z
1
) = 0
.
01
,I
(
z
2
)
/I
(
z
1
) = 0
.
005
).
Along the
x
axis of the APCW, the dipole trap
U
(
x,
0
,z
1
)
is
insensitive to the dielectric corrugation within a unit cell and
is nearly uniform to within
<
2%
around the central region
of the APCW. By contrast, atom emission into the fundamen-
tal TE-like mode is strongly modulated with
Γ
1D
(
x,
0
,z
1
)
'
Γ
1D
cos
2
(
kx
)
due to the Bloch mode function near the band
edge of the APCW (
k
π/a
), as shown in the inset of
Fig. 1(a). Thus, even for atoms uniformly distributed along
the
x
axis of the trapping potential, only those close to the
center of a unit cell can strongly couple to the guided mode,
greatly facilitating phase-matched symmetric excitation of the
atoms. In our experiment, we have chosen a 50
μ
m waist for
the SI beam to provide weak confinement along the
x
axis,
with atoms localized near the central region (
x
10
μ
m)
of the APCW for the estimated temperature
50
μ
K from a
time-of-flight measurement in free space. The SI beam for
dipole trapping is 220 GHz red-detuned with respect to the
D
2
line and has a total power of 50 mW for all measurements
reported.
Cold atoms from a MOT that surrounds the APCW [5] are
loaded into the dipole trap during an optical molasses phase
(
5
ms) and then optically pumped to
6
S
1
/
2
,
F
= 3
for
1
ms. Atoms are held in the dipole trap for time
t
hold
relative to
the end of the loading sequence, and then free-space absorp-
tion imaging is initiated over the interval (
t
hold
, t
hold
+ ∆
t
m
)
with
t
m
= 0
.
2
ms.
We introduce the measured time
t
m
=
t
hold
+ ∆
t
m
/
2
, centered in the measurement window.
As shown in Fig. 2(a), we measure a trap lifetime
τ
fs
= 54
±
5
ms and find a peak density
ρ
0
2
×
10
11
cm
3
near the
APCW. The atom density
ρ
near the APCW can be adjusted
over a wide range
0
.
06
.
ρ/ρ
0
6
1
by varying the duration
of the MOT loading cycle while keeping all other procedures
identical.
To determine the lifetime for trapped atoms near the
APCW, we again hold atoms for
t
hold
, and then launch
E
in
3
as a resonant GM probe in measurement interval
t
m
±
t
m
/
2
with
t
m
= 5
ms. From the recorded transmitted signals, we
compute
T/T
0
, where
T
0
is the transmission without atoms.
During the probe period, we also apply free-space repump
beams, tuned to the D
2
,
6
S
1
/
2
, F
= 4
6
P
3
/
2
, F
= 4
resonance, to remove population in the
6
S
1
/
2
,
F
= 4
, since
the probe excites an open transition. Fig. 2(b) shows
T/T
0
gradually recovering to
T/T
0
= 1
as
t
m
increases, with a fit
to the data giving a
1
/e
time of
τ
GM
= 28
±
2
ms [44].
τ
GM
is consistently shorter than
τ
fs
from free-space imaging, which
might be attributed to increased heating from the stronger light
intensity near the APCW, the effect of surface potentials, or
outgassing from the silicon chip and structures that support
the APCW. These contributions are being investigated in more
detail.
Our principal investigation of superradiance involves ob-
servation of the transient decay of emission from an array of
atoms trapped along the APCW. For a collection of
N >
1
atoms, superradiance is heralded by a total decay rate
Γ
tot
=
Γ
SR
+ Γ
(1)
tot
that is enhanced beyond the total rate of decay
for one atom
Γ
(1)
tot
= Γ
1D
+ Γ
.
Γ
SR
is the
N
-dependent su-
perradiant rate operationally determined from
Γ
tot
and
Γ
(1)
tot
.
Here,
Γ
is the radiative decay rate into all channels other
than the TE-like GM of the APCW. We numerically evalu-
ate
Γ
/
Γ
0
1
.
1
for an atom at the trap site
z
1
in Fig. 1(b)
along the APCW, with
Γ
0
the free-space decay rate for the D
1
transition [14, 46]. Cooperative level shifts
|
H
dd
| 
Γ
1D
are
neglected for the current configuration of our experiment [44].
We record the temporal profiles of atomic emission into
the fundamental TE-like GM following short-pulse (
10 ns
FWHM), resonant excitations via
E
in
. To ensure small popu-
lation in the excited state, we choose a pulse intensity well be-
low the saturation intensity (
I/I
sat
<
0
.
1
). After a time
t
hold
the excitation cycle is repeated every
500
ns for
t
m
= 6
ms,
and detection events are accumulated for the reflected inten-
sity
|
rE
in
|
2
by an avalanche photodiode (APD). We consider
decay curves of GM emission at
15 ns
< t
e
<
70
ns after the
center of the excitation pulse (i.e., after the excitation pulse
is sufficiently extinguished,
t
e
>
15
ns, and while the back-
ground counts are negligible compared to the atomic emis-
sion,
t
e
.
70
ns [44]). The total decay rate
̄
Γ
tot
is extracted
by simple exponential fits as shown in the inset of Fig. 3(a).
The deviation from the exponential fit at
t
e
&
60
ns is due
to the spatially varying coupling rate
Γ
1D
cos
2
(
kx
)
, which is
captured by a detailed model discussed later [44].
Enhanced total decay rate with increasing atom number is
clearly evidenced in Fig. 3(a), where the atom number can
be adjusted by varying trap hold time
t
hold
prior to the mea-
surement. At the shortest measurement time
t
m
= 3
ms with
t
hold
= 0
ms (i.e., the maximum number of trapped atoms),
the measured total decay rate is largest at
̄
Γ
tot
/
Γ
0
2
.
9
.
At
t
m
= 63
ms much longer than the trap lifetime
τ
GM
=
28
±
2
ms, the total decay rate settles to
̄
Γ
tot
/
Γ
0
2
.
0
. This
asymptotic behavior suggests that
̄
Γ
tot
at long hold time cor-
responds to the single-atom decay rate
̄
Γ
(1)
tot
.
0
10
20
30
40
50
60
2.0
2.2
2.4
2.6
2.8
3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
2.0
2.2
2.4
2.6
2.8
3.0
0
20
40
60
0.01
0.1
1
(a)
(b)
FIG. 3: Decay rate and atom number dependence (a) Fitted total de-
cay rate
̄
Γ
tot
normalized with free-space decay rate
Γ
0
(circles) as a
function of measurement time
t
m
. The solid line is a simple exponen-
tial fit to determine the superradiant decay rate
̄
Γ
SR
/
Γ
0
= 1
.
1
±
0
.
1
and the single-atom decay rate
̄
Γ
(1)
tot
/
Γ
0
= 2
.
0
±
0
.
1
with
τ
SR
=
17
±
3
ms. The inset shows the temporal profiles of normalized
guided-mode emission
I
p
/I
p0
(circles) with
I
p0
the peak emission.
Exponential fits (solid curves):
t
m
= 3
ms (red), 13 ms (green), and
63 ms (blue). The black dashed curve shows a exponential decay
with free-space decay rate
Γ
0
. (b) Fitted total decay rate
̄
Γ
tot
nor-
malized with
Γ
0
as a function of mean number of trapped atoms
̄
N
from a detailed model [44]. We adjust
̄
N
by changing the trap hold
time (red circles) or atom loading time (blue circles). The black line
is a linear fit to the combined data sets, giving
̄
Γ
SR
=
η
·
̄
N
·
Γ
1D
with
η
= 0
.
34
±
0
.
06
.
To determine quantitatively the superradiant and single-
atom emission rates from our measurements of decaying GM
emission, we present two different analyses that yield consis-
tent results. First is a simple and intuitive analysis applied
to Fig. 3(a) in which we employ an empirical exponential
fit,
̄
Γ
tot
(
t
m
) =
̄
Γ
SR
e
t
m
SR
+
̄
Γ
(1)
tot
, with the superradiant
̄
Γ
SR
, single-atom
̄
Γ
(1)
tot
, and
τ
SR
characterizing decay of su-
perradiance due to the atom loss. The fit yields the maximum
superradiant rate
̄
Γ
SR
/
Γ
0
= 1
.
1
±
0
.
1
with
τ
SR
= 17
±
3
ms, and a reasonable correspondence to the measured de-
cay rates
̄
Γ
tot
, as shown by the red curve in Fig. 3(a). The
asymptote
̄
Γ
(1)
tot
/
Γ
0
= 2
.
0
±
0
.
1
gives the total single-atom
decay rate. With
Γ
/
Γ
0
1
.
1
determined numerically for an
atom at trap site
z
1
along the APCW (Fig. 1(b)), we deduce
̄
Γ
1D
/
Γ
0
= 0
.
9
±
0
.
1
for the single-atom decay rate into the
GM of the APCW.
To substantiate this simple emphirical model, our second
analysis is a detailed number treatment based upon transfer
matrix calculations [44]. Decay curves are generated for a
4
fixed number of atoms
N
distributed randomly along along
the x-axis of the APCW with uniform probability density but
with spatially varying spatially varying coupling
Γ
1D
(
x
)
'
Γ
1D
cos
2
(
kx
)
. These
N
-dependent, spatially-averaged decay
curves are further averaged over a Poisson distribution with
mean atom number
̄
N
, capturing the variation of atom num-
ber
N
as we repeat experiments for data accumulation. Fitting
to this model, we extract
Γ
1D
/
Γ
0
= 1
.
1
±
0
.
1
for measure-
ments at long hold time (e.g., at
t
m
= 63
ms in Fig. 3(a)).
Since the intensity of the fluorescence from a single atom is
spatially modulated by
cos
4
(
kx
)
, only an atom near the cen-
ter of unit cell can strongly couple to the GM, resulting in the
small difference between averaged
̄
Γ
1D
and peak
Γ
1D
. Also,
the decay curve for GM emission at
t
m
= 3
ms can be well fit-
ted with
̄
N
= 2
.
6
±
0
.
3
atoms [44]. The red points in Fig. 3 (b)
display the total decay rate
̄
Γ
tot
as a function of
̄
N
extracted
from fits of the transfer matrix model to the measured decay
curves, which clearly shows that superradiance emission rate
is proportional to
̄
N
.
The value
Γ
1D
/
Γ
0
= 1
.
1
±
0
.
1
from our measurements
agrees reasonably well with the theoretical value
Γ
1D
/
Γ
0
1
.
2
determined by FDTD calculations [43, 44], despite sev-
eral uncertainties (e.g., locations of trap minima relative to
the APCW with uncertainty below
10
nm). The agreement
validates the absolute control of our fabrication process (in-
cluding the negligible effect of loss and disorder along the
APCW), as well as the power of the theoretical tools that we
have developed [14, 41, 42].
We confirm that the variation of
̄
Γ
tot
in Fig. 3(a) is not due
to the heating of atomic motion during the trap hold time. To
see this, we adjust
̄
N
via different MOT loading times and
measure the decay rate at the shortest hold time (
t
m
= 3
ms),
as shown by blue points in Fig. 3(b) . These observations
are consistent with those from varying the trap hold time (red
points in Fig. 3(b)), and lead to an almost identical single-
atom decay rate
̄
Γ
(1)
tot
/
Γ
0
= 2
.
0
±
0
.
1
at the shortest loading
time, corresponding to
ρ/ρ
0
= 0
.
16
and
̄
N

1
.
The data and our analysis related to Fig. 3 strongly support
the observation of superradiant decay for atoms trapped along
the APCW. Assuming
̄
Γ
tot
=
̄
Γ
SR
+
̄
Γ
(1)
tot
and fitting
̄
Γ
tot
lin-
early with
̄
N
, as shown in Fig. 3(b), we find that the superra-
diant rate is given by
̄
Γ
SR
=
η
·
̄
N
·
Γ
1D
with
η
= 0
.
34
±
0
.
06
.
The slope
η
is reduced below unity by the random distribution
of atoms along the
x
-axis [44].
This observation of superradiant decay is complemented by
line broadening for steady-state transmission spectra
T
(∆)
measured at
t
m
= 3
ms with
t
m
= 5
ms, as show in Fig.
4. The measured linewidths
̄
Γ
m
are significantly broader than
the free-space width (FWHM)
Γ
0
/
2
π
= 4
.
56
MHz [46], pre-
dominantly due to cooperative atomic coupling to the GM of
the APCW. We also observe a significant drop in
T/T
0
at line
center due to strong atom-photon coupling. Indeed, in Fig. 4
(a), we measure
T/T
0
'
0
.
30
(i.e., a
70%
attenuation of the
GM flux
|
E
in
|
2
) for maximum density
ρ
0
, and
T/T
0
'
0
.
95
at the lowest density investigated,
ρ/ρ
0
0
.
06
.
0
10
20
30
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
2.0
2.5
3.0
3.5
(a)
(b)
FIG. 4: Steady-state transmission spectra
T
(∆)
and fitted atomic
linewidth
̄
Γ
m
. (a)
T
(∆)
with
∆ = 0
corresponding to the free-space
line center. The three sets of points are measured at relative densities
ρ/ρ
0
= 0
.
12
(black), 0.24 (blue), and 1 (red), where the transmission
without atoms is
T
0
. Solid curves are Lorentzian fits to determine
the linewidth
̄
Γ
m
. Each point in the spectra is an average over 10
experiment repetitions. (b) Fitted linewidths (circles) normalized to
Γ
0
as a function of
ρ/ρ
0
. The solid line is a linear fit with intercept
of
̄
Γ
(1)
m
/
Γ
0
= 2
.
1
±
0
.
1
.
No clear density dependent shift is observed in Fig. 4(a),
in support of our neglect of cooperative energy shifts
|
H
dd
|
[44]. The shift in line center for
T
(∆)
from
∆ = 0
in free
space to
∆ = 14
MHz for atoms trapped along the APCW
is induced by the dipole trap. Furthermore, trapped atoms
should suffer small inhomogeneous broadening in the spec-
tra shown in Fig. 4, since the FORT shift is small (
<
1 MHz)
for the
6
P
1
/
2
,F
= 4
excited state, and atoms are well lo-
calized around the trap center due to their low temperature
T
50
μ
K, corresponding to a small range of light shifts
.
1
MHz for atoms in the ground state.
In Fig. 4 (b), we plot the linewidths
̄
Γ
m
extracted from
T
(∆)
as a function of
ρ/ρ
0
.
̄
Γ
m
/
Γ
0
3
.
4
is largest at
ρ/ρ
0
= 1
, and reduces to
̄
Γ
m
/
Γ
0
2
.
1
at
ρ/ρ
0
= 0
.
06
.
From linear extrapolation, the single-atom linewidth is esti-
mated to be
̄
Γ
(1)
m
/
Γ
0
= 2
.
1
±
0
.
1
. Absent inhomogeneous
broadening, we expect that
̄
Γ
(1)
m
=
̄
Γ
1D
+ Γ
. With the cal-
culated
Γ
/
Γ
0
1
.
1
, the single-atom coupling rate can be
simply deduced as
̄
Γ
1D
/
Γ
0
1
.
0
±
0
.
1
. A simple estimate
of the maximum mean number of atoms then follows from
̄
N
m
= (
̄
Γ
m
(
ρ
0
)
Γ
)
/
̄
Γ
1D
'
2
.
4
±
0
.
4
atoms [47].
In conclusion, we have used an integrated optical circuit
with a photonic crystal waveguide to trap and interface atoms
with guided photons. Superradiance for atoms trapped along
our APCW has been demonstrated and a peak single-atom
emission rate into the APCW of
Γ
1D
/
Γ
0
= 1
.
1
±
0
.
1
inferred.
5
Our current uniform trap along the APCW is a promising plat-
form to study optomechanical behavior induced by the inter-
play between sizable single-atom reflectivity and large opti-
cal forces (e.g., self organization [31, 32]). By optimizing the
power and detuning of an auxiliary guided mode field near the
air band of the APCW, it should be possible to achieve stable
atomic trapping and ground state cooling [48, 49] at trap sites
centered within the vacuum gap, thereby increasing
Γ
1D
five-
fold [14]. Opportunities for new physics in the APCW arise
by fabricating devices with the atomic resonance inside the
band gap to induce long-range atom-atom interactions [40–
42], thereby enabling investigations of novel quantum trans-
port and many-body phenomena.
Acknowledgements
We gratefully acknowledge the contri-
butions of D. J. Alton, D. E. Chang, K. S. Choi, J. D. Co-
hen, J. H. Lee, M. Lu, M. J. Martin, A. C. McClung, S. M.
Meenehan, L. Peng, and R. Norte. Funding is provided by the
IQIM, an NSF Physics Frontiers Center with support of the
Moore Foundation, and by the DoD NSSEFF program (HJK),
the AFOSR QuMPASS MURI, NSF PHY-1205729 (HJK) and
the DARPA ORCHID program. AG is supported by the Naka-
jima Foundation. SPY and JAM acknowledge support from
the International Fulbright Science and Technology Award.
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