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Strong Interactions of Single Atoms and Photons near a Dielectric Boundary
D. J. Alton,
1,
N. P. Stern,
1,
Takao Aoki,
2
H. Lee,
3
E. Ostby,
3
K. J. Vahala,
3
and H. J. Kimble
1
1
Norman Bridge Laboratory of Physics MC 12-33,
California Institute of Technology, Pasadena, California 91125, USA
2
Department of Physics, Kyoto University, Kyoto, Japan
3
T. J. Watson Laboratory of Applied Physics MC 128-95,
California Institute of Technology, Pasadena, California 91125, USA
Modern research in optical physics has achieved quantum control of strong interactions between
a single atom and one photon within the setting of cavity quantum electrodynamics (cQED)
1
.
However, to move beyond current proof-of-principle experiments involving one or two conventional
optical cavities to more complex scalable systems that employ
N

1 microscopic resonators
2
requires the localization of individual atoms on distance scales
.
100nm from a resonator’s surface.
In this regime an atom can be strongly coupled to a single intracavity photon
3
while at the same
time experiencing significant radiative interactions with the dielectric boundaries of the resonator
4
.
Here, we report an initial step into this new regime of cQED by way of real-time detection and
high-bandwidth feedback to select and monitor single Cesium atoms localized
100 nm from the
surface of a micro-toroidal optical resonator. We employ strong radiative interactions of atom and
cavity field to probe atomic motion through the evanescent field of the resonator. Direct temporal
and spectral measurements reveal both the significant role of Casimir-Polder attraction
5
and the
manifestly quantum nature of the atom-cavity dynamics. Our work sets the stage for trapping atoms
near micro- and nano-scopic optical resonators for applications in quantum information science,
including the creation of scalable quantum networks composed of many atom-cavity systems that
coherently interact via coherent exchanges of single photons
2
.
The proximity of dielectric boundaries fundamentally
alters atomic radiative processes as compared to quan-
tum electrodynamics in free space. For example, free-
space Lamb shifts and Einstein-
A
coefficients (i.e., level
positions and decay rates) are modified for atom-surface
distances comparable to the relevant transition wave-
lengths, as considered in the pioneering analyses of
Casimir and Polder
5
and of Purcell
6
in the late 1940s.
Seminal experiments in the 1970s investigated radiative
decay for organic dye molecules near a metal mirror
7
and were followed in the 1980s by landmark observations
of the inhibition of spontaneous emission for a trapped
electron
8
and an atom in a waveguide
9
. The ensuing
years have witnessed the development of cavity quantum
electrodynamics (cQED) in this
perturbative
regime of
boundary-modified linewidths and level shifts
4,10,11
, with
applications ranging from measurements of fundamental
constants
12
to the development of novel semiconductor
devices
13
.
With increased interaction strength, a
non-perturbative
regime of cQED becomes possible and is character-
ized not by irreversible decay but rather by the cyclic,
reversible exchange of excitation between atom and
photon
14
.
The experimental quest for strong atom-
photon coupling had its initial success in 1985 in the mi-
crowave regime with the realization of the micromaser
15
,
with strong coupling in the optical domain achieved some
years later
16
. By now the coherent control of atomic ra-
diative dynamics has become possible on a photon-by-
photon basis
1,17
. Strong coupling has also been demon-
strated for a wide class of physical systems
18
beyond
single atoms, including quantum dots coupled to mi-
cropillars and photonic bandgap cavities
19
and Cooper-
pairs interacting with superconducting resonators
20,21
.
This non-perturbative regime of cQED with strong light-
matter interactions mediated by single photons has led to
new scientific capabilities, ranging from a laser that oper-
ates with one-and-the-same atom
22
to the deterministic
generation of entangled photon pairs
23
to a two-qubit su-
perconducting quantum processor
24
.
To a large degree, advances in the perturbative and
non-perturbative regimes of cQED have been made inde-
pendently. For example, for one atom localized near the
center of a Fabry-Perot cavity with volume (
l
)
3
(10
μ
m)
3
, the coherent coupling
g
to an optical resonance
can be large compared to radiative decay character-
ized by the Einstein-
A
coefficient and cavity loss rate
κ
,
namely
g

(
γ
0
) where
γ
0
=
A/
2, placing the system
in the regime of strong, non-perturbative atom-photon
coupling
1
. Nevertheless, corrections to the atomic Lamb
shift and Einstein-
A
coefficient arising from surface in-
teractions with the cavity boundaries remain small (e.g.,
δA/A
10
5
). However, many applications in Quan-
tum Information Science could benefit from strong atom-
photon interactions with micro- and nano-scopic optical
resonators
25–28
. Atomic localization on a sub-wavelength
scale near a resonator’s surface is then required, with as-
pects of both perturbative and non-perturbative cQED
necessarily coming into play.
In this manuscript we investigate such a regime for
single Cesium atoms radiatively coupled to a high-
Q
mi-
crotoroidal cavity
3,26
and localized near the resonator’s
dielectric surface. As illustrated in Fig. 1a, cold Cesium
atoms are released from an optical dipole-force trap and
randomly fall past the microtoroid. A real-time detection
scheme based upon strong radiative interactions between
one atom and the evanescent field of the cavity selects
atomic trajectories localized within
d
.
300 nm from
arXiv:1011.0740v1 [quant-ph] 2 Nov 2010
2
Cs
Cs cloud
10
12
14
-2
0
2
z
m)
ρ (μ
m)
U
/
ћγ
0
20
40
0
400
800
1
1.5
2
γ/γ
0
z
g
/
1
-1
0
80
40
0
d
(nm)
40
20
P
in
z
=
0
U
s
U
( )
d
Δ
=
0
ca
γ
γ
P
T
P
R
(a)
(b)
(c)
γ
0
0
U
( )
d
Δ
= 15γ
ca
0
U
( )
d
Δ
= -15γ
ca
0
g
/
γ
0
0
g
/
γ
0
φ
ρ
r
(
t
)
(i)
(ii)
(iii)
FIG. 1.
Radiative interactions and optical potentials
for an atom near the surface of a toroidal resonator.
a,
Simple overview of the experiment showing a cloud of cold
Cesium atoms that is released with then a few atoms falling
near a microtoroidal resonator. Light in a tapered optical
fiber excites the resonator with input power
P
in
at frequency
ω
p
, leading to transmitted and reflected outputs
P
T
,P
R
.
b,
Cross section of the microtoroid at
φ
= 0 showing the coher-
ent coupling coefficient
|
g
(
~r
) =
g
(
ρ,z,φ
)
|
for a TE polarized
whispering-gallery mode. The microtoroid has principal and
minor diameters (
D
p
,D
m
) = (24
,
3)
μ
m, respectively.
c,
(i)
Coherent coupling
|
g
(
d,z,φ
)
|
for the external evanescent field
as a function of distance
d
=
ρ
D
p
/
2 from the toroid’s sur-
face for (
z,φ
) = (0
,
0). (ii) The effective dipole potentials
U
d
for resonant
ω
p
=
ω
(0)
a
, red
ω
p
< ω
(0)
a
and blue
ω
p
> ω
(0)
a
free-
space detunings of the probe
P
in
. The Casimir-Polder surface
potential
U
s
for the ground state of atomic Cs is also shown.
(iii) The atomic decay rate
γ
(
d
) as a function of distance
d
from the toroid’s surface for TE (
γ
) and TM (
γ
) modes.
All rates in this figure are scaled to the decay rate in free
space for the amplitude of the Cs 6
P
3
/
2
6
S
1
/
2
transition,
γ
0
/
2
π
= 2
.
6 MHz. The approximate distance scale probed in
our experiment is 0
< d <
300 nm.
the resonator’s surface, with a large fraction of atoms
passing below 100 nm and crashing into the surface.
On this scale, the atom’s coherent interaction with the
cavity field is characterized by strong, non-perturbative
coupling [Fig. 1b, 1c(i)], which we demonstrate by di-
rect measurements of so-called “vacuum-Rabi” spectra
for light transmitted and reflected by the atom-cavity
system, as well as by observations of photon antibunch-
ing for the transmitted light. On the other hand, the
atom’s motion and level structure are significantly in-
fluenced by the (perturbative) Casimir-Polder potential
from the surface’s proximity [Fig. 1c(ii)], which we infer
from measurements of the time dependence of the cavity
transmission during an atomic transit event, as well as
from modifications of the spectra recorded for the trans-
mitted and reflected fields. These observations are in
reasonable agreement with a theoretical model that we
have implemented by Monte-Carlo simulation and which
gives insight into the underlying atomic dynamics, as de-
tailed in Ref. 29.
For the identification of atoms near the surface of the
microtoroid in the regime shown in Fig. 1c, we rely on the
strong interaction of atom and cavity field to modify the
light transmitted by the cavity. Specifically, because the
atom-cavity coupling coefficient
g
(
~r
(
t
)) depends upon
the atomic trajectory
~r
(
t
), we can select single atoms lo-
calized in the cavity mode by demanding a minimum
criterion for the change in cavity transmission due to
the atomic trajectory. Our scheme for single-atom detec-
tion is similar to that used in previous work
3,30,31
, but
with significant modifications. Namely, by implementing
fast digital logic, we achieve reliable real-time identifica-
tion of atomic transit events in times as short as 250 ns
from the photoelectric counts from the transmitted power
P
T
(
t
). Given the identification of a localized atom, the
control logic switches the power
P
in
and frequency
ω
p
of
the probe input within
'
100 ns and records subsequent
photoelectric counts for the transmitted
P
T
(
t
) and re-
flected
P
R
(
t
) outputs from the cavity. These records of
photoelectric counts form the basis for our analysis that
follows, with further details presented in the Appendix
and Supplementary Information (SI).
To address experimentally the question of the distance
scale for the recorded atom transit events, we first ex-
amine the time dependence of the cavity transmission
T
(
t
) immediately following a trigger heralding the ar-
rival of an atom into the cavity mode. Figure 2a shows
T
(
t
) =
P
T
(
t
)
/P
in
for the case of resonant excitation,
namely ∆
pa
=
ω
p
ω
(0)
a
= 0 and ∆
ca
=
ω
c
ω
(0)
a
= 0,
where
ω
(0)
a
is the free-space atomic frequency for the
6
S
1
/
2
,F
= 4
6
P
3
/
2
,F
= 5 transition in atomic Cs
and
ω
c
is the resonant frequency of the toroidal cav-
ity. Two characteristic decay times are evident, with the
background subtracted transmission
T
B
(
t
)
T
(
t
)
B
fitted well by the sum of an exponential (
e
t/δt
I
)
with
δt
I
= 0
.
78
±
0
.
02
μ
s and a Gaussian (
e
(
t/δt
II
)
2
)
with
δt
II
= 3
.
75
±
0
.
09
μ
s. Here, the background level
B
T
(
t

δt
I,II
) is determined from the cavity trans-
mission for times long compared to the duration of the
transit event.
The time constants
δt
I
,δt
II
can be associated with dis-
tance scales
d
I
,d
II
by way of the average velocity ̄
v
with
which atoms arrive at the toroid’s mode following release
from the optical trap, namely ̄
v
0
.
17 m/s, leading to
d
I
'
130 nm and
d
II
'
640 nm. For comparison, the scale
length for
g
(
d
) in the radial direction is
λ
= 1
/k
0
= 136
nm (Fig. 1c(i)), while in the vertical direction, the vari-
ation of
g
(
z
) is approximately Gaussian (
e
(
z/w
0
)
2
)
with waist
w
0
'
590 nm (Fig. 1b). The comparisons
d
I
λ
and
d
II
w
0
suggest that the short-lived compo-
nent
δt
I
in Fig. 2a arises from atomic trajectories that