We report the first measurement of the real-time evolution of the complex field amplitude brought on by single atom transits. We show the variation in time of both quadrature amplitudes (simultaneously recorded) of the light transmitted through the cavity, as well the resultant optical phase for a single atom transit event. In this particular measurement, the cavity and laser were both detuned by 10 MHz from the Cs resonance

Chapman, M. S.

Hood, C. J.

Kimble, H. J.

Lynn, T. W.

Mabuchi, H.

Ye, J.

English

Caltech Authors - Main

6 / lQEC'98 / MONDAY MORNING 
behavior was observed for the mode located at 
point S. However, a slight decrease in the sec- 
ondary amplitude (transition R + Q) leads to 
the instability gain g,, - 2 q l  a1 ( 1 - A) ( lacrl 1 - 
l a ~ ) / ~ a c r l ~ ( l  + h), < 1, la/ < lacrll, and the 
SLM gets unstable [Fig. 2(b)]. Another type of 
unstable evolution is shown in Fig. 2(c). It 
takes place for SLM located in region I11 with 
the gain g,,, - z / ( a  - a,,)/2. 
The asymmetric SLM propagates stable if 
the ratio of peak amplitudes AIB exceeds some 
critical value. Therefore, a slight change in the 
peak amplitude in the vicinity of this point 
destroys the mode. Because of an "intrinsic 
bias" of the mode, this SLM decays more rap- 
idly than the symmetric twisted modes. Hence, 
using such modes in all-optical signal process- 
ing seems to be also promising, because less 
power is needed to switch the output state. 
1. A. Aceves et al., Phys. Rev. E 53, 1172 
(1996) (and references therein). 
QMB4 9:15 am 
Directional coupling with optical vortex 
soliton pair 
C.T. Law, X. Zhang, G.A. Swartzlander, Jr.,* 
Department of Electrical Engineering and 
Computer Science, University of Wisconsin, 
Milwaukee, Wisconsin 53201 
An optical vortex is a distinctive waveform that 
has a dark circular core on a bright back- 
ground. Seen from head on, a beam with an 
optical vortex appears as a bright doughnut of 
light. The dark core is the result of destructive 
interference caused by a 257 phase ramp above 
the core, another characteristic of optical vor- 
tex. Very similar to hurricanes or tornadoes, 
optical vortices in linear medium' eventually 
dissipate. In other words, diffraction causes 
expansion ofvortex core and washes awayvor- 
tices. Owing to the special intensity profile of 
vortices, linear optical vortices have been used 
in trapping and guiding small particles.2 In a 
nonlinear medium, such as self-defocusing 
Kerr material, the nonlinear refractive index 
induced by the vortex intensity profile coun- 
teracts diffraction. As a result, a stable and 
stationary core with well-defined size is 
formed inside a light beam. Because the core is 
immune from instability and its size remains 
constant with propagation distance, this opti- 
cal vortex is the only known cylindrical soliton 
in Kerr media,3 so-called optical vortex soli- 
tons (OVSs). 
We have demonstrated the propagation of 
an OVS in the center of a green Ar ion laser 
beam in a self-defocusing nonlinear medium. 
The dark core of an OVS has actually a grade 
refractive-index profile, which is the imprint 
of the OVS in the nonlinear medium. Inside 
the dark core where there is no light, the refrac- 
tive index maintains its linear value, no, while 
the refractive index under the influence of the 
bright background is reduced to a smaller 
value, no - I n21 I,, where I , ,  is the background 
intensity, and nz is the nonlinear refractive- 
index coefficient. In our first experiment, the 
guiding of an He-Ne (red) beam within an 
OVS was demonstrated. The guiding of a light 
beam of different polarization with an OVS is 
also possible.* 
The light-induced fiber provides a means 
for light-light interaction, such as optical 
switching and modulation.5 Moreover, the 
well-defined core size of an OVS enables a 
natural extension of hydrodynamics to optics. 
The fluidlike motion of OVS has been demon- 
strated experimentally,6 with phase and inten- 
sity profile of an OVS behaving like the flow 
potential and density of a fluid, respectively. 
One way to induce OVS motion is to introduce 
another OVS. Owing to the interaction be- 
tween two vortices, they will either spiral 
round each other (if they have the same circu- 
lation directions) or drift together (ifthey have 
opposite circulation directions). Another 
method is to modify the background intensity 
and leads to attraction or repulsion between 
vortices. 
We have performed numerical experiments 
that simulate the copropagation of OVS pairs 
with a weak guided beam of various intensity 
profiles. Our results confirm that OVS pairs 
with the same circulation direction rotate 
about the center of axis between the two vorti- 
ces. Their rate of rotation with respect to 
propagation distance is close to the theoretical 
limit, 2/k, 8, where k, is the wave number, and 
d is the separation between two vortices. This 
limit becomes exact if the core size is infinitesi- 
mally small. In other words, the rotation 
strength decreases as the core size increases. 
Our numerical experiments also demon- 
strate that the weak guided beam follows the 
rotation of the OVS. If the propagation dis- 
tance is long enough, we can realize a spatial 
switch with more than 90". Moreover, each 
vortex in an OVS pair behaves like an isolated 
entity in terms of waveguiding when the spac- 
ing between vortices is more than five times the 
core size. When the spacing between vortices is 
small, complete switch over of guided beam 
from one OVS to another, i.e., directional cou- 
pling, is possible. The directional coupling can 
enhance the spatial switching effect under cer- 
tain conditions. Various means, including 
wavelength of the guided beam, spacing, and 
guided beam size, to optimize the directional 
coupling as well as the spatial switching effect 
will be discussed. 
This work was supported by the National 
Science Foundation. 
*Department of Physics, Worcester Polytechnic 
Institute, Worcester, Massachusetts 01 609-2280 
1. N.B. Baranova, A.V. Mamaev, N.F. Pili- 
petsky,V.V. Shkunov, B. Ya. Zel'dovich, J. 
Opt. Soc. Am. 73,525 (1983). 
K.T. Gahagan, G.A. Swartzlander, Jr., Opt. 
Lett. 21,827-829 (1996). 
G.A. Swartzlander, Jr., C.T. Law, Phys. 
Rev. Lett. 69,2503 (1992);R.Y. Chiao, I.H. 
Deutsch, J.C. Garrison, E.M. Wright, in 
Serge Akhmanov: A Memorial Volume, H. 
Walther, ed. (Adam Hilger, Bristol, 1992); 
A.W. Snyder, I. Poladian, D.J. Mitchell, 
Opt. Lett. 17, 789 (1992). 
C.T. Law, G.A. Swartzlander, Jr., CHAOS 
4, 1759 (1994). 
G.A. Swartzlander, Jr., D.L. Drugan, N. 
Hallak, M.O. Freeman, C.T. Law, Laser 
Phys. 5,704 (1995). 
6. G.A. Swartzlander, Jr., D. Rozas, Z.S. 
Sacks, Fluid-Like Motion of Optical Vorti- 
ces, Phys. Rev. Lett. (to be published). 
2. 
3. 
4. 
5. 
8:OO am-10:OO am 
Room 270-276 
QMC 
Cavity QED/Trapped Atoms 
G. Rempe, Universztat Konstanz, Germany, 
Presider 
QMCl (Invited) 8:OO am 
Real-time cavity QED with single atoms 
C.J. Hood, T.W. Lynn, H. Mabuchi, M.S. 
Chapman, J. Ye, H.J. Kimble, Cultech 12-33, 
Pasadena, Californza 91 125 
The use of laser-cooling techniques in optical 
cavity QED' effects a dramatic separation of 
dynamical timescales, with the coherent inter- 
action rate go dominating over both the cavity 
field decay rate K and the atomic dipole decay 
rate yI, which are in turn much larger than 
rates T' associated with atomic motion 
through the spatially varying cavity eigen- 
mode. Belowwe describe two separate ongoing 
experiments that explore phenomena 
uniquely accessible in this regime of true cou- 
pling. 
Photon-covalent binding of one atom and an 
optical cavity: A very small high-finesse optical 
cavity gives us the highest coupling go in an 
optical system to date: (go, K, yI, T1)/257 = 
(120, 40, 2.6, 0.002) MHz. Our first experi- 
ment exploits this strong coupling to confine 
single atoms in a cavity field with 5 1  photon. 
Sub-photon intracavity fields can be used to 
trap atoms because weak excitation by a coher- 
ent probe tuned to A - -go gives rise to a 
pseudo-potential with depth figo/kB 7 mK 2 
time ( 8 )  
time (S) 
QMCl Fig. 1. Example of atom trapping us- 
ing the quantized cavity field. The probe beam 
shown has A / ~ T  = - 100 MHz and is triggered 
ON by the entrance of an atom into the cavity 
mode, as discussed in the text. (a) An atom transit 
where mechanical effects are not important (ki- 
netic energy dominates coupling strength). (b) A 
localized atom: the atom stays strongly coupled 
for -300 ps, after which it exits the cavity and the 
probe transmission returns to the lower empty 
cavity level. Maximum dwell times in the absence 
of mechanical effects are T -  100 bs. 
MONDAY MORNING / IQEC'98 / 7 
QMCl Fig. 2. Real-time evolution of the 
complex field amplitude, brought by single atom 
transits. A,B,C represent atom positions. Larger 
detunings from the atomic resonance will elicit 
more dominant responses in the phase quadra- 
ture. 
KEacOmz. In this context, the quantity ?zg,lk, 
may be interpreted as a covalent atom-cavity 
binding energy associated with the oscillatory 
exchange of a single photon. Experimentally, 
an atom entering the cavity mode causes a 
drop in transmission of a first probe beam 
close to resonance; this signal is used to trigger 
OFF the resonant beam and trigger ON a sec- 
ond probe beam at A - g, to create a trapping 
potential. Figure 1 shows an example of an 
atom which has been held in the cavity field for 
>300 ps, whereas the longest possible transit 
times expected without mechanical effects are 
=IO0 ps. Such data demonstrate the use of 
strong coupling to exercise significant control 
over the system's evolution. 
Our continuing work addresses the issue of 
lengthening the atom-cavity interaction time 
in order to perform arbitrary coherent ma- 
nipulation of the system. Atom dwell times in 
the cavity may be increased by cooling the 
atomic motion in the cavity mode structure. 
One possible mechanism involves a Sisyphus- 
like force induced by the cavity's finite re- 
sponse time to a moving atom.5 Another av- 
enue for cooling is to use our real-time atomic 
trajectory information to feed back to the 
atom-cavity system by modulating the well 
depth to cool the atom. Yet another approach 
to long interaction times would be to trap the 
atom via a dipole trapping scheme with far- 
detuned probe light. In general our investiga- 
tions of this system are enabled by the realiza- 
tion of a very high single-atom cooperativity 
C, = d ( 2 ~ 7 , ) ~ '  - 70. Detection of light 
leaving the system via cavity decay yields dy- 
namical information which can be used to 
QMCl Fig. 3. Simultaneous recording of 
both quadratures ofthe complex amplitude of the 
cavity output field (10 kHz filter bandwidth). An 
optical phase shift of 1 rad is the result of a single 
atom transit with the probe detuned by -10 
MHz. 
achieve real-time control of the coupled atom- 
cavity system. 
Continuous measurement ofsingle-atom tra- 
jectories: In an independent apparatus with (go, 
K ) / ~ T  = (1 1,3.5) MHz, the cavityleakage field 
is continuously observed to estimate the intra- 
cavity motion of individual atoms. In hopes of 
eventually reaching the Standard Quantum 
Limit for monitoring the position of a free 
mass, we minimize the measurement back ac- 
tion on the CM motion by detuning the probe 
field from atomic re~onance.~ The experimen- 
tal protocol then involves determination of the 
phase of the output field with shot-noise-lim- 
ited accuracy and bandwidth. Our technical 
achievements in this regard should enable in- 
vestigation of the strong conditioning of sys- 
tem evolution on measurement results and the 
realization of quantum feedback contr01.~ 
Here we report the first measurement ofthe 
real-time evolution of the complex field ampli- 
tude brought by single atom trasits (see Fig. 2). 
Figure 3 shows the variation in time of both 
quadrature amplitudes (simultaneously re- 
corded) of the light transmitted through the 
cavity, as well the resultant optical phase for a 
single atom transit event. In this particular 
measurement, the cavity and laser were both 
detuned -10 MHz from the Cs resonance. 
Notice the 1 radian optical phase shift caused 
by a single atom. At -50 MHz detuning we 
observe a phase shift of 0.5 rad and a signal-to- 
noise ratio about 3 at 300 kHz bandwidth, very 
near the shot noise limit. With improved con- 
trol over the initial atomic center-of-mass 
states, the achieved SNR-bandwidth should 
enable direct observation of single-atom CM 
oscillations within potential wells associated 
with the dipole force exerted by the cavity field 
itself (-5- 10 photons). 
1. H. Mabuchi et al ,  Opt. Lett. 21, 1393 
( 1996). 
2. A.S. Parkins, unpublished notes (1995). 
3. P. Storey et al., Phys. Rev. Lett. 68, 472 
( 1992). 
4. H.M. Wiseman et al., Phys. Rev. Lett. 70, 
548 (1993). 
5. P. Horak et al., Phys. Rev. Lett. 79, 4974 
(1997). 
QMCZ 8:30 am 
Engineering the vibronic coupling of a 
trapped atom 
R.L. de Matos Filho, W. Vogel, Arbeitsgruppe 
Quantenoptik, Fachbereick Pkysik, Universitat 
Rostock, Universitatsplatz 3, D - 18051 
Rostock, Germany 
The recent progress in trapping and cooling of 
atoms allowed us to prepare and to measure 
various nonclassical states of atomic motion.' 
These methods make use of the laser-assisted 
vibronic interaction of the trapped atom. The 
interaction Hamiltonian for the laser being 
resonant to the kth vibrational sideband reads 
in the interaction picture asz 
I?inc = kOLazl jk (A)dk  + H.c., (1) 
where A( A) depends on the vibrational num- 
ber operator A = dtd as 
Here, a,, (i ,  j = 1,2) and d, respectively, are the 
electronic (two-level) flip operator and the an- 
nihilation operator of a quantum of the vibra- 
tional motion, q is the Lamb-Dicke parameter, 
and OL is the Rabi frequency. The dependence 
of the Hamiltonian on the vibrational number 
operator opens several applications, includ- 
ing quantum nondemoliton measurements, 
quantum computing, and nonlinear coherent 
states. However, these applications are limited 
by the given form of the function fk( i r ) .  
To overcome this limitation, we present a 
scheme that allows one to engineer the excita- 
tion dependence of the Hamiltonian.' It con- 
sists in the excitation of the kth vibrational 
sideband of the atom by N lasers of the same 
frequency but of arbitrary Rabi frequencies Oj 
and Lamb-Dicke parameters q,( j = 1, . . . , N). 
The latter can be controlled by the geometry of 
excitation. In this case the Hamiltonian reads 
(3) I?,", = hnRAzl&(A)dk + H.C., 
R, is a reference Rabi frequency and 
A! 
X- 
(A - I ) !  ' (4) 
-0.21 I 
%{a) 
- 4  -2  0 2 4 
QMCZ Fig. 1. The Wigner function W 
(Re{a},Im{a}) atIm{a} = Oisshownforaneven 
coherent state for different values of the ampli- 
tude p: theoretical curve (full line), measurement 
using the engineering method (dotted line), and 
measurement using the method of Ref. 3 (shaded 
line). 


Real-time cavity QED with single atoms

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Real-time cavity QED with single atoms

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