VOLUME 80, NUMBER 2 PHYSICAL REVIEW LETTERS 12 JANUARY 1998
Many-Body Effects in a Frozen Rydberg Gas
I. Mourachko, D. Comparat, F. de Tomasi, A. Fioretti, P. Nosbaum,* V. M. Akulin,
²
and P. Pillet
Laboratoire Aimé Cotton, CNRS II, Bât. 505, Campus d’Orsay, 91405 Orsay Cedex, France
(Received 4 August 1997)
We studied the properties of a cold (100 mK) and dense (10
8 10
cm
23
) atomic Rydberg Cs gas,
and found that the observed widths and shapes of resonances in population transfers cannot be explained
in the framework of a usual gas model. We propose a “frozen Rydberg gas” model, where the interplay
between two-body and many-body phenomena affects in an unexpected way the width and the shape of
spectral lines. [S0031-9007(97)04903-X]
PACS numbers: 32.80.Rm, 32.80.Pj, 34.60. + z
Recent demonstrations of Bose-Einstein condensation
have pointed out the role of collisional processes in the
evaporative cooling method [1 – 3]. Relatively dense cold
atomic samples have revealed, in turn, a rich variety of
new phenomena in atomic collision [4], and in particular
a strong excitation exchange effect. Usually one expands
the physical characteristics of a gas in the power series in
density that corresponds to one-, two-, three-, etc., body
phenomena. The excitation exchange is governed by the
two-body interactions, whereas the many-body effects in
sparse systems are usually considered as small. But does
such a gas at low temperature and density remain a sparse
system? In this Letter we show that the situation may
change completely for an ensemble of ultracold atoms
when the typical collision time considerably exceeds the
time corresponding to the inverse of typical interaction
energy between two neighboring atoms. In this regime
the many-body phenomena play an equally important role.
Observation of such phenomena becomes possible due
to the recent development of a laser cooling technique,
which brings new tools for atomic and molecular physics.
We report the first results of experiments performed
with cold cesium atoms in Rydberg states along with a
theoretical model and show how the interplay between
two-body and many-body processes affects, in an unex-
pected way, the width and the shape of the resonances in
the population transfer induced by the energy exchange.
The fact that the excited Cs atoms obtained by pulsed
laser irradiation are slow and are excited to high Rydberg
states plays the crucial role: the large size, the large dipole
moment, and the long lifetime of the Rydberg atoms allow
one to reach experimental conditions where many-body
phenomena become important.
The atomic sample contains N
d
10
8
10
10
highly ex-
cited Cs atoms per cm
3
at a temperature T 100 mK in a
chosen Rydberg p-state with the principal quantum num-
ber n 20 30. The typical displacement DR yt
10 300 nm of atoms moving at an average velocity y
10 cms during the experiment time of t 0.1 3 ms is
much less than the average distance R 34p N
d
13
5 20 mm between neighboring atoms. It is of the same
order of magnitude as the size of the Rydberg orbits R
0
4n
2
a.u. 80 nm (for n 20), whereas the nuclear
de Broglie wavelength is about l
dB
30 nm. It means
that one can ignore completely the motion of atoms
and consider the atomic ensemble as a “frozen Rydberg
gas” [5].
We trace the number of atoms in s states created in the
energy exchange process [7]
Cs
A
np
32
1 Cs
B
np
32
! Cs
A
ns 1 Cs
B
n 1 1s ,
(1)
when one of the atoms A makes a downward transition
from the Rydberg state jnp
32
to a lower Rydberg state
jns
12
, whereas the other atom (B) makes an upward
transition jnp
32
!jn 1 1s
12
. For each of the atoms
it corresponds to an allowed dipole transition, and hence
the typical interaction V
AB
m
A
m
B
R
3
AB
depends on the
matrix elements m
A
and m
B
of the dipole moment and the
distance R
AB
between the atoms. The reaction of Eq. (1)
is tuned into resonance by a Stark shift of the p
32
state in
the static electric field E , as is shown in the level scheme
in Fig. 1(a). Aside from the creation of ss
0
couple, that
is, two s states in Eq. (1), the processes of excitation
exchange with other atoms (C, D, etc.)
Cs
C
np
32
1 Cs
A
ns ! Cs
C
ns 1 Cs
A
np
32
Cs
D
np
32
1 Cs
B
n 1 1s ! Cs
D
n 1 1s (2)
1 Cs
B
np
32
are also possible. They are always resonant and have the
same order of magnitude as the process in Eq. (1) but do
not create new ss
0
couples. They allow for the migration
of s states over the “frozen” atoms. We therefore have
to consider a novel quantum system of Rydberg atoms at
rest, which evolves in the course of the energy exchange
processes Eqs. (1) and (2). One can say in the spirit of the
concept of quasiparticles that the ss
0
couples are created
and that each of the s states independently moves over a
media of a frozen Rydberg gas. This system resembles
an amorphous glass, where the centers are randomly
distributed over the sample.
The basic scheme of the experiment is as follows.
The cold Cs atoms are produced in a vapor-loaded MOT
cell [8] created at the intersection of three pairs of
mutually orthogonal, counterpropagating s
1
2s
2
-laser
0031-9007 98 80(2) 253(4)$15.00 © 1998 The American Physical Society 253