16 August 1999
Ž.
Physics Letters A 259 1999 178–184
www.elsevier.nlrlocaterphysleta
External noise effects in laser cooling: Inversion of
electronic-vibrational states and gain
G.Yu. Kryuchkyan
a,b,c,1
, B. Kneer
a
a
Abteilung fur Quantenphysik, UniÕersitat Ulm, D-89069 Ulm, Germany
¨¨
b
YereÕan State UniÕersity, Alex Manookian 1, 375049 YereÕan, Armenia
c
Institute of Physical Research, Armenian National Academy of Sciences, 378410 Ashtarak-2, Armenia
Received 18 January 1999; received in revised form 26 April 1999; accepted 19 June 1999
Communicated by P.R. Holland
Abstract
We investigate the effect of external white noise to resolved-sideband cooling of a single trapped ion. By studying the
equilibrium state of the ion beyond the Lamb–Dicke limit, we find population inversion between electronic-vibrational
states. Furthermore, we study the effect of gain on the emitted radiation of the system. q1999 Published by Elsevier Science
B.V. All rights reserved.
PACS: 42.50.Vk; 32.80.Pj; 42.55.-f
Keywords: Laser cooling; population inversion; trapping of atoms; white noise; absorption spectrum; amplification of light
1. The problem
Laser cooling to the ground state of the center-
of-mass motion has been realized experimentally for
single trapped ions by using sideband-cooling tech-
wx
niques 1 . Sideband cooling of an ion confined in a
harmonic trap is achieved by tuning a laser beam to
the low-frequency sideband of an internal transition.
This effect of cooling certainly takes place in the
Ž. wx
Lamb–Dicke L-D limit 2 , where the spatial width
a of the ground state is much smaller than the
0
1
Fax: q49 731 5023086, E-mail: kry@physik.uni-ulm.de or
Fax: q37 42 151097, E-mail: kry@ipr.sci.am.
wavelength
l
of the cooling laser, i.e. the L-D
L
parameter
h
s2
p
a r
l
<1. The other require-
0L
ment for sideband cooling is the strong confinement
limit, where the width
g
of the internal excited state
is much smaller than the trap frequency
n
, i.e.
g
<
n
. Therefore, the motional sidebands are spec-
troscopically resolved.
The preparation of the motional ground state by
resolved-sideband cooling is always the start-up for
experiments on the generation of Fock, coherent,
wx
squeezed, and Schrodinger cat states 3 . Further-
¨
more, this ability is the basis for theoretical propos-
als of the preparation of arbitrary motional and en-
wx
tangled quantum states 4 . Moreover, ground-state
laser-cooling is important for the realization of quan-
0375-9601r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved.
Ž.
PII: S0375-9601 99 00421-1