INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL
J. Phys. A: Math. Gen. 36 (2003) L409–L415 PII: S0305-4470(03)63087-8
LETTER TO THE EDITOR
Trapping of particles by lasers: the quantum
Kapitza pendulum
Ido Gilary
1
, Nimrod Moiseyev
1
, Saar Rahav
2
and Shmuel Fishman
2
1
Department of Chemistry and Minerva Center of Nonlinear Physics in Complex Systems,
Technion—Israel Institute of Technology, Haifa 32000, Israel
2
Department of Physics and Minerva Center of Nonlinear Physics in Complex Systems,
Technion—Israel Institute of Technology, Haifa 32000, Israel
Received 6 May 2003
Published 12 June 2003
Online at stacks.iop.org/JPhysA/36/L409
Abstract
It is demonstrated that a bound rapidly oscillating potential typically traps
particles even if its time average vanishes. In particular, it is shown that in
one dimension there is always a resonance state and its energy and lifetime are
calculated from an effective time-independent potential. This is the quantum
analogue of the classical Kapitza pendulum. This work may be relevant for
the manipulation of cold atoms and for the suppression of photo-ionization by
electromagnetic fields.
PACS numbers: 32.80.Pj, 03.65.Xp, 03.65.Nk, 42.50.Hz
The effect of trapping and cooling of particles, specifically atoms, is of great interest due to
the applicability in fields such as atom optics, precision spectroscopy, optical communication,
and in the developing field of quantum computing [1].
In this letter we will demonstrate that typically a rapidly oscillating, smooth, bounded
one-dimensional potential with vanishing average leads to trapping of particles. This sounds
counter intuitive since one may expect that because of the high energy of the photons the
particles will rapidly obtain energy that will be sufficient to overcome any potential barrier.
It will be demonstrated that this is not the case and the situation is similar to that found in
classical mechanics, where stabilization by a rapidly oscillating potential with vanishing mean
is possible.
Trapping of a classical particle can be achieved by introducing an external rapid time
periodic potential V(q,t) = V
0
(q) + V
1
(q,t) [2, 3]. The classical particle is trapped by an
effective time-independent potential which is approximately given by
V
eff
(q) = V
0
(q) + F
2
(q)/(2mω
2
) (1)
where F
2
(q) is the time average of the square of the force F =−∂V
1
(q,t)/∂q , which
is exerted by the oscillating field V
1
(q,t) = V
1
(q,t + T), where T = 2π/ω and its time
average
¯
V
1
vanishes. In this case the trapping is obtained when the frequency of the external
oscillatory field, ω, is much larger than the frequency of the bound motion or the inverse
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