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arXiv:cond-mat/0108508 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Dynamic critical phenomena in trapped Bose gases

Vyacheslav I. Yukalov, Elizaveta P. Yukalova, Vanderlei Salvador Bagnato

Published May 9, 2001• 2 citations
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Abstract

Nonlinear dynamics of a trapped Bose-Einstein condensate, subject to the action of a resonant external field, is studied. This field produces a spatio-temporal modulation of the trapping potential with the frequency close to the transition frequency between the ground state and a higher energy level. The evolution equations of fractional populations display a kind of critical phenomena at a critical line on the manifold of the system parameters. It is demonstrated that there exists a direct analogy between dynamical instability at this line and critical phenomena at a critical line of a related averaged system.

DOI
10.1117/12.426688

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Nonlinear dynamics of a trapped Bose-Einstein condensate, subject to the action of a resonant external field, is studied. This field produces a spatio-temporal modulation of the trapping potential with the frequency close to the transition frequency between the ground state and a higher energy level. The evolution equations of fractional populations display a kind of critical phenomena at a critical line on the manifold of the system parameters. It is demonstrated that there exists a direct analogy between dynamical instability at this line and critical phenomena at a critical line of a related averaged system.
Nonlinear dynamics of a trapped Bose-Einstein condensate, subject to the action of a resonant external field, is studied. This field produces a spatio-temporal modulation of the trapping potential with the frequency close to the transition frequency between the ground state and a higher energy level. The evolution equations of fractional populations display a kind of critical phenomena at a critical line on the manifold of the system parameters. It is demonstrated that there exists a direct analogy between dynamical instability at this line and critical phenomena at a critical line of a related averaged system.
The population dynamics of a trapped Bose-Einstein condensate, subject to the action of an external field, is studied. This field produces a spatio-temporal modulation of the trapping potential with the frequency close to the transition frequency between the ground state and a higher energy level. For the evolution equations of fractional populations, a critical line is found. It is demonstrated that there exists a direct analogy between dynamical instability at this line and critical phenomena at a critical line of an averaged system. The related critical indices are calculated. The spatio-temporal evolution of atomic density is analyzed.
The population dynamics of a trapped Bose-Einstein condensate, subject to the action of an oscillatory field, is studied. This field produces a modulation of the trapping potential with the frequency close to the transition frequency between the ground state and an excited energy level. Unusual critical effects are found exhibiting sharp qualitative changes in the population dynamics. An effective averaged system is constructed explicitly illustrating the occurrence of critical phenomena. The related critical indices are calculated.
Nonlinear coherent modes are the collective states of trapped Bose atoms, corresponding to different energy levels. These modes can be created starting from the ground-state condensate that can be excited by means of a resonant alternating field. A thorough theory for the resonant excitation of the coherent modes is presented. The necessary and sufficient conditions for the feasibility of this process are found. Temporal behavior of fractional populations and of relative phases exhibits dynamic critical phenomena on a critical line of the parametric manifold. The origin of these critical phenomena is elucidated by analyzing the structure of the phase space. An atomic cloud, containing the coherent modes, possesses several interesting features, such as interference patterns, interference current, spin squeezing, and massive entanglement. The developed theory suggests a generalization of resonant effects in optics to nonlinear systems of Bose-condensed atoms.
Multiple mode couplings in topological coherent modes of Bose–Einstein condensate are considered, by introducing an external alternating (resonating) field in the system. This analysis is based on the analytical solutions of nonlinear Gross–Pitaevskii equation for a trapped Bose gas at nearly absolute zero temperature. The dynamics of fractional populations of the generated coherent modes are analysed, particularly for a three-level system in the limit of small to large detuning of the intermediate state. These coupled topological modes, though nonlinear, are analogous to a resonant atom and exhibit a variety of significant non-trivial phenomena (effects), like: dynamic phase transitions, interference patterns, critical phenomena, mode-locking and chaotic motion.
The resonant formation of nonlinear coherent modes in trapped Bose-Einstein condensates is studied. These modes represent nonground-state Bose condensates. The methods of describing the spectrum of the nonlinear modes are discussed. The latter can be created by modulating the trapping potential with a frequency tuned close to the transition frequency between the two chosen modes. The requirement that the transition amplitudes be smaller than the transition frequency implies a constraint on the number of particles that can be transferred to an excited mode. The resonant Bose condensate serves as a collective analog of a single resonant atom. Such a condensate, displaying the coherent resonance, possesses several interesting features, among which are: mode locking, critical dynamics, interference patterns, interference current, atomic squeezing, and multiparticle entanglement.