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Title: Transition to instability in a periodically kicked Bose-Einstein condensate on a ring

Abstract

A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor, where the nonlinearity stems from the mean-field interactions between the condensed atoms. For weak interactions, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. In the stable regime, the system remains predominantly in the two lowest energy states and may be mapped onto a spin model, from which we obtain an analytic expression for the beat frequency and discuss the route to instability. We numerically explore a parameter regime for the occurrence of instability and reveal the characteristic density profile for both condensed and noncondensed atoms. The Arnold diffusion to higher energy levels is found to be responsible for the transition to instability. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.

Authors:
 [1];  [2]; ;  [3];  [2];  [3]
  1. Institute of Applied Physics and Computational Mathematics, Beijing 100088 (China)
  2. (United States)
  3. Department of Physics, University of Texas, Austin, Texas 78712-1081 (United States)
Publication Date:
OSTI Identifier:
20786743
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.73.013601; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; BOSE-EINSTEIN CONDENSATION; CHAOS THEORY; DIFFUSION; ENERGY LEVELS; INSTABILITY; MEAN-FIELD THEORY; NONLINEAR PROBLEMS; PERIODICITY; SPIN; STRONG INTERACTIONS; WEAK INTERACTIONS

Citation Formats

Liu Jie, Department of Physics, University of Texas, Austin, Texas 78712-1081, Zhang Chuanwei, Raizen, Mark G., Center for Nonlinear Dynamics, University of Texas, Austin, Texas 78712-1081, and Niu Qian. Transition to instability in a periodically kicked Bose-Einstein condensate on a ring. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Liu Jie, Department of Physics, University of Texas, Austin, Texas 78712-1081, Zhang Chuanwei, Raizen, Mark G., Center for Nonlinear Dynamics, University of Texas, Austin, Texas 78712-1081, & Niu Qian. Transition to instability in a periodically kicked Bose-Einstein condensate on a ring. United States. doi:10.1103/PHYSREVA.73.0.
Liu Jie, Department of Physics, University of Texas, Austin, Texas 78712-1081, Zhang Chuanwei, Raizen, Mark G., Center for Nonlinear Dynamics, University of Texas, Austin, Texas 78712-1081, and Niu Qian. Sun . "Transition to instability in a periodically kicked Bose-Einstein condensate on a ring". United States. doi:10.1103/PHYSREVA.73.0.
@article{osti_20786743,
title = {Transition to instability in a periodically kicked Bose-Einstein condensate on a ring},
author = {Liu Jie and Department of Physics, University of Texas, Austin, Texas 78712-1081 and Zhang Chuanwei and Raizen, Mark G. and Center for Nonlinear Dynamics, University of Texas, Austin, Texas 78712-1081 and Niu Qian},
abstractNote = {A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor, where the nonlinearity stems from the mean-field interactions between the condensed atoms. For weak interactions, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. In the stable regime, the system remains predominantly in the two lowest energy states and may be mapped onto a spin model, from which we obtain an analytic expression for the beat frequency and discuss the route to instability. We numerically explore a parameter regime for the occurrence of instability and reveal the characteristic density profile for both condensed and noncondensed atoms. The Arnold diffusion to higher energy levels is found to be responsible for the transition to instability. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 1,
volume = 73,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}