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Title: Mode locking of a driven Bose-Einstein condensate

Abstract

We consider the dynamics of a driven Bose-Einstein condensate with positive scattering length. Employing an accustomed variational treatment we show that when the scattering length is time modulated as a(1+{epsilon} sin[{omega}(t)t]), where {omega}(t) increases linearly in time, i.e., {omega}(t)={gamma}t, the response frequency of the condensate locks to the eigenfrequency for small values of {epsilon} and {gamma}. A simple analytical model is presented which explains this phenomenon by mapping it to an auto-resonance, i.e., close to resonance the reduced equations describing the collective behavior of the condensate are equivalent to those of a virtual particle trapped in a finite-depth energy minimum of an effective potential.

Authors:
; ;  [1];  [2];  [3]
  1. Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100 (Denmark) and Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
  2. (Denmark)
  3. (United States)
Publication Date:
OSTI Identifier:
21072402
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevE.75.036208; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN CONDENSATION; EIGENFREQUENCY; MODE LOCKING; POTENTIALS; RESONANCE; SCATTERING LENGTHS; SOLITONS; TRAPPING; VARIATIONAL METHODS; VIRTUAL PARTICLES

Citation Formats

Nicolin, Alexandru I., Jensen, Mogens H., Carretero-Gonzalez, R., Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100, and Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720. Mode locking of a driven Bose-Einstein condensate. United States: N. p., 2007. Web. doi:10.1103/PHYSREVE.75.036208.
Nicolin, Alexandru I., Jensen, Mogens H., Carretero-Gonzalez, R., Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100, & Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720. Mode locking of a driven Bose-Einstein condensate. United States. doi:10.1103/PHYSREVE.75.036208.
Nicolin, Alexandru I., Jensen, Mogens H., Carretero-Gonzalez, R., Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100, and Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720. Thu . "Mode locking of a driven Bose-Einstein condensate". United States. doi:10.1103/PHYSREVE.75.036208.
@article{osti_21072402,
title = {Mode locking of a driven Bose-Einstein condensate},
author = {Nicolin, Alexandru I. and Jensen, Mogens H. and Carretero-Gonzalez, R. and Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100 and Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720},
abstractNote = {We consider the dynamics of a driven Bose-Einstein condensate with positive scattering length. Employing an accustomed variational treatment we show that when the scattering length is time modulated as a(1+{epsilon} sin[{omega}(t)t]), where {omega}(t) increases linearly in time, i.e., {omega}(t)={gamma}t, the response frequency of the condensate locks to the eigenfrequency for small values of {epsilon} and {gamma}. A simple analytical model is presented which explains this phenomenon by mapping it to an auto-resonance, i.e., close to resonance the reduced equations describing the collective behavior of the condensate are equivalent to those of a virtual particle trapped in a finite-depth energy minimum of an effective potential.},
doi = {10.1103/PHYSREVE.75.036208},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}