Phys. Rev. E 75, 036208 (2007) [5 pages]Mode locking of a driven Bose-Einstein condensateReceived 21 September 2006; revised 6 November 2006; published 13 March 2007 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+ϵ sin[ω(t)t]}, where ω(t) increases linearly in time, i.e., ω(t)=γt, the response frequency of the condensate locks to the eigenfrequency for small values of ϵ and γ. 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. © 2007 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.75.036208
DOI:
10.1103/PhysRevE.75.036208
PACS:
05.45.Xt, 03.75.Nt
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