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Journal of Low Temperature Physics

Quantum Field Theoretical Description of Dynamical Instability of Trapped Bose–Einstein Condensates

M. Mine, Masahiko Okumura, Tomoka Sunaga, Y. Yamanaka

Published May 29, 2007• 3 citations
Publisher
DOI
10.1007/s10909-007-9393-y

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We study the Bloch dynamics of a quasi-one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type. The corresponding mean-field system described by a discrete nonlinear Schr\"odinger equation can exhibit dynamical (or modulation) instability due to chaotic dynamics and equipartition over the quasimomentum modes. It is shown that these phenomena are related to Bogoliubov's depletion of the Bose-Einstein condensate and a decoherence of the condensate in the many-particle description. Three types of dynamics are distinguished: (i) decaying oscillations in the region of dynamical instability and (ii) persisting Bloch oscillations or (iii) periodic decay and revivals in the region of stability.