Josephson plasma oscillations and the Gross-Pitaevskii equation: Bogoliubov approach vs two-mode model
arXiv:1607.02908 · doi:10.1103/PhysRevA.95.023627
Abstract
We show that the Josephson plasma frequency for a condensate in a double-well potential, whose dynamics is described by the Gross-Pitaevskii (GP) equation, can be obtained with great precision by means of the usual Bogoliubov approach, whereas the two-mode model - commonly constructed by means of a linear combinations of the low-lying states of the GP equation - generally provides accurate results only for weak interactions. A proper two-mode model in terms of the Bogoliubov functions is also discussed, revealing that in general a two-mode approach is formally justified only for not too large interactions, even in the limit of very small amplitude oscillations. Here we consider specifically the case of a one-dimensional system, but the results are expected to be valid in arbitrary dimensions.
arXiv commentLatex, 8 pages, 5 figures; improved discussion, new fig. 3
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