Josephson plasma oscillations and the Gross-Pitaevskii equation: Bogoliubov approach vs two-mode model

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.

Latex, 8 pages, 5 figures; improved discussion, new fig. 3

References in corpus (5)

• Dynamics of a tunable superfluid junction
• The Josephson effect throughout the BCS-BEC crossover
• DC Josephson Effect with Fermi gases in the Bose-Einstein regime
• Beyond standard two-mode dynamics in Bosonic Josephson junctions
• Matter-wave dark solitons in a double-well potential

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• Dissipation in a Finite Temperature Atomic Josephson Junction
• Josephson dynamics and localization revivals in ultradilute quantum liquids
• Self-Adapted Josephson Oscillation of Dark-Bright Solitons under Constant Forces
• Phase diffusion and fluctuations in a dissipative Bose-Josephson junction
• Assessing small accelerations using a bosonic Josephson junction
• Many-Body Quantum Dynamics of a Bosonic Josephson Junction with a Finite-Range Interaction
• Many-body effects in a composite bosonic Josephson junction
• Interference of longitudinal and transversal fragmentations in the Josephson tunneling dynamics of Bose-Einstein condensates
• Square wave oscillation of soliton in double-well potential trapped BEC
• Collective modes of two-species Bose-Einstein condensates in a Josephson junction barrier
• Bi-Josephson Effect in a Driven-Dissipative Supersolid