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

Alessia Burchianti; Chiara Fort; Michele Modugno

doi:10.1103/PhysRevA.95.023627

← Back to search

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

Alessia Burchianti, Chiara Fort, Michele Modugno

DOI 10.1103/PhysRevA.95.023627 · Physical Review A

T1

Active bibliographic source — not scientific approval

Bibliographic access preserves source history; it does not approve extracted materials or validate reported claims. Review warnings on each occurrence separately.

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 combination 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.