Scientific Results

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

Year: 2017

Authors: Burchianti A., Fort C., Modugno M.

Autors Affiliation: LENS European Laboratory for Non-linear Spectroscopy, and Dipartimento di Fisica e Astronomia – Università di Firenze,
I-50019 Sesto Fiorentino, Italy; CNR-INO Istituto Nazionale di Ottica, I-50019 Sesto Fiorentino, Italy; Depto. de Fisica Teorica e Hist. de la Ciencia, Universidad del Pais Vasco UPV/EHU, 48080 Bilbao, Spain; IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain

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.


Volume: 95 (2)      Pages from: 023627-1  to: 023627-7

More Information: We acknowledge useful discussions with M. Fattori, G. Roati, and G. Barontini. This work has been supported by the University of Basque Country UPV/EHU under program UFI 11/55, the Spanish Ministry of Economy, Industry and Competitiveness and the European Regional Development Fund FEDER through Grant No. FIS201567161-P (MINECO/FEDER), and the Basque Government through Grant No. IT986-16. A. B. was supported by European Research Council Grant No. 307032 QuFerm2D.
KeyWords: Bose-Einstein condensation, Arbitrary dimension; Double-well potential; Gross-Pitaevskii equation; Josephson plasmas; Linear combinations; One-dimensional systems; Small-amplitude oscillations; Weak interactions, Plasma oscillations
DOI: 10.1103/PhysRevA.95.023627

Citations: 21
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