2009/09/04 by Eduardo Toshio Domingues Matsushita, E. T. D. Matsushita, Matsushita, E. T. D. +2
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Electrodynamics and Casimir Effect #Quantum Gases (cond-mat.quant-gas) #Strong Light-Matter Interactions #cond-mat.quant-gas
paper · pdf · doi:10.48550/arxiv.0909.0920
11 pages,2 figures, 5 tables
arxiv created 2009/09/04 · openalex publication_date 2009/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The properties of the superfluid phase of ultra cold bosonic atoms loaded in a circular array are investigated in the framework of the Bose-Hubbard model and the Bogoliubov theory. We derive and solve the Gross-Pitaevskii equation of the model to find that the atoms condense in states of well-defined quasimomentum. A detailed analysis of the coupling structure in the effective quadratic grand-canonical Hamiltonian shows that only pairs of distinct and identical quasimomenta are coupled. Solving the corresponding Bogoliubov-de Gennes equations we see that each pair of distinct quasimomenta gives raise to doublets in the excitation energy spectrum and that the quasimomenta of the zero-energy mode and of the occupied state in the condensates are identical. The dynamical and energetic stabilities of the condensates are determined by studying the behavior of the elementary excitations in the control parameters space. Our investigation establishes that superflow condensates exists only in the central region of the first Brillouin zone whereas there is none in the last quarters since they are energetically unstable, independently of the control parameters.