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International Journal of Theoretical Physics

Geometric Phase in a Time-Dependent Bose-Fermi System

Zhao-Xian Yu, Zhi-Yong Jiao

Published Dec 22, 2009• 0 citations
Publisher
DOI
10.1007/s10773-009-0231-7

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We describe the behavior of two coupled Bose-Einstein condensates in time-dependent (TD) trap potentials and TD Rabi (or tunneling) frequency using the two-mode approach. Starting from Bloch states, we succeed in obtaining analytical solutions for the TD Schr\"odinger equation and present a detailed analysis of the relative and geometric phases acquired by the wave function of the condensates, as well as their population imbalance. We also establish a connection between the geometric phases and constants of motion which characterize the dynamic of the system. Besides analyzing the affects of temporality on condensates that differ by hyperfine degrees of freedom (internal Josephson effect), we also do present a brief discussion of a one-species condensate in a double-well potential (external Josephson effect).