Control of the geometric phase and pseudo-spin dynamics on coupled Bose-Einstein condensates

Abstract

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 to get analytical solutions for the TD Schroedinger 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 differs by hyperfine degrees of freedom (internal Josephson effect), we also do present a brief discussion of a one specie condensate in a double-well potential (external Josephson effect).

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References in corpus (2)

• Measurement of geometric phase for mixed states using single photon interferometry
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects

Cited by in corpus (4)

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• Spin coherent states in NMR quadrupolar system: experimental and theoretical applications
• A general treatment of geometric phases and dynamical invariants
• Implementation of quantum logic gates using coupled Bose-Einstein condensates