Dynamics and Berry phase of two-species Bose-Einstein condensates

TL;DR

This paper derives exact solutions for the dynamics of two-species Bose-Einstein condensates under time-varying Raman coupling, revealing phenomena like Berry phase dependence on atom number parity and conditions for self-trapping.

Contribution

It provides analytic formulas for the evolution of population imbalance and phase, highlighting the role of initial states and coupling parameters in BEC dynamics.

Findings

Berry phase depends on atom number parity

Collapse and revival of oscillations are particle number dependent

Self-trapping and phase locking are achievable with proper initial states

Abstract

In terms of exact solutions of the time-dependent Schrodinger equation for an effective giant spin modeled from a coupled two-mode Bose-Einstein condensate (BEC) with adiabatic and cyclic time-varying Raman coupling between two hyperfine states of the BEC, we obtain analytic time-evolution formulas of the population imbalance and relative phase between two components with various initial states, especially the SU(2)coherent state. We find the Berry phase depending on the number parity of atoms, and particle number dependence of the collapse revival of population-imbalance oscillation. It is shown that self-trapping and phase locking can be achieved from initial SU(2) coherent states with proper parameters.