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Communications in Theoretical Physics

Phase of Two-Component Bose–Einstein Condensates with a Coupling Drive

Zhao-Xian Yu, Shuo Jin, Jiao Zhi-Yong, Ji‐Suo Wang

Published May 1, 2007• 0 citations
Publisher

Abstract

By using the invariant theory, we study the phases of two-component Bose–Einstein condensates with a coupling drive under the case that the strength of the interatomic interaction in each condensate equals the interspecies interaction. The dynamical and geometric phases are presented respectively. The Aharonov–Anandan phase is also obtained under the cyclical evolution.

DOI
10.1088/0253-6102/47/5/007

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By using the invariant theory, we study the phases of two-component Bose–Einstein condensates with a coupling drive under the case that the strength of the interatomic interaction in each condensate equals the interspecies interaction. The dynamical and geometric phases are presented respectively. The Aharonov–Anandan phase is also obtained under the cyclical evolution.
The dynamics of two-component Bose-Einstein condensates with coupling drive is studied using a pair of bosonic operators. We demonstrate that the effect of the coupling drive on the evolution of the relative phase of the two-component Bose-Einstein condensates depends on the initial relative phase difference between the two condensates. In some special initial phase differences $(\ensuremath{\varphi}=0$ and $\ensuremath{\pi})$ the condensate density are not sinusoidal functions of time, and the interference pattern is not steady either. The coupling drive also reduces the amplitude and the period of the oscillation. Our theoretical result confirms the experimental observations reported in Phys. Rev. Lett. 81, 1543 (1998).
Using the numerical calculation,we have investigated the long-time evolution of atomicity density of two-component BEC,and have found that the evolution of condensate density in long time,which presents a typical quantumn collapse and revival with a complex period,is rather different from that in short time,which displays a regular cosine oscillation.Futhermore,we have also discussed the influence of the Rabi frequency of coupling drive field,various values for the relative phase,the strength of the coupling drive,the strength of the interatomic interaction in each condensate and the strength of the interspecies interaction on the evolution properties of atomicity density.
We study the interactions between two atomic species in a binary Bose-Einstein condensate to revisit the conditions for miscibility, oscillatory dynamics between the species, steady-state solutions, and their stability. By employing a variational approach for a quasi-one-dimensional, two-atomic species condensate, we obtain equations of motion for the parameters of each species: amplitude, width, position, and phase. A further simplification leads to a reduction of the dynamics into a simple classical Newtonian system where components oscillate in an effective potential with a frequency that depends on the harmonic trap strength and the interspecies coupling parameter. We develop explicit conditions for miscibility that can be interpreted as a phase diagram that depends on the harmonic trap's strength and the interspecies coupling parameter. We numerically illustrate the bifurcation scenario whereby nontopological, phase-separated states of increasing complexity emerge out of a symmetric state as the interspecies coupling is increased. The symmetry-breaking dynamical evolution of some of these states is numerically monitored and the associated asymmetric states are also explored.
The Rabi oscillations in two-component Bose-Einstein condensates with a coupling drive are studiedby means of a pair of bosonic operators. The coupling drive and initial phase difference will affect the amplitudeand the period of the Rabi oscillations. The Rabi oscillations will vanish in the evolution of the condensate densityfor some special initial phase differences (ψ = 0 or π). Our theory provides not only an analytical framework forquantitative predictions for two-component condensates, but also gives an intuitive understanding of some mysteriousfeatures observed in experiments and numerical. simulations.