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Physical Review A

Time evolution of the relative phase in two-component Bose-Einstein condensates with a coupling drive

Weidong Li, Xiaoji Zhou, Y. Q. Wang, J.-Q. Liang, Wu‐Ming Liu

Published Jun 8, 2001• 39 citations
Publisher

Abstract

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).

DOI
10.1103/physreva.64.015602

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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 (\ensuremathφ=0(\ensuremath{\varphi}=0(\ensuremathφ=0 and \ensuremathπ)\ensuremath{\pi})\ensuremathπ) 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).
The Rabi oscillations in two-component Bose-Einstein condensates with a coupling drive are studied by means of a pair of bosonic operators. The coupling drive and initial phase difference, will affect the amplitude and the period of the Rabi oscillations. The Rabi oscillations will vanish in the evolution of the condensate density for some special initial phase differences (phi = 0 or pi). Our theory provides not only an analytical framework for quantitative predictions for two-component condensates, but also gives ail intuitive understanding of some mysterious features observed in experiments and numerical simulations.
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.
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.
In this paper, we have studied the atomic population difference and the atomic tunneling current of two-component Bose-Einstein condensates with a coupling drive. It is found that when the two-component Bose-Einstein condensates are initially in the coherent states, the atomic population difference may exhibit the step structure, in which the numbers of the step increase with the decrease of the Rabi frequency and with the increment of the initial phase difference. The atomic population difference may exhibit collapses, and revivals, in which their periods are affected dramatically by the Rabi frequency and the initial phase difference. The atomic tunneling current may exhibit damping oscillation behaviors, and exist the step structure for the time range of second.
In this paper, we have studied the atomic population difference and the atomic tunneling current of twocomponent Bose-Einstein condensates with a coupling drive. It is found that when the two-component Bose-Einstein condensates are initially in the coherent states, the atomic population difference may exhibit the step structure, in which the numbers of the step increase with the decrease of the Rabi frequency and with the increment of the initial phase difference. The atomic population difference may exhibit collapses, and revivals, in which their periods are affected dramatically by the Rabi frequency and the initial phase difference. The atomic tunneling current may exhibit damping oscillation behaviors, and exist the step structure for the time range of 10-10 ～ 10-9 second.