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Annalen der Physik

Dynamical properties of partially coherent Bose‐Einstein condensates in double wells

Li-Hua Lü, You‐Quan Li

Published Feb 27, 2012• 0 citations
Publisher

Abstract

Abstract Some dynamical features of partially coherent Bose‐Einstein condensate systems confined in double‐well potentials are investigated in mean field approximation. For one‐component system, the phenomena of self‐trapping is studied and it is shown that the partially coherent system, like completely coherent one, can also exhibit self‐trapping phenomena which are affected by both the degree of coherence and the initial relative phase. The adiabatic properties are also studied by introducing the fidelity for mixed state. It is shown that the introduced fidelity can characterize the adiabatic condition of the partially coherent system. For two‐component system, the time evolution of the degree of coherence for a time‐dependent tunneling strength is investigated. The corresponding results imply that the degree of coherence for such a two‐component system can exhibit decoherence phenomena even without the condensate‐environment coupling.

DOI
10.1002/andp.201100252

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Abstract Some dynamical features of partially coherent Bose‐Einstein condensate systems confined in double‐well potentials are investigated in mean field approximation. For one‐component system, the phenomena of self‐trapping is studied and it is shown that the partially coherent system, like completely coherent one, can also exhibit self‐trapping phenomena which are affected by both the degree of coherence and the initial relative phase. The adiabatic properties are also studied by introducing the fidelity for mixed state. It is shown that the introduced fidelity can characterize the adiabatic condition of the partially coherent system. For two‐component system, the time evolution of the degree of coherence for a time‐dependent tunneling strength is investigated. The corresponding results imply that the degree of coherence for such a two‐component system can exhibit decoherence phenomena even without the condensate‐environment coupling.
The dynamical properties of partially coherent Bose-Einstein condensates in double wells are investigated in three typical regimes. In the extreme Fock regime, the time evolution of the degree of coherence is shown to decay rapidly. In the Rabi regime, a relation between the amplitude of Rabi oscillation and the degree of coherence is obtained, which is expected to determine the degree of coherence by measuring the amplitude of Rabi oscillation. The study on the self-trapping phenomena in the Josephson regime exhibits that both the degree of coherence and the initial relative phase can affect the final particle distribution.
Coherence dynamics of two-species Bose–Einstein condensates in double wells is investigated in the mean-field approximation. We show that the system can exhibit decoherence phenomena even without the condensate–environment coupling and the variation tendency of the degree of coherence depends not only on the parameters of the system but also the initial states. We also investigate the time evolution of the degree of coherence for a Rosen–Zener form of tunnelling strength, and propose a method to get a condensate system with a certain degree of coherence through a time-dependent tunnelling strength.
Based on the mean-field approximation and a phase-space analysis, we discuss the dynamics of Bose-Einstein condensates (BECs) in a double-well potential. The condensates are found to be trapped in the time-dependent eigenstates of the effective Hamiltonian; we refer to this effect as time-dependent self-trapping of BECs. By comparison of this self-trapping with the adiabatic evolution, we find that adiabatic evolution beyond the traditional adiabatic condition can be achieved in BECs. Furthermore, the population imbalance of the BECs in the wells can be controlled by manipulating the atom-atom couplings and the driving field. The fixed points for the system are also calculated and discussed.
We study the dynamics of a Bose-Einstein condensate in a double-well potential in the mean-field approximation. Decoherence effects are considered by analyzing the couplings of the condensate to the environment. Two kinds of coupling are taken into account. With the first kind of coupling dominating, decoherence can enhance self-trapping by increasing the damping of the oscillations in the dynamics, while decoherence from the second kind of condensate-environment coupling leads to spoiling of the quantum tunneling and self-trapping.
Abstract We investigate the dynamical phase transition of two-component Bose–Einstein condensate with nonlinear tunneling, which is trapped inside a double-well and dispersively coupled to a single mode of a high-finesse optical cavity with one moving end mirror driven by a single mode standing field. In the mean-field approximation, the Hamiltonian of the system with nonlinear tunneling is characterized by the population difference of the particles and relative phase in double wells. The characteristics of the system’s stability points are determined by the corresponding Hessian matrices. However, the number of the system’s stability points depends on the roots of the first derivative of the energy. In the absence of the nonlinearity, the Hamiltonian of the system is a binary quadratic equation. When there is nonlinear tunneling, the Hamiltonian of the system is a binary quartic equation. Therefore, from a mathematical point of view, it can be found that the roots of the equation will increase, which means that the number of stability points in the system will increase. We also build the phase portrait from classical analysis. Considering the strong pair tunneling case, we confirm that nonlinear tunneling interaction leads to an increment of stability points and enriches the phase diagram of the system. We further analyze the phase portrait with the moving end mirror. It is shown that the semiclassical dynamics of the system undergoes a bifurcation of stability points with an increase in the coupling strength or detuning. In other words, the system experiences a phase transition.
We study quantum dynamical properties of a spin-1 atomic Bose-Einstein condensate in a double-well potential. Adopting a mean field theory and single spatial mode approximation, we characterize our model system as two coupled spins. For certain initial states, we find full magnetization oscillations between wells not accompanied by mass (or atom numbers) exchange. We identify dynamic regimes of collective spin variables arising from nonlinear self-interactions that are different from the usual Josephson oscillations. We also discuss magnetization beats and incomplete oscillations of collective spin variables other than the magnetization. Our study points to an alternative approach to observe coherent tunnelling of a condensate through a (spatial) potential barrier.