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Chinese Physics B

Josephson junction of two-species Bose—Einstein condensates in a high-finesse optical cavity

Bin Wang, Lei Tan, 吕纯海, 谭文婷

Published Nov 1, 2010• 4 citations
Publisher

Abstract

The mean-field dynamics of undistinguishable two-species Bose Josephson junction coupled to a single mode highfinesse optical cavity is investigated. From the Hamiltonian, the phase portrait and the stationary points are given. It is shown that the role of the interspecies interaction equals the intraspecies interaction under suitable conditions. As the interspecies interaction increases, the trapped atoms will start tunneling between the two wells unnaturally for some special cases.

DOI
10.1088/1674-1056/19/11/117402

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The mean-field dynamics of undistinguishable two-species Bose Josephson junction coupled to a single mode highfinesse optical cavity is investigated. From the Hamiltonian, the phase portrait and the stationary points are given. It is shown that the role of the interspecies interaction equals the intraspecies interaction under suitable conditions. As the interspecies interaction increases, the trapped atoms will start tunneling between the two wells unnaturally for some special cases.
We study the mean-field dynamics of a Bose Josephson junction which is dispersively coupled to a single mode of a high-finesse optical cavity. An effective classical Hamiltonian for the Bose Josephson junction is derived, and its dynamics is studied from the perspective of a phase portrait. It is shown that the strong condensate-field interplay does alter the dynamics of the Bose Josephson junction drastically. The possibility of coherent manipulating and in situ observation of the dynamics of the Bose Josephson junction is discussed.
The periodic modulation on dynamic behavior of Bose–Josephson junction dispersively coupled to a single mode high-finesse optical cavity is investigated. The eigenenergies and the phase diagram of the system are obtained using the numerical methods under the mean field approximation. It is shown that the large atomic interaction strength will lead the eigenenergies to show a bistable and a loop structure. It is also found that the periodic modulation can change the period and frequency of the motion of the atoms and the intra cavity photons drastically. Furthermore, the strong condensate-field interplay will enhance the oscillation of the atoms and make some trapped atoms start oscillating. For certain parameters of the cavity field, the relative population oscillation exhibits a process from order to chaos.
We study undistinguishable two-species Bose-Einstein condensates (BECs) trapped in double wells. In the mean-field approximation we map the quantum system into a classical model and investigate the existence and stability of the fixed point solutions. By appropriately varying the amplitude of the high-frequency periodic modulation on the energy bias between the two wells, we tune the tunneling strength in the adiabatic Rosen-Zener type effectively. Starting from two typical initial states, we study the evolution of the system and find that the interspecies interaction can produce totally distinct results, which is expected to provide a route to manipulate the BEC distribution.
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 the dynamics of a two-species Bose-Einstein condensate in a double well. Such a system is characterized by the intraspecies and interspecies sss-wave scattering as well as the Josephson tunneling between the two wells and the population transfer between the two species. We investigate the dynamics for some interesting regimes and present numerical results to support our conclusions. In the case of vanishing intraspecies scattering lengths and a weak interspecies scattering length, we find collapses and revivals in the population dynamics. A possible experimental implementation of our proposal is briefly discussed.