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Chinese Physics

Energy spectrum and entanglement of two tunnel- coupled Bose–Einstein condensates

Cheng Rong, Liang Jiu-Qing

Published Feb 26, 2007• 7 citations
Publisher

Abstract

This paper obtains the energy-spectrum and eigenstate corrections of two-mode Bose–Einstein condensates (BECs) coupled by quantum tunnelling by perturbation method in both strong and weak tunnelling regions. The population imbalance between two BECs are then studied in terms of the low-lying eigenstates which also characterize the intrinsic entanglement between the two-mode BECs. The strong parity effect in the weak tunnelling region is also investigated.

DOI
10.1088/1009-1963/16/3/046

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This paper obtains the energy-spectrum and eigenstate corrections of two-mode Bose–Einstein condensates (BECs) coupled by quantum tunnelling by perturbation method in both strong and weak tunnelling regions. The population imbalance between two BECs are then studied in terms of the low-lying eigenstates which also characterize the intrinsic entanglement between the two-mode BECs. The strong parity effect in the weak tunnelling region is also investigated.
A model describing coherent quantum tunnelling between two trapped Bose–Einstein condensates is discussed. It is not well known that the model admits an exact solution, obtained some time ago, with the energy spectrum derived through the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations leads us to explicit expressions for the energies of the ground and the first excited states in the limit of weak tunnelling and all energies for strong tunnelling. The results are used to extract the asymptotic limits of the quantum fluctuations of the boson number difference between the two Bose–Einstein condensates and to characterize the degree of coherence in the system.
In this paper, we study the dissipative dynamics of a system which is composed of two atomic Bose–Einstein condensates (BECs) interacting through the Josephson-like coupling. To model a more realistic physical system, the inevitable dissipation effect is considered via the interaction between the system and its environment, in particular, a thermal reservoir. In this respect, after introducing a proper Hamiltonian for the model, we analytically solve the corresponding quantum Heisenberg–Langevin equations and then obtain explicit analytical expressions for population imbalance, macroscopic tunneling current and intermodal entanglement. Generally, the dynamics of the system is very sensitive to the chosen values of tunneling coupling strength, initial population as well as the characteristics of interaction between the system and its reservoirs. Also, the time evolution of the above-mentioned physical quantities shows oscillatory decaying behavior where the frequency of oscillations depends on the strength of tunneling interaction between the two subsystems. The oscillatory pattern of population imbalance and tunneling current is more regular in comparison with the intermodal entanglement. Although the system is always separable for low initial population, we show that it tends to an entangled state as its initial population is increased. In particular, the amount and the time interval of the entanglement can be effectively controlled via the dissipation parameter. Also, to get an insight into the effect of nonlinear interaction on the behavior of dynamical evolution of the considered system, we numerically investigate the population imbalance in the absence and presence of such interactions. A qualitative comparison shows that the previous theoretical works and numerical simulations confirm our obtained results.
We study the coherent atomic tunneling between two zero-temperature Bose-Einstein condensates (BEC) confined in a double-well magnetic trap. Two Gross-Pitaevskii equations for the self-interacting BEC amplitudes, coupled by a transfer matrix element, describe the dynamics in terms of the interwell phase difference and population imbalance. In addition to the anharmonic generalization of the familiar ac Josephson effect and plasma oscillations occurring in superconductor junctions, the nonlinear BEC tunneling dynamics sustains a self-maintained population imbalance: a novel ``macroscopic quantum self-trapping'' effect.
We study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driven by a double-frequency periodic field. Under the Melnikov's chaos criterion, we divide the parameter space into three parts of different types, regular region, low-chaoticity region, and high-chaoticity region, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particularly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.