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Chinese Physics Letters

Mean-Field Dynamics of a Two-Mode Bose-Einstein Condensate Subject to Decoherence

B. Cui, Wu Song-Lin, YI Xue-Xi

Published Jul 1, 2010• 2 citations
Publisher

Abstract

We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherence (or particle loss). Starting from the full many-body dynamics described by the master equation, an effective Gross-Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.

DOI
10.1088/0256-307x/27/7/070303

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We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherence (or particle loss). Starting from the full many-body dynamics described by the master equation, an effective Gross-Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.
We discuss the dynamics of an open two-mode Bose–Hubbard system subject to phase noise and particle dissipation. Starting from the full many-body dynamics described by a master equation the mean-field limit is derived resulting in an effective non-Hermitian (discrete) Gross–Pitaevskii equation which has been introduced only phenomenologically up to now. The familiar mean-field phase-space structure is substantially altered by the dissipation. In particular, the character of the fixed points shows an abrupt transition from elliptic or hyperbolic to attractive or repulsive, respectively. This reflects the metastable behaviour of the corresponding many-body system which surprisingly also leads to a significant increase of the purity of the condensate. A comparison of the mean-field approximation to simulations of the full master equation using the Monte Carlo wavefunction method shows an excellent agreement for wide parameter ranges.
Dynamics of the repulsive Bose–Einstein condensate (BEC) in a double-well trap is explored within the 3D time-dependent Gross–Pitaevskii equation. The model avoids numerous common approximations (two-mode treatment, time-space factorization, fixed values of the chemical potential and barrier penetrability, etc) and thus may provide a realistic description of BEC dynamics, including both weak-coupling (sub-barrier) and strong-coupling (above-barrier) regimes and their crossover. The strong coupling regime is achieved by increasing the number N of BEC atoms and thus the chemical potential. The evolution with N of Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) is examined and the crucial impact of the BEC interaction is demonstrated. At weak coupling, the calculations well reproduce the JO/MQST experimental data. At strong coupling with a significant overlap of the left and right BECs, we observe a remarkable persistence of the Josephson-like dynamics: the JO and MQST converge to a high-frequency JO-like mode where both population imbalance and phase difference oscillate around the zero averages.
我们在一个双井潜力题目讨论 Bose 爱因斯坦冷凝物的动力学到 decoherence (或粒子损失) 。从完整的许多身体动力学开始由主人方程描述了，一个有效 Gross-Pitaevskii-like 方程在吝啬地的近似被导出。由数字地解决 GP 方程，我们发现那宏观的量自我套住为强壮的 decoherence 消失，当概括时自我套住发生在弱 decoherence 下面。固定的点被计算了，并且我们发现那一个突然的变化从对一个引起注意的人和 repeller 椭圆形发生，在这些附近反映系统的亚稳的行为指。[从作者抽象]
The dynamics of Bose-Einstein condensates in a double-well magnetic trap is studied using the Gross-Pitaevskii equation (GPE) and a two-mode approximation. The self-trapping instability occurs when a sufficiently high potential barrier is formed in the centre of the trap. Close to the instability threshold, the GPE is reduced to a simple amplitude equation. In the case where weakly dissipative effects are taken into account, the condensate exhibits aperiodic oscillations which can be described by the Lorenz thermal convection model.