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arXiv:1302.6654 · Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of double-well Bose–Einstein condensates subject to external Gaussian white noise

Hanlei Zheng, Yajiang Hao, Qiang Gu

Published Feb 26, 2013• 4 citations
arXivHTMLPDF

Abstract

Dynamical properties of the Bose–Einstein condensate in a double-well potential subject to Gaussian white noise are investigated by numerically solving the time-dependent Gross–Pitaevskii equation. The Gaussian white noise is used to describe influence of the random environmental disturbance on the double-well condensate. Dynamical evolutions from three different initial states, the Josephson oscillation state, the running phase and π-mode macroscopic quantum self-trapping states, are considered. It is shown that the system is rather robust with respect to the weak noise whose strength is small and change rate is high. If the evolution time is sufficiently long, the weak noise will finally drive the system to evolve from high-energy states to low-energy states, but in a manner rather different from the energy-dissipation effect. In the presence of strong noise with either large strength or slow change rate, the double-well condensate may exhibit very irregular dynamical behaviours.

DOI
10.1088/0953-4075/46/6/065301

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Dynamical properties of the Bose–Einstein condensate in a double-well potential subject to Gaussian white noise are investigated by numerically solving the time-dependent Gross–Pitaevskii equation. The Gaussian white noise is used to describe influence of the random environmental disturbance on the double-well condensate. Dynamical evolutions from three different initial states, the Josephson oscillation state, the running phase and π-mode macroscopic quantum self-trapping states, are considered. It is shown that the system is rather robust with respect to the weak noise whose strength is small and change rate is high. If the evolution time is sufficiently long, the weak noise will finally drive the system to evolve from high-energy states to low-energy states, but in a manner rather different from the energy-dissipation effect. In the presence of strong noise with either large strength or slow change rate, the double-well condensate may exhibit very irregular dynamical behaviours.
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.
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.
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.
Josephson effect of Bose-Einstein condensate in double-well potential is an obvious manifestation of macroscopic quantum coherence. Most of researches focus on the symmetric double-well potential. In this work, we investigate the dynamic of Bose-Einstein condensates in an asymmetric double-well potential by using two-mode theory and computer simulation. In the absence of the interaction between atoms, the dynamic equation of condensate can be solved analytically. The amplitude as a function of energy difference of two wells is obtained. We can find that the change of energy difference will lead to the different dynamic behaviors of condensate. If the energy difference is relatively large, the condensate will primarily occupy the well that is occupied more than the other well at the beginning time. It is interesting that such a trap phenomenon is not dependent on the position of the high energy potential well nor the position of low energy potential well. If the energy difference becomes small, the tunneling and oscillation of condensate will be enhanced. When the interaction between atoms is present, our numerical calculations show that as the nonlinear interaction increases, the dynamic behavior of condensate exhibits different characteristics, such as trapping in a well, enhancing the tunneling and oscillation between two wells, and enhancing the trapping in a well at large nonlinear interaction, which is similar to the dynamic change caused by the energy difference in the case of ideal condensate. That is to say, on the one hand, the nonlinear interaction can lead to the trap of condensate as well as the dynamic trap to happen in symmetric double-well potential. On the other hand, the nonlinearity can promote the tunneling of condensate, counteracting the effect of the asymmetry of potential. And, this counteracting effect is related to the difference in energy between asymmetric potential wells. To understand the underlying mechanism, the full dynamic behavior of two-mode model is illustrated and the dynamic transition can be seen clearly. Combining the results obtained with and without interaction, regarding nonlinear interaction as effective potential provides a clear way to explain dynamic transition of condensate in an asymmetric double-well potential. In addition, we also perform the numerical simulations of the Gross-Pitaevskii equation, and the results are consistent with the conclusions obtained by using the two-mode theory.
In this paper, we study the dynamics of a dissipative double-well BEC driven by sinusoidally oscillating time-dependent inter-particle interaction. The phase space of the system is illustrated physically by its population imbalance and phase difference. The macroscopic dynamics of the model are generated within the Mean-field limit neglecting a single moment for random noise but their two-point noise-noise correlation persists. Equilibrium stability fixed points are observed for systems subjected to constant inter-particle interaction. The time-dependent (sinusoidal) inter-particle interactions in contrast, however, drive the system into the complex dynamic. The system's phase-space dynamics is sensitive to small changes in the initial conditions. We found dissipation concurrent with large driving amplitude or frequency of inter-particle interaction enhances the route to chaos.