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Journal of Shanxi Normal University

Nonlinear Tunneling Effect based on Quantum Operator Fluctuation

Shu Peng-l

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

The nonlinear tunneling effect of quantum operator fluctuation in Bose-Einstein condensation systems( BECs) is discnssed in this paper. Through calculating the time evolution about particles of BECs in symmetric double well potentials,the system has also shown Josephson-effect and self-tapping phenomena by means of introducing the quantum operator fluctuation. The conclusion not only considerably supplements the theory of nonlinear tunneling effect based on the mean-filed approximation and quantum description,but also provides a theoretical basis for the experiment of nonlinear tunneling in BECs.

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The nonlinear tunneling effect of quantum operator fluctuation in Bose-Einstein condensation systems( BECs) is discnssed in this paper. Through calculating the time evolution about particles of BECs in symmetric double well potentials,the system has also shown Josephson-effect and self-tapping phenomena by means of introducing the quantum operator fluctuation. The conclusion not only considerably supplements the theory of nonlinear tunneling effect based on the mean-filed approximation and quantum description,but also provides a theoretical basis for the experiment of nonlinear tunneling in BECs.
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.
Abstract In this paper, we study the influence of quantum fluctuations (QFs) on the macroscopic quantum tunneling and self-trapping (ST) of a two-component Bose–Einstein condensate in a double-well trap. QFs are described by the Lee–Huang–Yang (LHY) term in the modified Gross–Pitaevskii (GP) equation. Employing the modified GP equation in a scalar approximation, we derive a dimer model using a two-mode approximation. The frequencies of Josephson oscillations and ST conditions under QFs are found analytically and proven by numerical simulations of the modified GP equation. The tunneling and localization phenomena are also investigated for the case of the LHY fluid loaded in a double-well potential.
Abstract We investigate Rosen-Zener tunneling for Bose-Einstein condensates in a triple-well potential within the framework of mean-field treatment. Firstly, we exactly calculate tunneling dynamics for triple-well in the linear case, where the population evolution of each well is robust, and all atoms are finally trapped in the single well, that is initially uploaded. In this case, tunneling dynamics are symmetrical when all atoms are populated in the first well and third well. However, as the nonlinear interaction is introduced, tunneling dynamics will be significantly changed. On the one hand, the symmetry will be broken, some atoms will not be confined to the starting well. On the other hand, nonlinear Josephson oscillation will be presented within a fixing interval. When the interaction exceeds this interval, the self-trapping solution emerges.
Abstract We consider the properties of stationary states and the dynamics of Bose–Einstein condensates (BECs) in a double-well (DW) potential with pair tunneling by using a full quantum-mechanical treatment. Furthermore, we study the quantum quench dynamics of the DW system when subjected to a sudden change of the Peierls phase. It is shown that strong pair tunneling evidently influences the energy spectrum structure of the stationary states. For relatively weak repulsive interatomic interactions, the dynamics of the DW system with a maximal initial population difference evolves from Josephson oscillations to quantum self-trapping as one increases the pair tunneling strength, while for large repulsion the strong pair tunneling inhibits the quantum self-trapping. In the case of attractive interatomic interactions, strong pair tunneling tends to destroy the Josephson oscillations and quantum self-trapping, and the system eventually enters a symmetric regime of zero population difference. Finally, the effect of the Peierls phase on the quantum quench dynamics of the system is analyzed and discussed. These new features are remarkably different from the usual dynamical behaviors of a BEC in a DW potential.
The Josephson effect can be observed in a Bose-Einstein condensate in a double-well potential, which is attributed to the tunneling of bosons between two wells. We propose a multi-mode theory to investigate the dynamics of local excitations in a one-dimensional condensate in a double-well potential. We show that the system can be described by two independent two-mode models. The Josephson oscillation and the self-trapping of local collective excitations are predicted analytically and confirmed by numerical simulation.