原子约瑟夫森结的非线性量子模型
Nonlinear quantum model for atomic Josephson junctions with one and two bosonic species
摘要：
研究了双势阱中含有一种和两种玻色子的原子约瑟夫森结（AJJ）。从第二量子化哈密顿量出发，我们表明，它是可能的零温度AJJ的微观动力学通过扩展的Bose-Hubbard（EBH）模型，其中包括通常被忽视的非线性项。在平均场近似下，从这种双模模型导出的海森堡方程以常微分方程（ODE）的形式描述了AJJ的宏观动力学。我们讨论了区分拉比，约瑟夫森和福克制度的可能性，在宏观参数出现在EBH哈密顿，然后，在常微分方程。我们比较了从双模常微分方程的数值解中得到的两个阱中玻色气体原子相对布居的预测，以及从Gross-Pitaevskii方程（GPEs）的直接数值积分中得到的预测。我们的研究表明，ODEs的非线性项是至关重要的，以实现一个良好的协议之间的ODEs和GPEs的方法，特别是给定量预测的自陷制度。
英文摘要：
We study atomic Josephson junctions (AJJs) with one and two bosonic species confined by a double-well potential. Proceeding from the second quantized Hamiltonian, we show that it is possible to describe the zero-temperature AJJs microscopic dynamics by means of extended Bose-Hubbard (EBH) models, which include usually-neglected nonlinear terms. Within the mean-field approximation, the Heisenberg equations derived from such two-mode models provide a description of AJJs macroscopic dynamics in terms of ordinary differential equations (ODEs). We discuss the possibility to distinguish the Rabi, Josephson, and Fock regimes, in terms of the macroscopic parameters which appear in the EBH Hamiltonians and, then, in the ODEs. We compare the predictions for the relative populations of the Bose gases atoms in the two wells obtained from the numerical solutions of the two-mode ODEs, with those deriving from the direct numerical integration of the Gross-Pitaevskii equations (GPEs). Our investigations shows that the nonlinear terms of the ODEs are crucial to achieve a good agreement between ODEs and GPEs approaches, and in particular to give quantitative predictions of the self-trapping regime.
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