闭合厄米特系统中PT对称BEC子系统的实现
Realizing PT-symmetric BEC subsystems in closed hermitian systems
摘要：
在开放的双阱玻色-爱因斯坦凝聚体系统中，存在着平衡原子的输入和输出通量的非厄米PT对称哈密顿PT对称态。PT对称态服从宇称和时间反演对称性。我们解决的问题，如何在和流出可以实现，并引入一个厄米特系统中，两个PT对称子系统嵌入。该系统不再需要与环境的输入和输出耦合。我们发现，子系统仍然有PT对称的状态。此外，我们研究什么程度的细节是必要的正确建模的PT对称属性和这样一个系统的分叉结构。我们研究了一个四模矩阵模型和一个由一维全Gross-Pitaevskii方程描述的系统。我们看到，一个简单的矩阵模型正确地描述了系统的定性性质。对于充分隔离的井，也有与更先进的系统描述的定量协议。我们还研究了系统的波函数必须满足哪些属性，以允许PT对称状态。特别是系统的不同部分之间的相位差的要求进行检查。
英文摘要：
In open double-well Bose-Einstein condensate systems which balance in- and outfluxes of atoms and which are effectively described by a non-hermitian PT-symmetric Hamiltonian PT-symmetric states have been shown to exist. PT-symmetric states obey parity and time reversal symmetry. We tackle the question of how the in- and outfluxes can be realized and introduce a hermitian system in which two PT-symmetric subsystems are embedded. This system no longer requires an in- and outcoupling to and from the environment. We show that the subsystems still have PT-symmetric states. In addition we examine what degree of detail is necessary to correctly model the PT-symmetric properties and the bifurcation structure of such a system. We examine a four-mode matrix model and a system described by the full Gross-Pitaevskii equation in one dimension. We see that a simple matrix model correctly describes the qualitative properties of the system. For sufficiently isolated wells there is also quantitative agreement with the more advanced system descriptions. We also investigate which properties the wave functions of a system must fulfil to allow for PT-symmetric states. In particular the requirements for the phase difference between different parts of the system are examined.
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