PT-对称势中超冷量子气体非线性动力学

Non-Hermitian Hamiltonians are useful to describe the dynamics of open quantum systems, a great deal of attention has been given to parity-time-symmetric systems, due to these systems support a real spectrum. Bose-Einstein condensates (BEC) are macroscopic quantum phenomena, thus BECs trapped in a PT-symmetric potential are expected to provide interesting outcomes concerning basic physical principles. In this project, we start from the mean-field Gross-Pitaevskii (GP) equantion with a complex potential, understanding of the nonlinear dynamical behavior resulting from the combination of PT-symmetry and nonlinearity, where the nonlinearity stems from the atomic interactions. Specifically, we will consider the following three different scenarios: 1) For a cold Bosonic atoms system with a harmonic potential which apparently satisfies PT-symmetry, we will study the effects of the two- and three- body interaction on the dynamics and properties of nonlinear matter waves in this system. We will also investigate the quantum dynamics in the so-called BEC-BCS crossover for cold Fermi superfluid systems; 2) A PT-symmetric double-well potential is considered in this part. We will focus on the combined effects of the PT-symmetric potential and atomic interaction on the eigenvalues and stationay solutions of this open systems; 3)We will discuss the behavior of solitary wave solutions of ultracold atoms trapped in a PT-symmetric periodic potential, using a four-parameter variational approximation based on a dissipation functional formulation of the dynamics. Our project is not only interesting on theoretical side, but also provides important information for experimental efforts for the investigations of quantum dynamics of open systems.

开放系统的量子动力学可以用非厄米哈密顿量来描述，其中宇称时间(PT)对称量子体系由于可以具有实本征值而备受关注。玻色-爱因斯坦凝聚作为真正的宏观量子物质，它为观测PT对称效应提供了一个良好的量子平台。本项目以包含复势的Gross-Pitaevskii(GP)方程为出发点，研究PT对称势阱下，原子间相互作用引起的复杂非线性效应对该体系动力学的调控。具体研究内容包括：1）研究PT对称谐振子势阱中，玻色子间两体、三体相互作用，以及费米气体在BEC-BCS渡越区复杂的原子间相互作用下超冷原子系统非线性物质波动力学；2）研究PT对称双势阱中上述各种复杂的非线性效应对其本征能谱、稳态解的影响；3）利用基于动力学耗散泛函的四参数变分法研究PT对称周期势阱中超冷原子气体孤波动力学。本项目的开展对理解开放系统中量子气体非线性动力学具有重要的理论及实验参考意义。

在该项目的支持下，我们主要开展了以下三个方面的研究工作：.第一部分，考虑到复杂的非线性效应，比如，量子涨落效应以及三体相互作用效应， 研究了PT-对称势中玻色-爱因斯坦凝聚中孤波的存在性以及稳定性。利用变分法，我们研究了复杂非线性效应如何影响凝聚体的存在性，进一步利用Vakhitov–Kolokolov判据，研究复杂非线性项对孤波稳定性的影响。我们发现复杂非线性效应对孤波稳定性具有重要的调制作用。.第二部分，我们研究了光晶格中双组份玻色-爱因斯坦凝聚的非线性动力学问题，在非线性项以及光晶格的共同作用下，我们发现了各类多峰液滴的存在，我们发现光晶格对液滴稳定性具有重要的调制作用，故可以利用光晶格来操控实现多稳态量子液滴。.第三部分：该部分研究了分数维薛定谔方程中项链状光束的演化动力学，在饱和非线性以及分数维衍射效应下，可以产生载有整数或分数角动量且稳定传播的项链状光束。且研究发现随着利维指数的增大，项链状光束传播将会急剧减缓，究其物理本质是由于载有分数角动量的项链状光束中近邻珠间的能量交换，这与载有整数或半整数角动量的项链状光束的传播动力学行为完全不同，且第一次给出了分数维系统中项链状光束载有分数角动量传播的动力学实例。