低维离散量子液滴的调控及非线性动力学研究

The Quantum droplets (QDs), described by the Lee-Huang-Yang correction, attract extensive attentions in cold atom physics recently. The QDs can be used to study quantum simulation and quantum many-body theory since its formation is related to the quantum fluctuations beyond the mean-field theory. The potential applications of QDs include quantum information processing and quantum metrology. This project aims at revealing the variety of spatial structure and phase information of low-dimensional discrete QDs, obtaining the novel quantum states of QDs in low-dimensional discrete systems and studying their properties in the Bose-Bose-mixtures. Furthermore, we study the stability and dynamics of the system. An approach to control the dynamical evolution of QDs is proposed. This project includes studying the influences of the amplitudes of periodic potential and the velocities of QDs on scattering properties of QDs; developing the two-dimensional discrete models and obtaining stable high-angular momentum vortex QDs and their phases information; obtaining the off-site-centered vortex QDs. Also, the properties of gap QDs in the artificial gauge field are studied. This project provides a theoretical basis for control and potential applications of low-dimensional discrete QDs.

基于李-黄-杨修正项描述的量子液滴是近几年来冷原子科学中备受关注的研究课题，它的形成与多体量子涨落效应有关，因此可用于开展量子模拟和量子多体问题的理论与实验研究，且在量子信息处理和量子精密测量等方面有重要应用价值。本项目旨在揭示低维离散量子液滴形式和相位的多样性，研究玻色-玻色混合凝聚体系统中离散量子液滴的性质，获得新奇的低维量子液滴并研究其稳定性及动力学特性，进而提出调控其动力学演化行为的可行方案。主要研究内容包括：研究一维离散模型中势函数的振幅、液滴的横向速度等参量对量子液滴散射特性的影响，实现对传输方向的调控；建立二维离散模型，获得稳定高角动量涡旋量子液滴及相位信息，并实现稳定off-site-centered型涡旋量子液滴；研究人工规范场下量子液滴的性质，获取稳定一维带隙量子液滴。本项目的研究成果为低维离散量子液滴的调控及应用提供理论基础。

近年来，基于李黄杨修正项所描述的量子液滴为处理高维自由空间中不能形成稳定的非线性自局域态提供了新思路，其形成与量子多体涨落效应有关，同时其内部相互作用对涡旋的鲁棒性使其成为研究新奇涡旋自局域态的理想平台。本项目基于玻色-玻色混合气体量子液滴模型：在一维离散系统中，探究了紧束缚近似和准连续情况下的离散量子液滴，通过引入人工规范场，首次获得了稳定的staggered型离散量子液滴；在准二维自由空间中，分别获得了高角动量的涡旋量子液滴和隐秘涡旋量子液滴；在晶格系统中，获得了onsite型和offsite型晶格量子液滴；最后在环形势中，获得了环形量子液滴，并基于此构造了嵌套涡旋量子液滴。在各项研究中，分别探讨了各类量子液滴的密度分布、稳定参数范围、相位信息及动力学特性。本项目的研究结果为实验的观测提供理论指导，在量子信息存储等领域有着重要的应用价值。