微腔中超冷原子的非平衡多体效应及其调控

The research about the interaction between an ensemble of ultracold atoms and an high-finesse optical cavity is an important content in quantum optics and condensed matter physics. The system has a wealth of physical content and at the same time a broad application prospect in the field of quantum information and quantum computing. In 2010, it reports the Dicke quantum phase transition in an open system and observes the self-organization of a BEC in the experiment. And the nonlinear atom-photon interaction has been introduced, which is induced by the optical lattice potential. The competition between the nonlinear atom-photon interaction and the atom-field coupling strength leads to a novel quantum phase transition. Based on the previously established collective quantum dynamics, this project mainly discusses the following contents: it reveals the rich ground-state properties induced by considering a monochromatic nonadiabatic modulation of the atom-field coupling in an mixed optomechanical system and then explores that the monochromatic nonadiabatic modulation term is replaced with any form of time-dependent term, and finds a common gauge transformation; Using the spin-coherent-state transformation, the ground-state energies are obtained in a cavity-BEC system; An imaginary-time functional path integral approach is presented to study the finite-temperature properties of the cavity-BEC many-body system with time-dependent atom-field coupling strength.

超冷原子与超精细光腔相互作用研究是量子光学和凝聚态物理学的重要内容之一。该系统有着丰富的物理内容，同时在量子信息、量子计算等领域有着广泛的应用前景。2010年，实验报道了开放系统中Dicke量子相变的实现和BEC的自组织现象，并引入由光格势诱导的原子-光非线性相互作用。该系统中原子-光非线性相互作用与原子-场耦合强度的竞争导致新奇的量子相变。本项目将在集体量子动力学基础上，重点探讨以下内容：研究混合光机械系统中，原子-场耦合的单频非绝热调制对系统基态能量的影响，进而探讨将原子-场耦合的单频非绝热调制项用任意形式的含时项取代，并找到一种通用的规范变换项；用自旋相干态变换求腔-BEC系统基态能谱和波函数；用虚时函数路径积分方法探讨原子-场耦合强度含时的腔-BEC多体系统有限温度下的非平衡多体效应。这些研究成果将为进一步理解原子与光相互作用基本问题提供理论基础和实验依据。

开放系统中Dicke量子相变的实现为理论上探讨超冷原子与光腔相互作用提供了强有力的实验指导，而且该系统在量子信息与量子计算等领域有广泛的应用前景。我们主要探讨以下内容：基于Holstein-Primafoff变换方法和自旋相干态变分法研究了光腔内囚禁两组分超冷原子组的基态特性；讨论机械振子对光力腔系统的基态相图和量子相变的影响，尤其是机械振子共振阻尼下诱导的超辐射相的塌缩；Floquent理论和旋波近似理论指导下含时光力腔系统的非平衡量子相变及其多稳特性；基于虚时路径积分方法分析机械振子在有限温度下诱导的新奇量子相变和宏观多稳特性等。这些研究成果将为深入理解多组分原子与光腔或光力腔相互作用的多稳性及其量子相变提供理论基础和实验依据。