Ultracold bosonic gases coupled to an optical cavity mode

与光学腔的光子模式耦合的超冷原子显示出迷人的现象，如迪克相变。这是一种自组织相变，其中原子自发地排列成棋盘状密度模式，并且由于原子和光子模式之间的反馈机制而占据光子模式。在这个项目中，我们将研究耦合到光子模式并且仅限于光学晶格结构的玻色子原子。我们将主要关注PI提出的具有或不具有空间依赖相印记的原子隧道过程的新耦合。我们期望出现一些有趣的相，例如复杂的莫特绝缘相和超流体相的自组织，或者存在相印记、迈斯纳相和涡旋相。综合原子-腔系统动力学的完整解是非常苛刻的，主要是由于三个原因：(i)光学晶格中相互作用的玻色子原子的强相关性质，（ii）空间扩展腔模式与原子的耦合，它可以诱导原子之间有效的远程相互作用，以及（iii）由于不完美的反射镜导致光子从腔中泄漏而导致腔模式的耗散性质。我们用带有林德布莱德耗散量的马尔可夫主方程来描述组合耗散系统。为了确定结果动力学，我们将采用不同的方法。在第一种方法中，我们将通过绝热消除空腔模式将模型简化为具有自一致性条件的有效相互作用玻色子模型-具有远程过程。为了解决这个自洽模型，我们将与P6项目合作开发矩阵乘积状态（MPS）算法和量子蒙特卡罗方法的自洽实现。第二种方法旨在准一维系统的全数值模拟。考虑到具有大局部希尔伯特空间的耗散和扩展腔模式的时间相关mps的实现是该项目的主要挑战之一。

Ultracold atoms coupled to a photonic mode of an optical cavity show fascinating phenomena such asthe Dicke phase transition. This is a self-organized phase transition in which the atoms spontaneouslyorder into a checkerboard density pattern and the photonic mode becomes occupied due to thefeedback mechanism between the atoms and the photonic mode. In this project we will investigatebosonic atoms which are coupled to photonic modes and are additionally confined to optical latticestructures. We will mainly focus on a novel coupling dominantly to the tunneling process of the atomswith or without spatially dependent phase imprint which has been proposed by the PI. We expectinteresting phases to occur such as the self-organization of complex Mott-insulating and superfluidphases or in the presence of a phase imprint, Meissner and vortex phases.The full solution of the dynamics of the combined atom-cavity system is very demanding mainlydue to three reasons: (i) the strongly correlated nature of the interacting bosonic atoms in optical lat-tices, (ii) the coupling of the spatially extended cavity mode to the atoms, which can induce effective,long-range interactions between the atoms, and (iii) the dissipative nature of the cavity mode by theleaking of the photons out of the cavity due to imperfect mirrors. We describe the combined and dis-sipative system by a Markovian master equation with a Lindblad dissipator. In order to determine theresulting dynamics we will employ different approaches. In a first approach, we will reduce the modelby adiabatically eliminating the cavity mode to an effective interacting bosonic model - with long-rangeprocesses - subjected to a self-consistency condition. For the solution of this self-consistent modelwe will develop a self-consistent implementation of the matrix product state (MPS) algorithm andthe quantum Monte-Carlo method in collaboration with project P6. The second approach aims at afull numerical simulation in quasi-one-dimensional systems. The implementation of a time-dependentMPS taking into account the dissipative and extended cavity mode with a large local Hilbert space isone of the main challenges of the project.