Ultracold bosonic gases coupled to an optical cavity mode

与光腔的光子模耦合的超冷原子显示出令人着迷的现象，如Dicke相变。这是一种自组织相变，其中原子自发有序成棋盘密度图案，由于原子与光子模之间的反馈机制，光子模被占据。在这个项目中，我们将研究耦合到光子模的玻色子原子，并将其限制在光学晶格结构中。我们将主要集中在PI提出的一种新的耦合到原子的隧道过程，该过程有或没有空间相关的位相压印。我们预计会出现有趣的相，如复杂的Mott绝缘相和超流相的自组织，或者在位相印迹、迈斯纳相和涡旋相的存在下。原子-腔组合系统的动力学的完整解是非常困难的，主要是因为三个原因：(I)光学晶格中相互作用的玻色子原子的强关联性质，(Ii)空间扩展的腔模与原子的耦合，这可以诱导原子之间有效的长程相互作用，以及(Iii)由于不完善的反射镜将光子从腔中取出而产生的腔模的耗散性质。我们用一个带Lindblad耗散器的马尔可夫主方程来描述这个组合耗散系统。为了确定结果的动态，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腔模来简化模型，使其成为受自洽条件约束的具有长程过程的有效相互作用玻色子模型。对于这个自洽模型的解，我们将与P6项目合作开发矩阵乘积态(MPS)算法和量子蒙特卡罗方法的自洽实现。第二种方法是针对准一维系统的全船数值模拟。在大的局部希尔伯特空间中实现考虑耗散和扩展腔模的含时MPS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.