Cavity QED with two-dimensional quantum magnets

高反射电磁腔工程的最新进展使量子光与物质之间的有效相互作用的增加远远超过其在真空量子电动力学中的强度成为可能。虽然这种增强的光-物质相互作用对原子系统的影响已经在量子光学领域进行了研究，但如今，强光-物质相互作用在凝聚态物质应用中的潜力正变得越来越明显。在这里，空腔光子可以用来改变材料性质或稳定新的量子相。本项目的主要目的是探索强光-物质相互作用在物质系统中的作用，这些物质系统本身通过其固有的电子-电子相互作用进行强相互作用。作为一个特殊的例子，我将考虑量子磁体，其中电子电荷由于库仑排斥而不移动，电子自旋通过交换相互作用相互作用。因此，量子磁体的自由度减少了，但显示出从自发对称性破缺到拓扑秩序的大范围强相互作用现象。这个光谱的一个独特部分也是量子临界点和一般的量子临界现象，其特征是系统对某些外部影响的敏感性的发散。因此，例如，外部磁场或压力的微小变化可以对整个量子磁体产生很大的影响。在这个项目中，对量子临界磁体的外部影响是通过与腔光子场的耦合来给出的，导致磁自旋与腔光之间存在强相关性。在这样的设置中，使用不同的量子磁体微观模型，我将从三个不同的角度研究与腔的相互作用。首先，我将量化空腔对磁相图的影响，包括对现有相边界和临界温度或新磁相外观的影响。其次，我将考虑磁相关对腔的反向作用，这可能导致奇异的光子态。第三，融合前面两个问题，我将寻找由于系统中相互作用而产生的强纠缠光物质状态。这些目标的延伸将是确定现实的模型，以找到在实验中观察所研究现象的途径。此外，我将考虑在腔体中添加一个弱的少光子驱动，将本项目的主要结果推广到非平衡设置，这些结果将在热平衡中获得。

Recent advances in the engineering of highly reflective electromagnetic cavities have made it possible to increase the effective interactions between quantum light and matter far beyond their strength in vacuum quantum electrodynamics. While the influence of such enhanced light-matter interactions on atomic systems has been studied in the field of quantum optics, nowadays, the potential for strong light-matter interactions in condensed matter applications is becoming increasingly apparent. Here, cavity photons may be used to alter material properties or stabilize novel quantum phases.The main objective of this project is to explore the effects of strong light-matter interactions in matter systems which by themselves are strongly interacting via their intrinsic electron-electron interactions. As a particular example of this, I will consider quantum magnets, where the electronic charges are immobile due to the Coulomb repulsion and the electron spins interact through exchange interactions. Quantum magnets thus have a reduced number of degrees of freedom, yet show a large spectrum of strongly interacting phenomena from spontaneous symmetry breaking to topological order. A distinct part of this spectrum are also quantum critical points and quantum critical phenomena in general, which are characterized by the divergence of the susceptibility of the system to certain external influences. Thus, for example, a small change in the external magnetic field or pressure can have a large effect on the quantum magnet as a whole.In this project, the external influence on the quantum critical magnet is given by the coupling to the cavity photon field, leading to strong correlations between magnetic spins and cavity light. In such a setup, using different microscopic models of quantum magnets, I will investigate the interplay with a cavity from three distinct angles. First, I will quantify the effect of the cavity on the magnetic phase diagram, including for instance, the influence on existing phase boundaries and critical temperatures or the appearance of new magnetic phases. Second, I will consider the the back action of the magnetic correlations on the cavity, which may lead to exotic photonic states. Third, fusing the two previous questions, I will search for strongly entangled light-matter states that arise as a result of the interactions in the system.An extension to these goals will be the identification of realistic models to find pathways towards observing the studied phenomena in experiments. Further, I will consider the addition of a weak few-photon drive to the cavity, generalizing the main results of this project, which will be obtained in thermal equilibrium, to a nonequilibrium setting.