Beyond semiclassical approach in the study of light-matter interactions

The technological advances in the research of light-matter interaction over the last few years has led to considerable interest in the study of newer quantum protocols. The majority of theoretical and experimental studies on these systems have focused on two very distinct regimes: On the one hand, macroscopic ensemble of emitters and their collective properties have been investigated in the context of superradiance, protection against decoherence, and quantum memories. In this macroscopic limit, however, the light-matter interaction can be treated already on a semiclassical level. On the other hand, in the microscopic limit, where a single emitter couples to a cavity, the interaction demands full quantum solutions, resulting in exotic nonclassical phenomena such as entanglement, photon-blockade, and single-photon emission. There also lies a largely uncharted mesoscopic regime that offers the unique possibility to synergistically combine collective with non-classical features that are otherwise restricted to the two separate regimes mentioned above. In this talk, we will discuss theoretical approaches that take us beyond the semi-classical approach but are also not limited to very small systems. Using tools from many-body physics such as tensor-network algorithms, along with quantum trajectories and quantum regression theorem, we show how a large swathe of interesting physics remains to be explored ranging from non-equilibrium phase transitions in photon condensates to generation of nonclassical light and trapped entangled states in hybrid quantum systems.