Dissipation and Interactions in Quantum Optics

Abstract

Quantum optics, the study of light at the level of its building blocks, has been one of the frontiers of science. The arena of quantum optics has been fruitful for investigations of a wide range of interesting questions, from those on the fundamental structures in driven dissipative systems to those on applications of quantum information processing and quantum communication. The first part of this thesis is concerned with one of the holy grails of quantum optics: an efficient transfer of energy (coupling) between single photons and matter degrees of freedom. From a certain point of view, the problem of efficient coupling is purely geometrical. The efficiency of coupling between an atom and light is difficult because it is difficult to shape the wavefunction of a single photon such that it overlaps perfectly with the matter degree of freedom (emitter). The first contribution of this thesis is addressing this issue by considering an emitter which perfectly matches the single photon plane-wave. Moreover, luckily, such an emitter is already realized in nature in the form of a two-dimensional crystal. We show that a new generation of two-dimensional semiconductors, transition metal dichalcogenide (TMD) monolayers, have especially favorable characteristics for allowing highly efficient coupling between photons and matter degrees of freedom. One of the most important goals in realizing an efficient coupling between photons and matter degrees of freedom is that unlike photons, matter excitations interact with each other. Hence, if we would like to have photons which act as if they interact, one possible way is to first convert them into matter excitations, and then transfer the correlations due matter interactions back to photons. As the second contribution of this thesis, we demonstrate that TMD monolayers placed within a cavity can help us create photons which avoid each other as if they interact. The effect can be simply understood as the TMD monolayer acting as a filter for photons, such that it only allows the passage of one photon at a time. Besides being the fundamental building block of light, photons also serve as mediators of interactions between charged particles. In a sense, two positive charges repel each other because there is always a photon which lets them know that they are close to one another. On the other hand, systems of many interacting particles behave in a completely different way then when they are alone. It may even be argued that all physical phenomena at some level emerge from the behavior of many interacting constituents. Given this point of view, it is crucial to find ways to control photons in order to control the interactions that they mediate between matter degrees of freedom. As the third contribution of this thesis, we analyze an experimental scheme where the control of photonic degrees of freedom can allow an experimentalist to modify the strength and range of interactions between matter. In particular, we propose squeezed photon states as a resource to control such interactions. The second part of this thesis is concerned with the emergent phenomena arising in a system of many interacting particles. In particular, the fourth contribution of this thesis considers the combination of two fascinating phenomena which emerges such condensed matter systems: superconductivity and geometric effects in lattice band structures. Separately, both superconductivity and the non-trivial geometrical effects in lattice systems are well-established subfields of condensed matter physics. Yet only more recently, the combination of these two phenomena were investigated in the context of topological superconductors, as well as other superconducting states which emerge on top of band structures with non-trivial geometry. In our study, we attempt at clarifying one of the ways that the non-trivial geometry associated with the lattice band structure may affect the dynamics of an emergent superconducting state. Surprisingly, our analysis shows that one of the most robust characteristics of the superconductor, vortices enclosing a quantum of magnetic flux, can be modified due to geometrical effects.