Continuous-variable entanglement in quantum many-body nonlinear bosonic systems

Abstract

Entanglement is a property of composite physical systems distinct from any classical description and therefore has fundamental significance in quantum theory. Although a great deal of progress has been made in understanding entanglement, there is still much unknown about this phenomenon and interest in the nature of entanglement alone continues to motivate research in this area. Moreover, a better understanding of entanglement inevitably leads to a deeper knowledge of physical processes in quantum systems. This thesis explores continuous-variable entanglement in many-body nonlinear bosonic systems with the overall aim of broadening our knowledge of entanglement, and in turn, the quantum optical systems under consideration. The secondary aim of this thesis is to further the development of entanglement as a resource for use in quantum information, communication or computing. After introducing some of the terminology and basics of entanglement theory (Chapter 1), we then provide a brief review of the main theoretical tools employed throughout this thesis (Chapter 2). We begin our investigations of entanglement by considering an evanescently coupled pair of nonlinear crystals contained in a pumped optical cavity (Chapter 3). This two-mode system is known as the intracavity Kerr nonlinear coupler and it is the output beams emerging from the cavity that provide a source of continuous-variable entangled states. Within this framework, we examine the concept of steering, a term introduced by Schr{\"o}dinger to generalize the effect described by the Einstein-Podolsky-Rosen paradox. In particular, we investigate bipartite asymmetric steering. This is an effect whereby an inseparable bipartite system can be found to be described by either quantum mechanics or local hidden variable theories, depending on which one of Alice or Bob makes the required measurements. We show that, even with an inseparable bipartite system, situations can arise where Gaussian measurements on one half are not sufficient to answer the fundamental question of which theory gives an adequate description and the whole system must be considered. We predict that asymmetric steering should arise in experiments using the intracavity nonlinear coupler, at least in the case where Alice and Bob can only make Gaussian measurements. We continue our investigations of nonlinear quantum optical systems and entanglement by studying an experimentally feasible intra-cavity coupled down-conversion scheme that makes use of concurrent nonlinearities (Chapter 4). From a theoretical perspective, we demonstrate that this scheme gives rise to a set of continuous-variable multipartite entangled output beams. Specifically, we verify that genuine quadripartite entanglement is present in this system by calculating the output fluctuation spectra and then considering violations of multipartite entanglement inequalities. The entanglement characteristics both above and below the oscillation threshold of the cavity are considered. Finally, we build on these studies of quadripartite entanglement and examine a modified intra-cavity concurrent down-conversion scheme (Chapter 5). We analyze the feasibility and potential of this scheme for generating continuous-variable cluster states. Cluster states have been proposed as a resource state for continuous-variable one-way quantum computing. We demonstrate genuine quadripartite entanglement and investigate the degree of entanglement present. We find that above the oscillation threshold, the basic cluster state geometry under consideration suffers from phase diffusion. We alleviate this problem by incorporating a small injected signal into our analysis. We also investigate squeezed joint operators, which must approach zero in the limit of large squeezing if the cluster state defining relation is to be satisfied. While the squeezed joint operators approach zero in the undepleted regime, we find that this is not the case when we consider the full interaction Hamiltonian and the presence of a cavity. In fact, we find that the decay of these operators is minimal in a cavity and even depletion alone inhibits cluster state formation