Nonlinear Optical Generation of Multimode Entangled Squeezed Thermal States

Abstract

Squeezed states of light exhibit a reduction of quantum noise in one of their phase-space quadratures. They can be generated via a nonlinear interaction between a laser and a nonlinear dielectric material. Multimode squeezed states of light contain entanglement in the form of correlations between the quadratures of the modes in the state. Scattering loss in the dielectric material used to generate the squeezed state reduces the amount of squeezing and the strength of the correlations between the modes in the state. In this thesis, I consider the nonlinear generation of multimode squeezed states in resonant structures. The modes of these structures are inherently lossy due to scattering and coupling loss and also form a nonorthogonal basis in general. The central result of this thesis is that I show the analytic solution of the Lindblad master equation for the density operator of the generated light in the multiple lossy nonorthogonal modes of a structure has the form of a \textit{multimode squeezed thermal state}. I show that using the analytic solution makes it fast to calculate the amount of quadrature squeezing and the strength of the correlations between modes in the state as a function of time. I apply this theory to the nonlinear generation of a single-mode and two-mode squeezed thermal state in a microring resonator, and I optimize the coupling parameters of the ring to maximize the squeezing in the presence of loss or to obtain a two-mode squeezed thermal state in which the two modes are highly-correlated despite the loss. In addition, I derive a squeezing criterion that if the multimode squeezed thermal state obeys it can be considered as a cluster state and be used for continuous-variable quantum computing. Therefore, the multimode squeezed thermal state is the natural state to describe the nonlinearly generated light in systems of coupled-cavities and it provides a simply way to incorporate loss into a practical theory of entangled squeezed light generation, which opens a path to optimize this light for applications in quantum technologies.