Polaritonic quantum phase transition from a superfluid to Mott-insulator state and applications

The original idea of quantum computation and simulation proposed by R. Feynman in early 80's has been pursuit continuously by researchers in different fields in the past few decades. However, limited by the technology advance, the manipulation of microscopic objects such as single atoms, ions and excitons only becomes possible until very recently. In particular, semiconductor technology offers a unique platform for studying entities whose underlying physics are governed solely by quantum mechanics, which opens the possibility to construct on-chip quantum systems artificially with high degree of controllability.;In this thesis, we focus on the theoretical possibility to implement a quantum simulator of complex many-body physics based on solid-state devices. The specific model that we are interested in is the Bose-Hubbard model, which describes the strongly-interacting bosons in a periodic lattice potential. The quantum phase transition from a superfluid to Mott-insulator state in such a system was theoretically predicted in 1989 by M. P. A. Fisher et al. using mean field theory and experimentally confirmed in 2002 by M. Greiner et al. using ultracold atoms in an optical lattice. These ground-breaking results motivate researchers to build up quantum emulators for studying certain many-body phenomenon, e.g., the origin of High-Tc superconductors, which traditionally cannot be reliably handled by theoretical means.;The outline of this thesis is as the following. We first examine the basic concepts of Bose-Hubbard model in chapter 1, and describe two methods in chapter 2 and 3 regarding how to creative an in-plane superlattice for excitons in a semiconductor quantum well using piezoelectric acoustic waves. In chapter 4, instead of constructing excitonic superlattice, we introduce photonic superlattice by cascading optical microcavities based on photonic crystal and distributed-bragg-reflectors. By strongly coupling to impurity-bound excitons and quantum well excitons, we show the existence of characteristic superfluid to Mott-insulator quantum phase transition in these polaritonic systems. In chapter 5, we propose a massive parallel generation of nonclassical photons via polaritonic quantum phase transition, and show its deterministic and fault-tolerant nature compared to the existing proposals. Finally, we conclude this work by discussing the possible new research directions.