MAJORANA FERMION IN TOPOLOGICAL SUPERCONDUCTOR AND MOTT‐SUPERFLUID TRANSITION IN CIRCUIT‐QED SYSTEM

Abstract

The thesis contains two parts. In Part I, we study the Majorana fermion and its transport in the topological superconductors. In Chapter 2, we investigate the edge states and the vortex core states in the spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings. In Chapter 3, we use Keldysh non-equilibrium Green function method to study the two-lead tunneling in the superconducting nanowire with Rashba and Dresselhaus spin-orbit couplings with/without Coulomb interaction and disorder, and discuss the impact on the transport property. In Part II (Chapter 4), we propose a hybrid quantum architecture for engineering a photonic Mott insulator-superfluid phase transition. The phase diagrams in the case of real-value and complex-value photonic hopping are obtained. Also, the quantum jump technique is employed to describe the phase diagram when the dissipative effects are considered.