Single-photon Transport Property In Circuit QED

Quantum computer may solve certain problems much faster than classical computer due the principle of coherent superposition in quantum mechanics. Moreover, quantum computer may also solve some problems that are impossible by classical computer. Up to the present, many physical systems have been demonstrated successful to realize quantum computing, including nuclear magnetic resonance (NMR), quantum dots, ion traps, linear optics, superconducting Josephson junctions and cavity quantum electrodynamics (cavity QED). Each of these systems possesses its own advantages and disadvantages, and has been studied by different group. Nevertheless, superconducting Josephson junctions and cavity QED are two promising systems due to their long coherent time and good physical integration.Recently, the concept of cavity QED has been introduced superconducting Josephson junctions, and they form a new hybrid system to realize quantum computing and quantum information processing, i.e., circuit QED, which attracts increasing interest and obtains many progresses. In this thesis, we focus on the circuit QED system and study the photon transport property. It is shown that, dependent on the system's relaxation rates, an external weak microwave field can dramatically change the lineshapes of the transmission and reflection spectra. Fano-like resonant transmission and electromagnetically induced reflection lineshapes are predicted.This dissertation consists of five chapters.Chapter 1 gives some basic introduction to quantum computing and quantum information processing.In Chapter 2, we study superconducting Josephson qubits by introducing the BCS theory, the Ginzberg-Landau theory, and the dc and ac Josephson phenomena. In particular, we introduce a kind of Josephson charge qubit: the Cooper-pair box (CPB), and review some important experimental results concerning Josephson charge qubit. As a supplement, Josephson persistent charge qubit is also presented briefly.Chapter 3 focuses on cavity QED. We study in detail the interaction between a two-level atom and a single mode cavity, i.e., the standard Jaynes-Cummings model, and obtain its input-output formula.In Chapter 4, we describe the theory of the superconducting transmission-line resonator (TLR), and study the voltage distribution of the TLR.In Chapter 5, we study the coupled CPB-TLR system. We examine the interaction among two capacitively coupled CPBs and a 1D TLR, and obtained the photon transport property. It is numerically demonstrated that an external weak microwave (MW) field can dramatically change the lineshapes of the transmission and reflection spectra. We analyze the influence of many system parameters on the spectra, including the magnitude of the MW field, the cavity decay, the decay of the CPBs, the CPB-TLR detuning and the CPB-TLR coupling coefficient.