The Investigation Of Photonic Crystal One-atom Laser By Quantum Theory

In this paper, we applied the quantum theory to investigate the cavity field property of photonic crystal one-atom laser. Especially, the following two issues are discussed in detial:First of all, by calculating the photon number distribution and quantum degree of second order coherence of cavity field, we investigate the coherent properties and statistical properties of the photonic crystal one-atom laser. Contrary to the previous literatures which studied in the steady-state conditions, we consider the case in the transient regime. Under the secular approximation, we found that the cavity field photon statistics is super-Poissonian both in good cavity regime and bad cavity regime, and that an absolutely antibunching field cannot be generated. Furthermore, the time evolution of photon statistics and quantum degree of second-order coherence can be manipulated by the discontinuities in the photon density of states of photonic reservoir. However, their evolution processes are insensible to the jump of photonic density of states. In addition, by going beyond the secular approximation, we show that in the presence of non-secular terms the cavity field displays a variable degree of second-order coherence as a function of discontinuities in photonic density of states. For large discontinuities the cavity field is characterized by photon antibunching and sub-Poissonian. In the case of a vanishing photonic density of states on the lower Mollow sideband, we can obtain only weak antibunching [g(2)(0)=0.77]. If the jump in the photonic density of states is small, the bunching and super-Poissonian field is generated in the cavity. Consequently, the cavity exhibits certain non-classical features when non-secular terms are included into the dynamics of system. The study clearly illustrate the ability to control cavity field through suitable photonic crystal architectures and provide a further insight into one-atom laser in constructed vacuum.Moreover, we investigate the property of optical bistability in a photonic crystal one-atom laser when nonlinear microcavity is present. The physical system consists of a coherently driven two-level light emitter strongly coupled to a high-quality microcavity which is embedded within a photonic crystal, and another coherent probing field which has incident into the microcavity. In our case, the microcavity is fabricated by nonlinear material and placed as an impurity in photonic crystal. This study reveals that such a system can exhibit optical bistability. And the dependence of threshold value and hysteresis loop on the photonic band gap of the. photonic crystal, driving field Rabi frequency and dephasing processes are studied. Our results clearly illustrate the ability to control optical bistability through suitable photonic crystal architectures and external coherent driving field. And this study suggests that in a photonic crystal nonlinear microcavity the one-atom laser act as an effective controllable bistable device in the design of all-light digital computing systems in the near future.