Quantum Optical Coherence: Applications in Photon Switching, Control of Spontaneous Emission and Atom Localization

Quantum interference and coherence lead to many interesting phenomenon and applications in quantum optics. In this dissertation, we study the quantum coherent properties in the following systems and aspects. We first investigate the optical bistability in a combined cavity-cold atoms system. In such a system the atom-photon interaction provides an optical lattice to the atoms and affects the mechanical motion of the atoms while atoms induce a position dependent phase shift on the cavity field. This highly nonlinearity induces optical bistability of intra-cavity photon number with respect to the pumping light added along the cavity axis. We show that the presence of this bistability can be controlled by a second pumping field added perpendicular to the cavity axis. It is also found that the critical input intensity of switching from one branch of bistability to the other depends on the the way of the field being added. This behavior is similar to the anomalous switching of the dispersive optical bistability of atomic media in the cavity. We also study the effect of counter-rotating terms in the control of spontaneous emission. We make use of a unitary transformation method and investigate the effect of dynamic energy shifts on the spontaneous emission modification via quantum interference in a four-level atomic system. We show that the counter-rotating terms, which are normally neglected in the usual investigation of atomic systems, do produce a significant influence on the evolution of the atomic amplitudes and the emission spectrum. This effect of counter-rotating terms can be observed in the time scale of the decay rate even when the dipole moments of the two upper levels are orthogonal to each other. The effect of counter-rotating terms on the spontaneous emission in a 3-D anisotropic photonic crystal is also discussed. It is shown that the behavior of the emission is similar to the case making rotating wave approximation, i.e., the localized and propagating fields are also separated by two characteristic atomic transition frequencies. However, the two characteristic frequencies are shifted due to the full Lamb shift which is obtained with counter-rotating terms being included in the Hamiltonian. We also utilize the unitary transformation method to show how the Lamb shift in a multi-level atom can be controlled by a driving field. Finally, we propose a subwavelength atom localization scheme for an atom located in a standing-wave field. The strategy is based on the observation that the photon statistics of resonance fluorescence depends on the position-dependent Rabi frequency.