Atom-photon Interactions without Rotating-wave Approximation and Standing Wave Coupled Electromagnetically Induced Transparency System

This thesis includes two topics. Part 1 is on the various atom-photon interactions without rotating-wave approximation (RWA). Part 2 is on the reflection and transmission in a standing wave coupled electromagnetically induced transparency (EIT) system.;Part 1. In the RWA, the counter-rotating terms in the atom-photon interaction Hamiltonian are neglected. Its validity is the result of energy conservation. However, if the time scale is sufficiently small, the uncertainly in the energy can become large, according to the Heisenberg uncertainty principle. Thus the RWA can not be applied in the study of the short time behavior, such as the quantum Zeno effect (QZE) and anti-Zeno effect (QAZE), the Lamb shift, the non-resonant polarizability and shifts in the superradiance and subradiance. To go beyond RWA, we apply a unitary transformation on the Hamiltonian. In the transformed basis, there are only secular transitions due to rotating terms with modified coupling constants.;We start from the interactions between atom and vacuum. For the hydrogen atom, there is no QAZE in free vacuum. However, with the modification in the density of states of the vacuum by a cavity or a meta-material, the QAZE appears and the Lamb shift changes. We then turn to the atom in light field, where the polarizability of a two-level atom is calculated and the results satisfy the optical theorem. The unitary transformation is then applied to two identical atoms interacting with vacuum. Their various emission spectra of the superradiance and subradiance and the QZE and QAZE are studied.;Part 2. In an EIT system, if the coupling field is a standing wave, the susceptibility of the medium is periodically modified to form a one-dimensional photonic crystal (1DPC). In contrast to the conventional treatment with transfer matrix, we use Maxwell-Liouville coupled-wave equations and propose new criteria for the bandgap of the photonic crystal (PC). The relevant quantity is the ratio between the nonlinear coupling coefficient and the wave vector mismatch plus the linear susceptibility, which is the nonlinear effect over the linear effect.;First, we study the quantitative relation between the position and width of the photonic bandgap and the experimental parameters. We then show that, as the temperature rises, the 1DPC melts down and enters the Doppler-free wave-mixing regime. By introducing detuning between the two counter-propagating fields in the standing wave, we make the envelope of the standing wave move and form a ‘flying’ 1DPC. Owing to the Doppler Effect, the probe fields propagating along with or counter to the moving direction have different frequencies in the 1DPC frame. In the rest frame, the transmission spectra in two directions are thus shifted with respect to each other and we obtain an optical diode.