E-Book Overview
Recent experimental developments in electronic and optical technology have made it possible to experimentally realize in space and time well localized single photon quantum-mechanical states. In these lectures we will first remind ourselves about some basic quantum mechanics and then discuss in what sense quantum-mechanical single-photon interference has been observed experimentally. A relativist ic quantum-mechanical description of single-photon states will then be outlined. Within such a single-photon scheme a derivation of the Berry-phase for photons will given. In the second set of lectures we will discuss the highly idealized system of a single two-level atom interacting with a single-mode of the second quantized electro-magnetic field as e.g. realized in terms of the micromaser system. This system possesses a variety of dynamical phase transitions parameterized by the flux of atoms and the time-of-flight of the atom within the cavity as well as other parameters of the system. These phases may be revealed to an observer outside the cavity using the long-time correlation length in the atomic beam. It is explained that some of the phase transitions are not reflected in the average excitation level of the outgoing atom, which is one of the commonly used observable. The correlation length is directly related to the leading eigenvalue of a certain probability conserving time-evolution operator, which one can study in order to elucidate the phase structure. It is found that as a function of the time-of-flight the transition from the thermal to the maser phase is characterized by a sharp peak in the correlation length. For longer times-of-flight there is a transition to a phase where the correlation length grows exponentially with the atomic flux. Finally, we present a detailed numerical and analytical treatment of the different phases and discuss the physics behind them in terms of the physical parameters at hand.