Topics in Modern Quantum Optics

This is the written version of lectures presented at "The 17th Symposium on Theoretical Physics - Applied Field Theory", 29 June - 1 July, 1998, the Sangsan Mathematical Science Building, Seoul National University, Seoul, Korea.Comment: 97 pages, 23 figures, 187 references. Misprints corrected, most figures redrawn and references update

Thermally induced photon splitting

We calculate thermal corrections to the non-linear QED effective action for low-energy photon interactions in a background electromagnetic field. The high-temperature expansion shows that at $T \gg m$ the vacuum contribution is exactly cancelled to all orders in the external field except for a non-trivial two-point function contribution. The high-temperature expansion derived reveals a remarkable cancellation of infrared sensitive contributions. As a result photon-splitting in the presence of a magnetic field is suppressed in the presence of an electron-positron QED-plasma at very high temperatures. In a cold and dense plasma a similar suppression takes place. At the same time Compton scattering dominates for weak fields and the suppression is rarely important in physical situations.Comment: 15 pages, 2 ps figures, Late

Atomic beam correlations and the quantum state of the micromaser

Correlation measurements on the states of two-level atoms having passed through a micromaser at different times can be used to infer properties of the quantum state of the radiation field in the cavity. Long(short) correlation length in time is to some extent associated with super(sub)-Poissonian photon statistics. The correlation length is also an indicator of a phase structure much richer than what is revealed by the usual single-time observables, like the atomic inversion or the Mandel quality factor. In realistic experimental situations the correlations may extend over many times the decay time of the cavity. Our assertions are verified by comparing theoretical calculations with a high-precision Monte-Carlo simulation of the micromaser system.Comment: 4 pages, styles: aps, latex, times, epsf, More physical insight added, title and figures changed, more references. The paper can be retrieved as compressed file called elmfors.maser.ps.Z from http://connect.nbi.dk/pub/lautrup/ or via anonymous ftp at ftp://connect.nbi.dk/pub/lautrup

Anomalous Paths in Quantum Mechanical Path-Integrals

We investigate modifications of the discrete-time lattice action, for a quantum mechanical particle in one spatial dimension, that vanish in the na\"ive continuum limit but which, nevertheless, induce non-trivial effects due to quantum fluctuations. These effects are seen to modify the geometry of the paths contributing to the path-integral describing the time evolution of the particle, which we investigate through numerical simulations. In particular, we demonstrate the existence of a modified lattice action resulting in paths with any fractal dimension, d_f, between one and two. We argue that d_f=2 is a critical value, and we exhibit a type of lattice modification where the fluctuations in the position of the particle becomes independent of the time step, in which case the paths are interpreted as superdiffusive L\'{e}vy flights. We also consider the jaggedness of the paths, and show that this gives an independent classification of lattice theories.Comment: 7 pages,6 figure