Photon Correlations in Two-Mode Cavity Quantum Electrodynamics

Abstract

Cavity quantum electrodynamics (cavity QED) systems, in which two-level atoms interact with a single cavity mode, have been studied extensively over the past years. Recently, the first explicitly two-mode cavity QED experiments were carried out. In this thesis, we compute photon correlation functions in a cavity QED system where a single atom couples to two cavity modes with orthogonal linear polarisations. We take into account the full atomic level structure for an F = 3 to F0 = 4 transition, and consider the case where one cavity mode is resonantly driven by a coherent field, while light in the other cavity mode is generated only through atomic emission. From analytic investigations in the weak-excitation limit, we find that two orthogonal manifolds of basis states exist, with transitions between the two manifolds occurring precisely whenever a photon from the non-driven mode is emitted. As a qualitative result, the system displays correlations on two distinct time scales: one, a short time scale, determined by the atomic and cavity-mode decay times; the other (not present in single-mode cavity QED), a much longer time scale, determined by the non-driven-mode emission rate. For a quantitative treatment, we use standard quantum regression formulas and numerical solutions of the master equation for the system density operator to compute steady-state properties and photon correlation functions in the weak-excitation regime; for this, we truncate the cavity mode Hilbert spaces at two-photon states. As with our analytical investigations, we find an extremely long correlation time at the lowest level of excitation, and a shortening of this correlation time as the level of excitation is increased. From a Monte-Carlo simulation based on a quantum trajectory unravelling of the master equation, we recover this dynamic, and explore higher levels of excitations.