Linear beam splitters, mode coupling and interference in quantum optics

The third lesson dealt with the analysis of interference experiments in quantum optics. It began with a description of the linear splitter blades that are essential ingredients in these experiments. It is these blades that separate and recombine the beams, distributing the photons into their two output paths. We recalled how this photon distribution takes place, and showed how the combination of two blades was used to build the Mach-Zehnder interferometer, a simple prototype device that has been used to perform a number of fundamental quantum optics experiments. We have recalled some of these experiments, demonstrating both single-photon and two-photon interference effects. In the first case, interference corresponds to the passage of a single photon through two different paths at the same time. In the second, it is the combined system of the two particles that follows two different paths in state space before the corresponding probability amplitudes recombine in the detected coincidence signal. We emphasized that interference involves not the particle(s) themselves, but rather the probability amplitudes associated with the system. We also showed how a splitter blade could be used to make a homodyne measurement of a quadrature of the field, and illustrated this method by measuring the quadratures of a Schrödinger cat state.