Immanants and their applications in quantum optics

Abstract

The regular representation of Sn appears quite naturally in the combinatorial problem of the redistribution of quantum particles though an n-channel interferometer. By using tools from representation theory, it has been shown that the coincidence rate can expressed in terms of linear combinations of permuted immanants of the scattering matrix that describes the interferometer. This thesis introduces the delay matrix, whose entries are functions of the relative time delays between particles. The delay matrix is used with Gamas’ theorem to determine exactly which immanants appear in the coincidence rate for a given set of time delays, which improves our understanding of the Hong-Ou-Mandel effect for many-particle systems. Both bosonic and fermionic systems are considered in this thesis.