Generalized Coherent States and Phase-Space-Interface in Multi-Mode Systems

Abstract

The Hilbert space of a single mode quantum system is spanned by a countable set of orthonormal basis states denoted |n〉 for n = 0, 1, 2, … Such a basis can be used to define quasi-probability distributions over a two-dimensional quantum phase plane. Multi-mode quantum systems are spanned by orthonormal product states |n1,…nk〉 = |n1〉 ⊗ … ⊗ |nk〉 which can be used to define quasiprobability distributions over a 2k-dimensional phase volume. However, this multi-mode basis set is also countable and can be uniquely specified by a single integer label. This labeling allows us to define new collective operators and generalized coherent states to construct probability distributions over a new two-dimensional phase plane. These distributions represent the system's 2k-dimensional phase volume with perfect fidelity, and allow us to apply phase space interference (PSI) approaches to multi-mode quantum systems.