Efficient numerical solution of excitation number conserving quantum systems

Abstract

A system composed of a harmonic oscillator coupled to a two-level atom is one of the quantum systems, which can be completely solved. Although this system is simple, it is never a easy work for the quantum calculations, especially when the system consists of many such simple constituent parts. In this paper, we present a programming method, by which the calculation tasks for the matrix representation of the Hamiltonian of system can be automatically fulfilled. Coupled-cavity array systems are used to demonstrate our programming method. Some quantum properties of these systems are also discussed.