An algorithm for the optical equivalence theorem

TL;DR

This paper introduces a new algorithm based on Hermite polynomials for efficiently computing expectation values of polynomial normal ordered quantum operators using coherent state representations, applicable to single and multimode fields.

Contribution

It presents a novel, fast algorithm leveraging Hermite polynomial series for calculating quantum operator expectation values, extending to multimode fields.

Findings

Efficient computation of expectation values for single-mode states.

Algorithm applicability to coherent, number, and squeezed states.

Potential extension to multimode quantum fields.

Abstract

A coherent state representation of the expectation value of an arbitrary (but still polynomial) normal ordered quantum operator is discussed. This serves as a basis for developing a fast and easy-to-handle algorithm, based on series of Hermite polynomials, for calculating such quantities. The case of single mode field with number, coherent and squeezed states is treated in detail. Some hints on how to extend the algorithm to multimode fields are also given.