New approach for normalization and photon-number distributions of photon-added (-subtracted) squeezed thermal states

TL;DR

This paper introduces a novel method using thermal field dynamics to efficiently compute normalization and photon-number distributions of photon-added or subtracted squeezed thermal states, revealing a connection to Legendre polynomials.

Contribution

It presents a new, concise approach leveraging thermal field dynamics to derive photon-number distributions, extending to entangled states, and linking to Legendre polynomials.

Findings

Normalization and distributions expressed as Legendre polynomials

Method applicable to entangled states

Simplifies calculations of photon-added/subtracted states

Abstract

Using the thermal field dynamics theory to convert the thermal state to a "pure" state in doubled Fock space, it is found that the average value of e^{fa^{{\dag}}a} under squeezed thermal state (STS) is just the generating function of Legendre polynomials, a remarkable result. Based on this point, the normalization and photon-number distributions of m-photon added (or subtracted) STS are conviently obtained as the Legendre polynomials. This new concise method can be expanded to the entangled case.