Using the thermal field dynamics theory to convert the thermal state into a "pure" state in doubled Fock space, we find that the average value of <i>e<sup>fa†a</sup></i> under squeezed thermal state (STS) is just the generating function of Legendre polynomials. Based on this remarkable result, the normalization and photon-number distributions of m-photon added (or subtracted) STSs are conviently obtained as the Legendre polynomials. This new concise method can be expanded to the entangled case.
© 2012 Chinese Optics Letters
Liyun Hu and Zhiming Zhang, "New approach for normalization and photon-number distributions of photon-added (-subtracted) squeezed thermal states," Chin. Opt. Lett. 10, 082701- (2012)