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 efa†a 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)