Quasi-probability distributions and decoherence of Hermite-excited squeezed thermal states

Abstract

We theoretically put forward the Hermite-excited squeezed thermal states (HESTS) by applying operator Hermite polynomials on squeezed thermal states. Starting from the normally ordered density operator of squeezed thermal states and operator Hermite polynomials, the normalization factor is obtained, which is related to the Legendre polynomials. Several phase-space distribution functions, i.e., the Q function, P function, Wigner function (WF), and R function, are analytically derived. And the non-Gaussianity and nonclassicality are mainly reflected by the negativity of non-Gaussian WF and the existence of nonclassical depth. In addition, by deriving the normally ordered density operator and WF of HESTS in the laser channel, the decoherence effect is studied and discussed. Finally, the quantity in measuring non-Gaussianity is calculated to further quantitatively measure the non-Gaussianity of the resulting states.