Non-Gaussianity and decoherence of generalized photon-added coherent state as a Hermite-excited coherent state

Generalized photon-added coherent state (GPACS) is obtained by repeatedly acting the combination of Bose creation and annihilation operations on the coherent state. It is found that GPACS can be regarded as a Hermite-excited coherent state due to its normalization factor related to a Hermite polynomial. In addition, we adopt the Hilbert-Schmidt distance to quantify the non-Gaussian character of GPACS and discuss the decoherence of GPACS in dissipative channel by studying the loss of nonclassicality in reference of the negativity of Wigner function.