Wigner function for squeezed negative binomial state and evolution of density operator for amplitude decay *Project supported by the National Natural Science Foundation of China (Grant No. 11347026) and the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2016AM03 and ZR2017MA011). (September 2019) - Lv 吕, Heng-Yun 恒云; Wang 王, Ji-Suo 继锁; Zhang 张, Xiao-Yan 晓燕; Wu 吴, Meng-Yan 孟艳; Liang 梁, Bao-Long 宝龙; Meng 孟, Xiang-Guo 祥国
Abstract : Using the thermal-entangled state representation and the operator-ordering method, we investigate Wigner function (WF) for the squeezed negative binomial state (SNBS) and the analytical evolution law of density operator in the amplitude decay channel. The results show that the analytical WF is related to the square of the module of single-variable Hermite polynomials, which leads to a new two-variable special function and its generating function, and the parameters s and γ play opposite roles in the WF distributions. Besides, after undergoing this channel, the initial pure SNBS evolves into a new mixed state related to two operator Hermite polynomials within normal ordering, and fully loses its nonclassicality and decays to vacuum at long decay time.