Nonclassicality Of NonGaussian Operation On The Single And Two Mode Squeezed Vacuum State And Its Decoherence In Thermal Environment

In the first part, we studied the statistical properties of two-mode photon-addedsqueezed vacuum state (TPASV) and its decoherence in a thermal environment. Byconverting the TPASV to a squeezed Hermite polynomial excitation state, we obtain acompact expression for the normalization factor of m-TPASV, which is the Jacobipolynomial of the squeezing parameter. we also derive the explicit expression of WFof m-TPASV and find the negative region of WF in phase space. The decoherenceeffect on this state is then discussed by deriving the time evolution of the WF anddiscuss the loss of nonclassicality using the negativity of WF.In the second part, the nonclassical properties of m-coherent superpositionoperation (ua+va~t)~m on the single-mode squeezed vacuum state (M-SSVS) andits decoherence in a thermal environment have been studied. Converting the M-SSVSto a squeezed Hermite polynomial excitation state, we obtain a compact expressionfor the normalization factor of M-SSVS, which is the Legendre polynomial of thesqueezing parameter.We also derive the explicit expression of Wigner function (WF)of M-SSVS and find the negative region of WF in phase space. The decoherenceeffect on this state is then discussed by deriving the time evolution of the WF. Usingthe negativity of WF, the loss of nonclassicality has been discussed.