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Construction of Touchard polynomial’s photon added squeezing vacuum state and its nonclassical properties. (English) Zbl 1486.81136

Summary: Touchard polynomial’s photon added squeezing vacuum state (TPASVS) is constructed by operation of Touchard polynomial’s photon added operator on the squeezing vacuum state. By virtue of the technique of integration within an ordered product of operators, we derive its normalization coefficient. And its squeezing, anti-bunching effect, sub-Poissonian statistical property and Wigner function are studied. Numerical results show that TPASVS has not the squeezing effect, but it displays the anti-bunching effect and the sub-Poissonian statistical property, while its sub-Poissonian distribution property is strengthened with the increase of squeezing parameter. In addition, the negative volume of Wigner function of TPASVS decreases with the increase of squeezing parameter, until it disappears.

MSC:

81R30 Coherent states
81V80 Quantum optics
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
17B63 Poisson algebras
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