New Even and ODD Coherent States Attached to the Hermite Polynomials

Following systematic strategies, which were introduced by M. M. Nieto in 1995, coherent states (CSs) may be derived from their generating functions. In the present paper we generalize the latter procedure to new types of generating functions of even and odd Hermite polynomials. In this case, new CSs are obtained, as superposition of even and Fock states, and the generating functions are proportional to the corresponding even (odd) CSs. It is shown that they realize resolution of the identity conditions and can be considered as the nonlinear CSs. In addition, in each case, one can identify some of nonclassical features, such as sub-Poissonian statistics and quadrature squeezing effects, which occur simultaneously.