Nonclassical properties of Hermite polynomial's coherent state

In this paper, we introduce the Hermite polynomial's coherent state (HPCS) vertical bar alpha >(H), which is defined as H-n(X)vertical bar alpha > up to a normalization constant and where H-n(X) is the coordinate operator's Hermite polynomial of order n and vertical bar alpha > = exp(-1/2)vertical bar alpha vertical bar(2) + alpha alpha(dagger))vertical bar 0 >. This state may be produced by the superposition of some different photon added coherent states when n = 2. The mathematical and physical properties of HPCS are also studied. It is shown that HPCS has remarkable nonclassical state features such as sub-Poissonian and squeezing properties. (C) 2012 Optical Society of America