Nonclassical properties of Hermite polynomial’s coherent state

• DOI: 10.1364/josab.29.003412
• Publication Date: 2013-02-26T20:41:44Z
• Authors: Gang Ren; Jian-ming Du; Hai-jun Yu; Ye-jun Xu
• Keywords: 0103 physical sciences; 01 natural sciences

In this paper, we introduce the Hermite polynomial’s coherent state (HPCS) |α〉H, which is defined as Hn(X)|α〉 up to a normalization constant and where Hn(X) is the coordinate operator’s Hermite polynomial of order nand |α〉=exp(−(1/2)|α|2+αa†)|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.