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Acta Sinica Quantum Optica

Nonclassical Property of Inverse Coordinate Operator Excited Coherent States

余之松 YU Zhi-song, 任桂华 REN Gui-hua, 范洪义 FAN Hong-yi

Published Jan 1, 2013• 1 citation
Publisher
DOI
10.3788/asqo20131904.0296

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In this paper,we introduce a new nonclassical quantum state,an inverse coordinate operator excited coherent state.By using the IWOP technique,the normally ordering form of inverse coordinate operator and the normalization factor are derived.It is shown that the normally ordering form is related to Hermit polynomial.On the basis of the coherent state representation of the Wigner operator,the Wigner function is also calculated,whose negative property is used to discuss the nonclassical property of the nonclassical quantum state.
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.