Excited Two-Mode Generalized Squeezed Vacuum State as a Squeezed Two-Variable Hermite Polynomial Excitation State

• DOI: 10.1007/s10773-010-0290-9
• Publication Date: 2010-03-05T10:40:43Z
• Authors: Ye-Jun Xu; Hong-Chun Yuan; Qiu-Yu Liu
• Keywords: Wigner distribution function

A new class of excited two-mode generalized squeezed vacuum states denoted by |r,s,m,n〉 are presented, which are obtained by repeatedly applying creation operators a† and b† on the two-mode generalized squeezed vacuum state. We find that it is just regarded as a generalized squeezed two-variable Hermite polynomial excitation on the vacuum state and its normalization constant is just a Jacobi polynomial. Their statistical properties are investigated such as squeezing properties, photon number distribution and the violations of Cauchy-Schwartz inequality. Especially, the Wigner function for |r,s,m,n〉 depending on the excitation photon numbers is discussed graphically.