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

Abstract

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.

New operator identities with regard to the two-variable Hermite polynomial by virtue of entangled state representation

“…[7] In Refs. [8]- [10], it is pointed out that the two-mode squeezed number state is just a TVHP excitation on the two-mode squeezed vacuum state. Very recently, Ma's group has investigated the nonclassicality of a TVHP state, considered as a two-mode photon subtracted squeezed vacuum state.…”