Nonclassical properties of induced states from single-mode squeezed vacuum state related with Hermite excited elementary superposition operation

Abstract

Based on single-mode squeezed vacuum state (SVS) and Hermite-excited elementary superposition operator $ H_{m} (xa^{\dagger}+ya)$ , we induce two new quantum states, i.e., Hermite-excited squeezed vacuum state (HSVS) and Hermite-excite-orthogonalized squeezed vacuum state (HOSVS). HSVS is obtained by applying the operator on SVS and HOSVS is obtained by applying the orthogonalizer on SVS, where HSVS is just HOSVS for odd m. We study and compare mathematical and nonclassical properties for SVS, HSVS and HOSVS, including photon number distribution, Mandel’s Q parameter, quadrature squeezing, and Wigner function. Numerical results show that i) HSVS and HOSVS have only even (odd) photon components for even (odd) m; ii) HSVS and HOSVS can exhibit sub-Poissonian statistics in low-squeezing parameter regime and squeezing effect in large-squeezing parameter regime; iii) moreover, squeezing is always incompatible with sub-Poissonianity; iv) Wigner functions for HSVS and HOSVS have negative values in phase space.