Synthesis of Hermite polynomial excited squeezed vacuum states from two separate single-mode squeezed vacuum states

A projection synthesis scheme for generating Hermite polynomial excited squeezed vacuum states (HPESVSs, non-Gaussian quantum states) is proposed. Injecting two separate single-mode squeezed vacuum states into a beam splitter and counting the photons in one of the output channels (conditional measurement or post-detection), the conditional state in the other channel is just the HPESVS. The success probability, related to a Legendre polynomial form, is obtained analytically and analyzed numerically in detail. To exhibit the nonclassical effects of this conditional state, we also present the photon-number distribution, sub-Poissionian distribution, anti-bunching effect, quadrature squeezing effect, and Wigner function, respectively. The results show that by tuning the interaction parameters, a wide range of nonclassical phenomena can be created.