Hermite polynomial excited squeezed vacuum state: Generation and nonclassical properties

We proposed a theoretical scheme for generating a new kind of non-Gaussian state-Hermite polynomial excited squeezed vacuum states-by using parametric amplifier process and conditional measurement. Specially, two different single-mode squeezed vacuum states were injected into the signal and idler ports of parametric amplifier and m-photon was detected in idler output port, then the new non-Gaussian state is generated in signal port. It's normalization factor is found to be related with Legendre polynomials that corresponds to the success probability of such event. We investigated the nonclassical properties according to photon-number distribution, sub-Poissonian distribution, anti-bunching effect, quadrature squeezing effect, and Wigner function. It is shown that there is a wide range of nonclassical phenomena created by tuning the interaction parameters. Our study may provide a theoretical reference to generate nonclassical state for experiment.