Hermite polynomial excited squeezed vacuum as quantum optical vortex states

We introduce theoretically a kind of Hermite polynomial excited squeezed vacuum by extending the wave-packet states with a vortex structure to a general case. Its normalised factor is found to be the Legendre polynomial and the condition converting the general case to a special one is achieved. Then we consider its statistical properties according to the photon number distribution and the Wigner function. As an application, we investigate the performance of the teleportation of the coherent state. It is shown that these parameters in the generalised state can modulate all the above properties including the vortex structure. (letter)