What hide the Hermite coherent states?

Abstract

For the single mode the Hermite coherent states are wave packets analogous to the standard harmonic oscillator coherent states but constructed with complex Hermite polynomials substituting traditionally used complex monomials zn . Hermite coherent states unify the standard coherent and squeezed states within one class of quantum states whose representatives share all properties customarily required from the standard coherent states, in particular (over)completeness. Generalization of the Hermite coherent/squeezed states to the multimode case, illustrated on the bipartite states, shows that such states exhibit entanglement which presence or absence depends on the nature of squeezing but also on the choice of description method being used.