Destruction of higher-order squeezing by thermal noise

We examine the influence of thermal noise on several non-classical properties of squeezed number states. In order to evaluate arbitrary-order moments of both amplitude and quadrature operators of the superposition, we use a normal-ordering technique based on McCoy's theorem. Our analytical results are compact formulae involving Gauss hypergeometric functions. We find that the thermal mean occupancy sufficient to destroy squeezing to any order is less than 1/2. Other non-classical features of a squeezed number state, such as painwise oscillations in the photon number distribution, sub-Poissonian statistics and amplitude-squared squeezing disappear completely above this threshold.