Based on a criterion for non-classical effects in two-mode radiations recently introduced by the author and using the thermofield representation of thermal states, an expression for the minimum degree of squeezing necessary to make a two-mode thermal radiation non-classical is derived.
The thermofield introduced by Takahashi and Umezawa [Collect. Phenom. 2, 55 (1975)] is used to represent the thermal noise; it is generated from the absolute vacuum by a so-called thermalizing operator and serves as the initial state for generating two-mode squeezed states by squeeze and displacement operators. The ones obtained by applying the squeeze operator first followed by the displacement operator are called coherent squeezed states, while the others obtained by applying the displacement operator first are called squeezed coherent states. A criterion for the existence of nonclassical photon statistics in a two-mode radiation introduced by us in a previous paper [Phys. Rev. A 42, 1609 (1990)] is then used to study the conditions for the two types of squeezed states to be nonclassical states. Several three-dimensional plots are presented to illustrate the effects of thermal noise on squeezed states.