Nonclassical thermal-state superpositions: Analytical evolution law and decoherence behavior

Employing the integration technique within normal products of bosonic operators, we present normal product representations of thermal-state superpositions and investigate their nonclassical features, such as quadrature squeezing, sub-Poissonian distribution, and partial negativity of the Wigner function. We also analytically and numerically investigate their evolution law and decoherence characteristics in an amplitude-decay model via the variations of the probability distributions and the negative volumes of Wigner functions in phase space. The results indicate that the evolution formulas of two thermal component states for amplitude decay can be viewed as the same integral form as a displaced thermal state ρ(V,d), but governed by the combined action of photon loss and thermal noise. In addition, the larger values of the displacement d and noise V lead to faster decoherence for thermal-state superpositions.