Decoherence of superpositions of displaced number states

We study the decoherence of even and odd superpositions of displaced number states in the frameworks of the standard master equation, describing phase insensitive attenuators and amplifiers. We compare different possible definitions of the 'decoherence time' and show that the frequently used approaches based on the time derivatives of some quantities (such as the 'quantum purity'), taken at the initial moment, are not quite satisfactory for quantum states characterized by several parameters, due to the absence of the scaling laws. Defining the conditional decoherence time as the time necessary for diminishing the interference peak of the Wigner function to the given relative level, we study its dependence on the initial distance between peaks |α|, excitation number m and parameters of the reservoir. We show that highly excited states with can be more robust against decoherence than the coherent superpositions with m = 0.