Multiple Schrodinger cat states at finite temperature

A multiple Schrodinger cat state can be defined as a quantum superposition of an arbitrary number of coherent states. In this paper, we study the proc ess of decoherence of such multiple states in interaction with their enviro nments, using the model of a harmonic oscillator coupled to a thermal bath. The evolution of a superposition of various coherent states into a statist ical mixture is described with the Wigner distribution function. The decohe rence effect is expressed in analytic form, and it is seen that the damping time is very sensitive to the temperature. Multiple superpositions of stat es can be conveniently described using crystallographic group techniques; n umerical calculations of the Wigner functions for some typical groups are a lso presented.