Phase sensitive pumping and coherence of superposition states

The continuous parametric pumping of a superconducting lossy QED cavity sup porting a field prepared initially as a superposition of coherent states is discussed. In contrast to classical pumping, we verify that the phase sens itivity of the parametric pumping makes the asymptotic behaviour of the cav ity field state strongly dependent on the phase theta of the coherent state \ alpha > = \ alpha \e(i theta)>. Here we consider theta = pi /4, -pi /4 a nd we analyse the evolution of the purity of the superposition states with the help of the linear entropy and fidelity functions. We also analyse the decoherence process quantitatively through the Wigner function, for both st ates, verifying that the decay is slightly modified when compared to the fr ee decoherence case: for theta = -pi /4 the process is accelerated while fo r theta = pi /4 it is delayed.