Preparing superposition of squeezed coherent states under thermal reservoir

We propose a scheme for engineering a superposition of squeezed coherent states into a lossy cavity and study its evolution under the influence of a thermal reservoir, providing analytical results for the Wigner function as well as for the Glauber-Sudarshan P function. To characterize this state, we study both the fidelity and the atomic inversion for several parameters, including some parameters taken out from recent experiments in cavity QED.