Sensitivity of sub-Planck structures of mesoscopically superposed coherent states to the thermal reservoirs induced decoherence

We theoretically study the sensitivity of sub-Planck structures of mesoscopically superposed coherent states to the thermal reservoirs induced decoherence via dissipative and phase-damping processes, respectively. Under dissipative reservoir, we show that the size and area of the phase-space structures of cat and compass states do increase as the function of evolution-time, temperature of thermal reservoir, and cavity mode frequency. It is also shown that beyond the particular values of these parameters, the size and area of the phase-space structures remain no longer smaller than the limit set by the Heisenberg's uncertainty principle. Moreover we show that in contrast to the dissipative reservoir, the phase-space structures of the cat and compass states persist even in the infinitely-long evolution-time limit under phase-damped reservoir.