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Dissipation tends to wash out dynamical features observed at early evolutiontimes. In this paper we analyze a resonant single--atom two--photon quantumoptical amplifier both dynamically and thermodynamically. A detailedthermodynamic balance shows that the non--linear amplifier is thermodynamicallyequivalent to the linear amplifier discussed in (Phys. Rev. A, 74 (2006),063822). However, by calculating the Wigner quasi--probability distribution forvarious initial field states, we show that unique quantum features in opticalphase space, absent from the linear amplifier, are maintained for extendedtimes. These features are related to the discrete nature of the two--photonmatter--field interaction, and fingerprint the initial field state atthermodynamic times.

Thermodynamic indistinguishability and field state fingerprint of quantum optical amplifiers