Wigner-function theory and decoherence of the quantum-injected optical parametric amplifier

Recent experimental results demonstrated the generation of a macroscopic quantum superposition (MQS), involving a number of photons in excess of 5×10⁴, which showed a high resilience to losses. In order to perform a complete analysis on the effects of decoherence on these multiphoton fields, obtained through the quantum injected optical parametric amplifier, we investigate theoretically the evolution of the Wigner functions associated to these states in lossy conditions. Recognizing the presence of negative regions in the W representation as an evidence of nonclassicality, we focus our analysis on this feature. A close comparison with the MQS based on coherent |α⟩ states allows us to identify differences and analogies.