Continuous-variable polarization mode entanglement in a V-type micromaser

The micromaser is an archetype experimental setting where a beam of excited two-level atoms is injected into a high-finesse cavity. It has played a pivotal role as a testbed for predictions of quantum optics. We consider a generalized micromaser setting consisting of a high-quality cavity pumped by a beam of three -level atoms. The atoms are assumed to be prepared to carry quantum coherence between their excited state doublet. Our objective is to produce quantum entanglement between the right-handed circular (RHC) and left-handed circular (LHC) polarized photons in the cavity, exploiting the quantum coherence in the pump atoms. For that aim, we derive the generalized micromaser master equation for our system. We find that the dynamics of the micromaser field driven by the pump beam is equivalent to two non-interacting RHC and LHC photonic systems sharing a common non-equilibrium environment. The effect of the shared bath is to mediate an incoherent interaction between the otherwise non-interacting cavity photons, which emerges only if the atoms carry quantum coherence. We take into account cavity losses as a source of quantum decoherence and characterize the quantum entanglement between the LHC and RHC polarized photons in terms of logarithmic negativity, Hillery-Zubairy and spin squeezing criterion, calculated using the dynamical solution of the master equation. We show that, in the same parameter regime, one of the criteria shows entanglement while for the other never detects entanglement. Our results reveal that LHC and RHC polarized photons can be entangled in the transient regime according to the logarithmic negativity criterion.