  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 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
photonis 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, calculated using the
dynamical solution of the master equation. Our reseults reveal that while there
is no steady-state entanglement, LHC and RHC polarzied photons can be entangled
in the transient regime.
