  We estimate the axion properties i.e. its mass, topological susceptibility
and the self-coupling within the framework of Polyakov loop enhanced
Nambu-Jona-Lasinio (PNJL) model at finite temperature and quark chemical
potential. PNJL model, where quarks couple simultaneously to the chiral
condensate and to a background temporal quantum chromodynamics (QCD) gauge
field, includes two important features of QCD phase transition, i.e.
deconfinement and chiral symmetry restoration. The Polyakov loop in PNJL model
plays an important role near the critical temperature. We have shown
significant difference in the axion properties calculated in PNJL model
compared to the same obtained using Nambu-Jona-Lasinio (NJL) model. We find
that both the mass of the axion and its self-coupling are correlated with the
chiral transition as well as the confinement-deconfinement transition. We have
also estimated the axion properties at finite chemical potential. Across the
QCD transition temperature and/or quark chemical potential axion mass and its
self-coupling also changes significantly. Since the PNJL model includes both
the fermionic sector and the gauge fields, it can give reliable estimates of
the axion properties, i.e. it's mass and the self-coupling in a hot and dense
QCD medium. We also compare our results with the lattice QCD results whenever
available.
