  We study the relation between the continuum threshold as function of the
temperature $s_0(T)$ within finite energy sum rules and the trace of the
Polyakov loop $\Phi$ in the framework of a nonlocal SU(2) chiral quark model,
establishing a contact between both deconfinement order parameters at finite
temperature $T$ and chemical potential $\mu$. In our analysis, we also include
the order parameter for the chiral symmetry restoration, the chiral quark
condensate.
  We found that $s_0$ and $\Phi$ providing us the same information for the
deconfinement transition, both for the zero and finite chemical potential
cases. At zero density, the critical temperatures for both quantities coincide
exactly and, at finite $\mu$ both order parameters provide evidence for the
appearance of a quarkyonic phase.
