  A minimal model of a quantum thermal machine is analyzed, where a driven two
level working medium (WM) is embedded in an environment (reservoir) whose
spectrum possesses bandgaps. overlap with hot or cold reservoirs whose spectra
are separated by a bandgap. Approximate and exact treatments supported by
analytical considerations yield a complete characterization of this thermal
machine in the deep quantum domain. For slow to moderate modulation, the
spectral response of the reservoirs is close to equilibrium, exhibiting
sideband (Floquet) resonances in the heat currents and power output. In
contrast, for faster modulation, strong-coupling and non-Markovian features
give rise to correlations between the WM and the reservoirs and between the two
reservoirs. Power boost of strictly quantum origin ('quantum advantage') is
then found for both continuous and segmental fast modulation that leads to the
anti-Zeno effect of enhanced spectral reservoir response. Such features cannot
be captured by standard Markovian treatments.
