Mimimal model of a quantum heat engine in a bandgap environment

An elegant realization of a quantum thermal machine is analyzed, where a two level system is embedded in an environment (reservoir) whose spectrum possesses bandgaps. The transition frequency of the system is periodically modulated so as to be in alternating spectral overlap with hot or cold reservoirs whose spectra are disjunct. Approximate and fully exact treatments supported by analytical considerations yield a complete characterization of this thermal machine operating in the deep quantum domain is provided. Strong correlations between work medium and reservoir and even between reservoirs emerge. They give rise to a rich pattern in the respective heat currents, power outputs and efficiencies from side-band resonances for slow to moderate driving frequencies with reservoirs still close to equilibrium to collective nonlinear resonances appearing for fast driving with reservoirs pushed to non-equilibrium.