A photonic Carnot engine powered by a spin-star network

We propose a spin-star network, where a central spin-(1/2), acting as a quantum fuel, is coupled to N outer spin-(1/2) particles. If the network is in thermal equilibrium with a heat bath, the central spin can have an effective temperature, higher than that of the bath, scaling nonlinearly with N. Such temperature can be tuned with the anisotropy parameter of the coupling. Using a beam of such central spins to pump a micromaser cavity, we determine the dynamics of the cavity field using a coarse-grained master equation. We find that the central-spin beam effectively acts as a hot reservoir to the cavity field and brings it to a thermal steady state whose temperature benefits from the same nonlinear enhancement with N and results in a highly efficient photonic Carnot engine. The validity of our conclusions is tested against the presence of atomic and cavity damping using a microscopic master equation method for typical microwave cavity-QED parameters. The role played by quantum coherence and correlations on the scaling effect is pointed out. An alternative scheme where the spin-(1/2) is coupled to a macroscopic spin- particle is also discussed.