A photonic Carnot engine powered by a quantum spin-star network

We propose a spin-star network, where a central spin-$1/2$ is coupled with XXZ interaction to $N$ outer spin-$1/2$ particles, as a quantum fuel. If the network is in thermal equilibrium with a cold bath, the central spin can have an effective temperature larger than the bath one and scaling nonlinearly with $N$. The nonlinearity can be tuned to $N^2, N^3$ or $N^4$ with the anisotropy parameter of the coupling. Using a stream of central-spin particles to pump a micromaser cavity, we calculate the dynamics of the cavity field using a coarse-grained master equation. Our study reveals that the central-spin beam effectively acts as a hot reservoir to the cavity field and brings the field 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. An alternative equivalent scheme where the spin-$1/2$ is coupled to a macroscopic spin-$(N/2)$ particle is also discussed.