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 N², N³ or N⁴ 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.