Spin-mechanical thermal machines

We present a framework for developing quantum thermal machines—a quantum battery and a quantum Otto engine—using a single nitrogen-vacancy (NV) center coupled to a low-frequency mechanical oscillator. These machines are engineered to operate in a regime where the oscillator's frequency is much smaller than the NV center’s spin transition and relaxation rates. By employing carefully timed microwave pulses and rapid optical spin resets, we enable on-demand, coherent energy transfer between the NV center and the oscillator. In the quantum battery mode, energy is incrementally stored in or extracted from the oscillator's long-lived motional states via discrete spin flips. Furthermore, spin-driven protocols facilitate a cooling mechanism that reduces the oscillator's effective phonon population below thermal equilibrium, even for frequencies lower than the spin's decoherence scale, effectively engineering a cold bath. Integrating this spin-cooling mechanism into an Otto cycle while maintaining contact with a hot reservoir enables the realization of a single-bath quantum heat engine. This engine generates mechanical work with near-optimal efficiency in finite time without requiring environmental decoupling.