Optimal work extraction from quantum states by photo-assisted Cooper pair tunneling

We theoretically investigate work extraction from quantum states via an engine. The latter consists of a superconducting circuit, where a LC-resonator is coupled to a Josephson junction. The oscillator state fuels the engine, providing energy absorbed by Cooper pairs, thus producing work in the form of an electrical current against an external voltage bias. We show that this machine can extract the maximal amount of work from all single-mode Gaussian states as well as from all Fock states. Furthermore, we consider work extraction from a continuously stabilized oscillator state. In both scenarios, coherence between energy eigenstates is beneficial, increasing the power output of the machine. This is possible because the phase difference across the Josephson junction provides a phase reference. Our results demonstrate that fundamental bounds for work extraction, as derived in abstract theories of quantum thermodynamics, can be saturated in realistic scenarios, where control is limited and where work is a measurable and unambiguously useful quantity.