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.
Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom failsin the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization. The effect can be understood in a simple picture: Interaction requires an exchange of energy. In the quantum regime, the possible quanta of energy are discrete. If the extractable energy of one oscillator does not exactly match the amount the second oscillator may absorb, interaction, and thereby synchronization is blocked. We demon- strate this effect, which we coin quantum synchronization blockade, in the minimal example of two Kerr-type self-oscillators and predict consequences for small oscillator networks, where synchronization between blocked oscillators can be mediated via a detuned oscillator. We also propose concrete implementations with super- conducting circuits and trapped ions. This paves the way for investigations of new quantum synchronization phenomena in oscillator networks both theoretically and experimentally.