  Quantum many-body systems out of equilibrium can host intriguing phenomena
such as transitions to exotic dynamical states. Although this emergent
behaviour can be observed in experiments, its potential for technological
applications is largely unexplored. Here, we investigate the impact of
collective effects on quantum engines that extract mechanical work from a
many-body system. Using an opto-mechanical cavity setup with an interacting
atomic gas as a working fluid, we demonstrate theoretically that such engines
produce work under periodic driving. The stationary cycle of the working fluid
features nonequilibrium phase transitions, resulting in abrupt changes of the
work output. Remarkably, we find that our many-body quantum engine operates
even without periodic driving. This phenomenon occurs when its working fluid
enters a phase that breaks continuous time-translation symmetry: the emergent
time-crystalline phase can sustain the motion of a load generating mechanical
work. Our findings pave the way for designing novel nonequilibrium quantum
machines.
