From maximum work to maximum power in an optimally controlled quantum Ising Otto engine

In finite-time quantum Otto engines, maximizing power requires balancing the duration of the unitary strokes against the losses from nonadiabatic excitations. We address this trade-off in an Otto engine with a free-fermion working medium, using quantum optimal control. Having determined the single-particle energy scales that maximize ideal work at fixed reservoir temperatures, we realize them as the two endpoint Hamiltonians of a transverse-field Ising chain, connected by a path that crosses the quantum critical point. Optimal control of the unitary strokes yields near-ideal work on a time scale growing linearly with system size, instead of quadratically as for linear driving. We derive a time-rescaling relation that maps protocols with different energy scales onto a single reference problem and, for complete thermalization strokes of fixed duration, use it to build an analytical model of the cycle power. The model predicts two competing maximum-power regimes: a slow branch that approaches the ideal work, and a fast, size-independent branch that trades work for a shorter cycle and dominates above a crossover size, in quantitative agreement with numerical optimal-control results. It also identifies power-optimal energy scales that differ from the work-optimal ones and further increase the power. Our results provide a predictive approach to jointly optimizing the operating conditions and finite-time dynamics of quantum heat engines.