Spectral origin and decoupling cost of non-Markovian ergotropy revivals in quantum batteries

Abstract Because every quantum battery is an open system, environmental memory (non-Markovianity) has been widely proposed to revive the extractable work, or ergotropy, that dissipation destroys. These predictions rest on rotating-wave, zero-temperature or second-order treatments and evaluate the ergotropy of a still-coupled battery, leaving open whether the revival is physical and how much of it can be withdrawn. We address both questions with numerically exact hierarchical equations of motion, extended to time-dependent system–bath coupling, for single and collective qubit batteries in structured baths. The revival is physical but stems from spectral weight at the battery frequency, not from memory: baths with long memory but no such weight store less work than a Markovian bath. Disconnecting the battery costs work, which we obtain in closed form. In second-order theory a revival yields net work only if it exceeds the system–bath binding energy, a bound that a smooth coupling ramp lasting a few battery periods nearly reaches, whereas a fast local unitary avoids disconnection. In circuit quantum electrodynamics, these predictions are testable with 0.2–1 ns coupling ramps and qubit readout alone. The figure of merit of an open quantum battery is therefore set by how its energy is withdrawn.