Dissipative qutrit-mediated stable charging

In this work, we propose a stable charging scheme mediated by a three-level system (qutrit), which renders a unidirectional energy flow from an external power source to an $(N+1)$-dimensional quantum battery. By virtue of the qutrit dissipation, the battery avoids the spontaneous discharging induced by the time-reversal symmetry of any unitary-charging scheme. Irrespective of the initial state, the battery can be eventually stabilized at the maximal-ergotropy state as long as the charger-battery interaction is present. We use a Dyson series of Lindbladian superoperator to obtain an effective master equation for the battery, which is found to be equivalent to the high-order Fermi's golden rule adapted to the non-Hermitian Hamiltonian and spontaneous decay. We extract the optimization condition for charging efficiency and justify it in the finite-size battery with uniform energy splitting, the large spin battery, and the truncated harmonic-oscillator battery.