Bridging the daemonic gap en route to charge multi-mode batteries via a single auxiliary

We show that harnessing daemonic advantage is possible while charging a quantum battery by first time-evolving the battery collectively with an auxiliary charger, followed by an energy extraction via tracing out the charger. We define the difference between the minimum daemonic ergotropy and the maximum ergotropy of the battery as the daemonic gap at the time where the ergotropy of the battery is maximum. Considering a harmonic mode as the battery and a qubit as the auxiliary charger interacting via Jaynes-Cummings interaction, we show that the daemonic gap can be closed for specific initial passive states of the battery, including the ground state, truncated mixtures of low-lying states, and canonical thermal states. We further define the daemonic band as the difference between the maximum and the minimum daemonic ergotropy, and show that starting from the ground state of the single-mode battery, the daemonic band collapses. We also show that achieving a complete charging, along with accessing the full daemonic band, is possible for the single-mode battery using all of the other initial states by repeating the charging cycle and maximizing ergotropy in every round. We extend the battery-charger design to a multi-mode resonator battery and a qudit charger, and demonstrate, for a double-mode battery and a qutrit charger, that repeating the charging cycle is vital for simultaneously charging individual modes of the collective battery.