Optimizing Quantum Battery via Counterdiabatic driving

Abstract

We analyze the energy charging of a quantum battery within an open quantum framework, where the interaction between the battery element and an external power source is mediated by an ancilla system acting as a controllable switch. Specifically, we investigate the charging and discharging dynamics of a cavity-based quantum battery coupled to a driven qubit functioning as the charger. To ensure lossless power transfer, we utilize an adiabatic evolution protocol. Furthermore, we implement counterdiabatic driving, achieved by applying an auxiliary control field to the original Hamiltonian, to suppress undesired transitions and realize fast adiabatic dynamics. This scheme significantly accelerates the charging process. We demonstrate that the charging efficiency under adiabatic evolution is enhanced and exhibits stable, non-oscillatory behavior, and we determine the optimal duration for the operation. Finally, we show that counterdiabatic driving minimizes the path length between the initial and final states, inducing the shortest possible evolution distance.

The paper studies whether counterdiabatic (CD) control can accelerate charging of a lossy cavity quantum battery while retaining the smooth trajectory of slow driving. Its circuit-QED model comprises a classical microwave source, a dispersively coupled qubit mediator, and a storage cavity. Eliminating the qubit gives a linearly driven harmonic oscillator with zero-temperature photon loss at rate $\kappa$. Starting from vacuum, the reduced model remains in a pure coherent state. Charging therefore reduces to solving a linear equation for its amplitude, with stored energy and ergotropy both equal to $\hbar\omega_a|\alpha|^2$. Analytical solutions compare constant driving, a smooth $\sin^2$ ramp, and a CD-assisted ramp. The auxiliary complex envelope $\Omega_{\rm cd}=\dot\Omega/(i\omega_{\rm eff}+\kappa/2)$ enforces exact tracking of the instantaneous steady-state amplitude, suppressing transient oscillations at finite charging times. Using integrated squared drive amplitude as a control-cost metric, the paper obtains reference and auxiliary costs proportional to $t_f$ and $1/t_f$, respectively. Their sum is minimized at $t_f^{\rm opt}=\pi/(\sqrt{3}|i\omega_{\rm eff}+\kappa/2|)$, approximately $1.21$ ns for one parameter choice. It also reports near-unit geometric efficiency for CD trajectories. After switch-off, energy and ergotropy decay as $e^{-\kappa(t-t_f)}$; CD control does not improve retention lifetime. The analysis assumes dispersive qubit elimination, negligible thermal occupation, and Markovian cavity loss. Arbitrarily fast tracking requires diverging auxiliary-field fluence, limiting practical speed; the geometric and charging comparisons are established within this effective oscillator model.