Algebraic power scaling in a slowly-quenched bosonic quantum battery

Abstract

Bosonic modes provide a promising platform for quantum batteries as a result of their unbounded energy spectrum. However, the energy that can be stored during a coherent charging process is limited due to coherent oscillations between the charger and battery. In this Letter, we show that by introducing a slow quench in the interaction between a coherently driven quadratic oscillator battery and a charger system, the maximum battery power ($P_{B,m}$) scales algebraically with the quench duration ($τ_Q$), i.e., $P_{B,m} \propto τ_Q^α$, where $0<α\leq2$ is a function of the quench ramp exponent. This finding implies that, counterintuitively, slower quenches lead to faster charging. Such a quench suppresses coherent energy oscillations between the battery and the charger, allowing an unbounded increase in power. Furthermore, we discuss the effect of charger dissipation, which imposes a finite limit on the maximum power. We also show that the temporal extensive scaling occurs in a broader context by mapping the system to a coherently driven Tavis-Cummings battery.

Figures (3)

• Figure 1: Illustration of the oscillator quantum battery with a continuously quenched coupling $g(t)$. The charger is powered with a coherent external drive. Both the battery and charger are initially at the ground state.
• Figure 2: Temporal extensivity of the charging process in a lossless system ($\gamma=0$) with a linear quench profile ($r=1$). (a) Dynamics of the stored energy $E_B(t)$ (in units of $\omega_0 F^2$) for various quench durations $\tau_Q$. The envelope of the oscillations grows with $\tau_Q$, contrasting with the bounded behavior of the instantaneous quench ($r=0$) shown in the inset. The dashed line in the inset corresponds to the $t^2$ scaling. (b) Log-log plot of the maximum stored energy $E_{B,m}$ (blue circles) and maximum power $P_{B,m}$ (red squares) as functions of the quench duration $\tau_Q$ (in units of $1/\omega_0$). The dotted lines represent the analytical scaling laws predicted by Eq. (9), $E_{B,m} \propto \tau_Q^{2\alpha}$ and $P_{B,m} \propto \tau_Q^{\alpha}$ with $\alpha=0.5$, showing excellent agreement with numerical simulations.
• Figure 3: Effect of charger dissipation $\gamma$ on the battery performance. (a) Time evolution of the charger energy $E_A(t)$ (normalized by $F^2$) for some representative quench durations. In the presence of dissipation (three solid curves), the energy saturates at long times (black dashed line), deviating from the quadratic growth observed in the lossless limit (violet dashed line). (b) Maximum battery power $P_{B,m}$ versus quench duration $\tau_Q$ (in units of $1/\omega_0$) for the lossless case (blue circles) with $\gamma = 0$ and the dissipative case (red squares) with $\gamma = 0.1$. The blue and red dotted lines are guides for the eye to emphasize the analytical scaling laws. Note that while the algebraic scaling holds for short quenches ($\tau_Q < \tau_Q^{\text{max}}$), dissipation imposes a peak power at $\tau_Q^{\text{max}} \approx 2.513 \gamma^{-1}$, beyond which the power decays as $\tau_Q^{-1}$.