Boosting Work Extraction in Quantum Batteries via Continuous Environment Monitoring

TL;DR

The paper addresses the challenge that quantum correlations between a quantum battery and its charger reduce extractable work. It proposes that coupling the system to a continuously monitored environment, with work extracted via conditional operations based on measurement results, can mitigate these correlations and boost ergotropy beyond the ideal, closed-system limit. The authors analyze two models—a cavity-mediated spin–spin QB and a Dicke QB—under photodetection and homodyne detection, using stochastic Schrödinger equations to obtain conditional dynamics and average over trajectories to recover unconditional behavior. A central finding is that the daemonic ergotropy, which accounts for measurement information, can exceed the unconditional ergotropy and, in some regimes, even the dissipation-free value, with a daemonic efficiency $\eta$ approaching unity. These results suggest that tailored continuous measurements can serve as an active resource to enhance energy extraction and stabilization in quantum batteries, with potential implications for charging protocols and distributed quantum architectures.

Abstract

Quantum correlations that typically develop between a quantum battery and its charger reduce the amount of work extractable from the battery. We show that by coupling the system with an additional environment that can be continuously monitored, one can weaken these correlations and enhance work extraction beyond what is achievable in the ideal (closed system) limit. This general mechanism is illustrated using both a cavity-mediated spin-spin and Dicke quantum battery models.

Figures (9)

• Figure 1: (a) Schematic of a cavity--mediated spin–spin QB. (b,d) Unconditional and daemonic ergotropies (in units of $\omega$) (dashed and solid lines) and their corresponding energy upper bounds (dotted lines) for the weak-- and strong--coupling regimes, respectively. (c,e) Purity of the battery qubit as a function of the charging time. The black dotted--dashed line indicates the minimum achievable purity. Coupling strengths are $\bar{g}_B=\omega/10$, $\bar{g}_C = \omega/5$ (weak coupling) and $\bar{g}_B = \omega$, $\bar{g}_C = 2\omega$ (strong coupling). Here and in the following figures, conditional averages are over n= 1000 trajectories.
• Figure 2: (a–d) Energy, power, ergotropy and purity of the reduced Dicke battery state as a function of the charging time for the unconditional dynamics. (e,f) Daemonic ergotropy and purity for the conditional dynamics under the PD scheme. Parameter values: $\bar{\lambda} = \omega$, $N = 6$. Note that energy, ergotropy and power are rescaled to make them adimensional and highlight the well--known scalings laws Ferraro18$E_{\bar{\lambda}},\mathcal{E}_{\bar{\lambda}}\propto N$ and $P_{\bar{\lambda}}\propto N^{3/2}$.
• Figure 3: Contour plots of ergotropy in the noiseless scenario (a), HD daemonic ergotropy (b), and PD daemonic ergotropy (c) as a function of the coupling strength $\bar{\lambda}$ and the dissipation rate $\kappa$, for $N=6$. Note that ergotropies are calculated at the charging times for which the stored energy is at its maximum.
• Figure 4: Daemonic ergotropy enhancement ratio as a function of the coupling strength $\bar{\lambda}$ and the dissipation rate $\kappa$ for HD (a) and PD (b), for $N=6$. In the red regions of the plots, the presence of dissipation combined with continuous measurement leads to an increase in daemonic ergotropy compared to the ideal dissipation--free case.
• Figure 5: Maximum ergotropy as a function of $\bar{g}_C$ in the cavity--mediated spin--spin QB. The blue and red dotted lines indicate the upper energy bounds for the non-dissipative and dissipative ergotropies, respectively. The HD unraveling is averaged over $n=1000$ trajectories, and the shaded area represents one standard deviation of the daemonic ergotropy. (a) Weak-coupling case with $\bar{g}_B=\omega/10$; (b) strong-coupling case with $\bar{g}_B=\omega$.