Feedback-Enhanced Driven-Dissipative Quantum Batteries in Waveguide-QED Systems

TL;DR

This work tackles the challenge of energy losses in open quantum batteries by introducing driven-dissipative QB schemes in atom–waveguide-QED systems and leveraging feedback control. By combining measurement-based feedback (MFB) and coherent feedback (CFB), the authors demonstrate substantial improvements in stored energy and ergotropy for both a single-atom QB and a many-body QB array, including near-full charging under weak driving. In the array, feedback together with driving yields a rich dynamical phase diagram comprising a boundary time-crystal (BTC) phase and two stationary phases, with the stationary phase C achieving the highest energy storage and ergotropy. The results provide practical strategies for enhancing QB performance in open quantum systems and offer insights into phase-controlled energy storage in photonic platforms.

Abstract

Quantum batteries (QBs), acting as energy storage devices, have potential applications in future quantum science and technology. However, the QBs inevitably losses energy due to their interaction with environment. How to enhance the performance of the QBs in the open-system case remains an important challenge. Here we propose a scheme to realize the driven-dissipative QBs in atom-waveguide-QED systems and demonstrate significant improvements in both the stored energy and extractable work (ergotropy) of the QBs via feedback control. For a single-atom QB, we show that combining the measurement and coherent feedback controls enables nearly perfect stable charging under the weak coherent driving. For the QB array, the measurement-based feedback allows us to control different dynamical phases in the thermodynamic limit: (i) a continuous boundary time-crystal phase, where persistent periodic energy charge-discharge oscillations emerge despite the presence of the dissipation into the waveguide, and (ii) two stationary phases -- one reaches full charge while the other maintains only small energy storage. This work broadens the scope of driven-dissipative QBs and provides practical strategies for enhancing their performance.

Figures (4)

• Figure 1: Schematic of two different setups of the quantum battery (QB). (a) Setup I, a QB array (modeled as two-level atoms) is coupled to an open waveguide. (b) Setup II, a QB array is coupled to a semi-infinite waveguide, whose end lying at $x_{0}=0$ behaves as a perfect mirror. In both setups, an external laser persistently input energy into the QB array. The right-emitted photons are monitored via a homodyne detection, producing a corresponding photocurrent that is fed back to modulate the external laser field.
• Figure 2: Steady-state energy $\mathcal{E}^{ss}_{I}$ (a) and $\mathcal{E}^{ss}_{II}$ (b) versus the driving amplitude $\Omega$ and feedback strength $g$. Time evolutions of the energy and ergotropy for setups I (c) and II (d), comparing the cases with $g=0$ (without MFB) and $g=-1$, $-2$ (with MFB). In panels (c) and (d), the driving amplitude is fixed at $\Omega/\gamma=0.5$. Other parameters used are $\Delta\gamma=0$ and $\phi_{1}=2\pi$.
• Figure 3: (a) Steady-state energy $\mathcal{E}_{II}^{ss}$ versus $\Omega$ and $g$. (b) Eigenvalues $\lambda_{II}$ of the Liouvillian $\mathcal{L}$ are shown in the boundary time-crystal phase A ($\Omega/\Gamma=2$, blue dots) and in the stationary phase B ($\Omega/\Gamma=1$, red dots) with $g=1$. (c) and (d) Steady-state energy $\mathcal{E}_{II}^{ss}$ as a function of $\Omega$ at $g=1$ and $g=-2$, respectively. Dashed lines are the mean-field results for $N\rightarrow\infty$ and solid lines are obtained by finding the steady state of Eq. (\ref{['MATs_MQES_I_II']}) for setup II with various atom numbers $N$.
• Figure 4: (a) and (c) Stored energy $\mathcal{E}_{II}(t)$ as a function of time in the BTC phase A and stationary phase B for $\Omega/\Gamma=1$ and $\Omega/\Gamma=2$ with $g=1$. (b) and (d) Stored energy $\mathcal{E}_{II}(t)$ as a function of time in the stationary phase C for $\Omega/\Gamma=0.01$ and $g=-2$. Panels (a), (b), and (c) show $N=10$, $20$, $30$, $40$, $50$. Panel (d) shows instead more extensive comparison for $N=200$, $600$, $1000$, $1400$, $1800$. (e) Maximal energy $\mathcal{E}_{II}^{\text{max}}$ and ergotropy $\mathcal{W}_{II}^{\text{max}}$ versus $N$ in different phases.