Energy storage is a basic physical process with many applications. When considering this task at the quantum scale, it becomes important to optimise the non-equilibrium dynamics of energy transfer to the storage device or battery. Here, we tackle this problem using the methods of quantum feedback control. Specifically, we study the deposition of energy into a quantum battery via an auxiliary charger. The latter is a driven-dissipative two-level system subjected to a homodyne measurement whose output signal is fed back linearly into the driving field amplitude. We explore two different control strategies, aiming to stabilise either populations or quantum coherences in the state of the charger. In both cases, linear feedback is shown to counteract the randomising influence of environmental noise and allow for stable and effective battery charging. We analyse the effect of realistic control imprecisions, demonstrating that this good performance survives inefficient measurements and small feedback delays. Our results highlight the potential of continuous feedback for the control of energetic quantities in the quantum regime.
Energy storage is a basic physical process with many applications. When considering this task at the quantum scale, it becomes important to optimise the non-equilibrium dynamics of energy transfer to the storage device or battery. Here, we tackle this problem using the methods of quantum feedback control. Specifically, we study the deposition of energy into a quantum battery via an auxiliary charger. The latter is a driven-dissipative two-level system subjected to a homodyne measurement whose output signal is fed back linearly into the driving field amplitude. We explore two different control strategies, aiming to stabilise either populations or quantum coherences in the state of the charger. In both cases, linear feedback is shown to counteract the randomising influence of environmental noise and allow for stable and effective battery charging. We analyse the effect of realistic control imprecisions, demonstrating that this good performance survives inefficient measurements and small feedback delays. Our results highlight the potential of continuous feedback for the control of energetic quantities in the quantum regime.
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.
Abstract Quantum control allows us to address the problem of engineering quantum dynamics for special purposes. While recently the field of quantum batteries has attracted much attention, optimization of their charging has not benefited from the quantum control methods. Here we fill this gap by using an optimization method. We apply for the first time the convergent iterative method for the control of the population of a bipartite quantum system in two cases, starting with a qubit-qubit case. The quantum charger-battery system is considered here, where the energy is pumped into the charger by an external classical electromagnetic field. Secondly, we systematically extend our investigation to a second case involving two harmonic oscillators in the Gaussian regime, presenting an original formulation of the method. In both cases, the charger is considered to be an open dissipative system, as its interaction with the drive may require a more pronounced exposure to general interaction with environment. A key consideration in our optimization strategy is the practical concern of turning the charging external field on and off. We find that optimizing the pulse shape yields a substantial enhancement in both the power and efficiency of the charging process compared to a sinusoidal drive. The harmonic oscillator configuration of quantum batteries is particularly intriguing, as the optimal driving pulse remains effective regardless of the environmental temperature. This study introduces a novel approach to quantum battery charging optimization, opening avenues for enhanced performance in real-world applications.
Abstract Quality of charging and discharging of energy in quantum batteries are mostly affected by environmental dissipations, so the advantages of using such devices depend on the protection of them from the dissipations. In this work, we show that under a certain engineering of coupling strengths of each reservoir modes with elements of charging process (charger and battery), the extension of dissipative reservoir leads to a robust charging against the arisen dissipation. The extension of reservoir is provided by auxiliary systems each of which is similar to the coupled charger–battery system and has the same interactions with the reservoir modes as of the charger and battery constituents. It is demonstrated that the robustness of charging process is well controlled by the number of involved auxiliary systems. Furthermore, a method for stable charging is proposed which provides storing energy in a loss-free dark state of the battery. Also, we observe that the robustness of charging process is related to formation of bound state for the total system (charger–battery-extended reservoir) which in turns can be manipulated by the number of involved auxiliary systems.
Charger-mediated quantum batteries offer promising opportunities for efficient energy transfer and storage at the quantum level, with potential advantages beyond their classical counterparts. Here, we theoretically demonstrate that nonlinear charger-battery interactions can substantially accelerate the charging of quantum batteries. In the weak-driving regime, sufficiently strong nonlinear coupling can dominate over the effect of dephasing and significantly reduce the charging time. In the strong- and optimal-driving regimes, where the optimal driving strength maximizes the steady-state ergotropy in the linear-coupling regime, nonlinear coupling gives rise to a new optimum in the charging time beyond that of the linear-coupling regime, accompanied by nearly critically damped dynamics. Remarkably, even in the absence of external driving, nonlinear coupling alone can substantially reduce the charging time, providing an alternative route toward fast battery charging. Our results establish nonlinear charger-battery coupling as an effective resource for accelerating quantum-battery charging and broaden the scope of interaction-enabled quantum advantages in energy transfer and storage.
In this paper, we theoretically investigate the charging dynamics of a closed quantum battery embodied by a four-level atom in a diamond configuration, operating without dissipation. The system is coupled to a single-mode cavity field, which acts as the charger initially prepared in a coherent state, and is simultaneously manipulated by an external classical driving field. By solving the exact system dynamics, we provide a holistic analysis of key performance metrics, including stored energy, ergotropy, energy fluctuations, and von Neumann entropy, as a function of critical system parameters. Our investigation delineates a paramount trade-off; while larger initial charger amplitudes and optimized detunings substantially enhance the stored energy and extractable work, they concurrently amplify fluctuations and entropy, thereby diminishing the battery’s stability and quantum coherence. Crucially, we demonstrate that the coupling to the external drive exhibits a non-monotonic influence, revealing an optimal intermediate regime, specifically at a classical driving strength of λ 2 = 0.5 and detunings δ 1 = δ 3 = 1 ω f , that judiciously balances rapid energy uptake with stable, long-term storage. These results elucidate the complex interplay of coherent control and system parameters, offering critical insights for the rational design of efficient and robust quantum energy storage devices by effectively decoupling charging performance from operational instability.
We study the problem of charging a dissipative one-dimensional XXX spin-chain quantum battery using local magnetic fields in the presence of spin decay. The introduction of quantum feedback control based on homodyne measurement contributes to improving various performances of the quantum battery, such as energy storage, ergotropy, and effective space utilization rate. For the zero-temperature environment, there is a set of optimal parameters to ensure that the spin-chain quantum battery can be fully charged and the energy stored in the battery can be fully extracted under the perfect measurement condition, which is found through the analytical calculation of a simple two-site spin-chain quantum battery and further verified by numerical simulation of a four-site spin-chain counterpart. For completeness, the adverse effects of imperfect measurement, anisotropic parameter, and finite temperature on the charging process of the quantum battery are also considered.