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arXiv:2212.12397 · Physical Review Letters

Reinforcement Learning Optimization of the Charging of a Dicke Quantum Battery

Paolo Andrea Erdman, Gian Marcello Andolina, Vittorio Giovannetti, Frank Noé

Published Dec 13, 2024• 46 citations
arXivHTMLPDF

Abstract

Quantum batteries are energy-storing devices, governed by quantum mechanics, that promise high charging performance thanks to collective effects. Because of its experimental feasibility, the Dicke battery-which comprises N two-level systems coupled to a common photon mode-is one of the most promising designs for quantum batteries. However, the chaotic nature of the model severely hinders the extractable energy (ergotropy). Here, we use reinforcement learning to optimize the charging process of a Dicke battery either by modulating the coupling strength, or the system-cavity detuning. We find that the ergotropy and quantum mechanical energy fluctuations (charging precision) can be greatly improved with respect to standard charging strategies by countering the detrimental effect of quantum chaos. Notably, the collective speedup of the charging time can be preserved even when nearly fully charging the battery.

DOI
10.1103/physrevlett.133.243602

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Quantum batteries are energy-storing devices, governed by quantum mechanics, that promise high charging performance thanks to collective effects. Because of its experimental feasibility, the Dicke battery-which comprises N two-level systems coupled to a common photon mode-is one of the most promising designs for quantum batteries. However, the chaotic nature of the model severely hinders the extractable energy (ergotropy). Here, we use reinforcement learning to optimize the charging process of a Dicke battery either by modulating the coupling strength, or the system-cavity detuning. We find that the ergotropy and quantum mechanical energy fluctuations (charging precision) can be greatly improved with respect to standard charging strategies by countering the detrimental effect of quantum chaos. Notably, the collective speedup of the charging time can be preserved even when nearly fully charging the battery.
We consider a collection of two level systems, such as qubits, embedded into a microwave cavity as a promising candidate for the realization of high power quantum batteries. In this perspective, the possibility to design devices where the conventional single-photon coupling is suppressed and the dominant interaction is mediated by two-photon processes is investigated, opening the way to an even further enhancement of the charging performance. By solving a Dicke model with both single- and two-photon coupling we determine the range of parameters where the latter unconventional interaction dominates the dynamics of the system leading to better performances both in the charging times and average charging power of the QB compared to the single-photon case. In addition, the scaling of the maximum stored energy, fluctuations and charging power with the finite number of qubits NNN is inspected. While the energy and fluctuations scale linearly with NNN, the quadratic growth of the average power leads to a relevant improvement of the charging performance of quantum batteries based on this scheme with respect to the purely single-photon coupling case. Moreover, it is shown that the charging process is progressively faster by increasing the coupling from the weak to the ultra-strong regime.
Charging optimization is a key challenge to the implementation of quantum batteries, particularly under inhomogeneity and partial observability. This paper employs reinforcement learning to optimize piecewise-constant charging policies for an inhomogeneous Dicke battery. We systematically compare policies across four observability regimes, from full-state access to experimentally accessible observables (energies of individual two-level systems (TLSs), first-order averages, and second-order correlations). Simulation results demonstrate that full observability yields near-optimal ergotropy with low variability, while under partial observability, access to only single-TLS energies or energies plus first-order averages lags behind the fully observed baseline. However, augmenting partial observations with second-order correlations recovers most of the gap, reaching 94%-98% of the full-state baseline. The learned schedules are nonmyopic, trading temporary plateaus or declines for superior terminal outcomes. These findings highlight a practical route to effective fast-charging protocols under realistic information constraints.
Phase transitions (PTs) in quantum many-body systems offer a powerful route to manipulate the performance of quantum batteries (QBs). Here, we investigate an anisotropic Dicke QB with Kerr nonlinearity, focusing on the role of PTs in the charging process of the QB system. By analyzing how the Kerr nonlinearity reshapes the cavity level-spacing structure, we find that multiple near-degeneracies emerge at specific nonlinearity strengths. Away from the region of multiple near-degeneracies, the stable stored energy is governed primarily by the ergodic-nonergodic transition (ENET), whereas within this region it is controlled by first- and second-order dissipative phase transitions (DPTs). We employ Liouvillian spectral theory to quantify the critical slowing down associated with the DPTs, and use the Wigner function to characterize the properties of the cavity field in the vicinity of criticality. We optimize the charging process via reinforcement learning (RL) and reveal the physical mechanism underlying performance enhancement from the perspective of ergodic and nonergodic phase dynamics. Our results offer a feasible pathway for manipulating and optimizing quantum battery performance based on intrinsic PT behaviors.
Abstract In the realm of quantum batteries (QBs), model construction and performance optimization are central tasks which can be addressed by exploiting machine learning algorithms. Here, we propose a cavity-Heisenberg spin chain QB model with spin- j ( j = 1 / 2 , 1 , 3 / 2 ) and investigate the charging performance under both closed and open quantum cases, considering spin–spin interactions, ambient temperature, and cavity dissipation. By employing a reinforcement learning (RL) algorithm to modulate the cavity-battery coupling, we further optimize the QB performance, enhancing the charging capability of the spin chain. It is shown that the charging energy and the power of the QB are significantly improved with the spin size. In particular, the use of a RL algorithm in case of large spin ( j = 3 / 2 ) in presence of cavity losses allows for more stability in the optimization of the cavity-spin coupling strength, which in perspective makes an experimental realization more feasible. We analyze the optimization mechanism and find an intrinsic relationship between cavity-spin entanglement and charging performance: while in the closed-system scenario the charging energy increases together with the cavity-spin entanglement, in the open-system scenario the increase of the charging energy can be accompanied by a decrease of entanglement. Our results provide a possible scheme for design and optimization of QBs.
A quantum battery (QB) is an energy storage and extraction device that is governed by the principles of quantum mechanics. Here we propose a three-level Dicke QB and investigate its charging process by considering three quantum optical states: a Fock state, a coherent state, and a squeezed state. The performance of the QB in a coherent state is significantly superior to that in a Fock or squeezed state. We show that the locked energy is positively related to the entanglement between the charger and the battery, and diminishing the entanglement increases the ergotropy. The role of quantum phase transitions in the charging process of the QB system is analyzed and we find that the behavior of maximum stored energy is jointly determined by ground and excited-state quantum phase transitions. We further demonstrate that, no matter what the initial state is, the stored energy can be completely extracted when NNN is small (N=10N=10N=10), far below the thermodynamic limit, and the charging power follows a behavior consistent with that of the stored energy.
Controlling the charging process of a quantum battery involves strategies to efficiently transfer, store, and retain energy, while mitigating decoherence, energy dissipation, and inefficiencies caused by surrounding interactions. We develop a model to study the charging process of a quantum battery in an open quantum setting, where the battery interacts with a charger and a structured reservoir. To overcome the limitations of static charging protocols, a reinforcement learning (RL) charging strategy is proposed, which utilizes the deep deterministic policy gradient algorithm alongside long short-term memory (LSTM) networks. The LSTM networks enable the RL model to capture temporal correlations driven by non-Markovian dynamics, facilitating a continuous, adaptive charging strategy. The RL protocols consistently outperform conventional fixed heuristic strategies by real-time controlling the driving field amplitude and coupling parameters. By penalizing battery-to-charger backflow in the reward function, the RL-optimized charging strategy promotes efficient unidirectional energy transfer from charger to battery, achieving higher and more stable extractable work. The proposed RL controller would provide a framework for designing efficient charging schemes in broader configurations and multi-cell quantum batteries.