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Results in Engineering

Exact dynamics of a four-level quantum battery driven by an external field

Souha K. Badr, Hanaa Abu-Zinadah, Eied Mahmoud Khalil

Published Mar 19, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1016/j.rineng.2026.110154

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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.
Abstract This work presents a high-dimensional quantum battery model based on a V-type multi-level atom interacting with an amplified multi-mode cavity field under controllable Stark shifts. Using a nondimensionalized Hamiltonian and pair-coherent field states, we derive a full density-matrix description that captures the evolution of stored energy, ergotropy, charging efficiency, coherence, and entropy. Our findings show that multi-level quantum batteries outperform two-level systems by leveraging expanded Hilbert spaces to support larger energy storage, richer coherence, and multiple excitation pathways. The charging dynamics are strongly influenced by the field intensity, the shift between paired modes, and the Stark-induced detunings, which collectively determine resonance conditions and interference patterns. A fundamental trade-off emerges: increasing dimensions of quantum battery and field strength enhances energy uptake and coherence, but also raises entropy in the charger field, thereby reducing extractable work. A scaling analysis reveals robust and statistically significant behavioral laws, including quadratic growth of stored energy, exponential decay of efficiency, and exponential increases in coherence and entropy with system dimension. These results outline the energetic and informational limits of high-dimensional quantum batteries and establish a flexible, physically realistic framework for optimizing quantum charging in cavity and circuit QED platforms.
Abstract This study investigates the performance of a three-level quantum battery model, which aims to optimize the trade off between the high capacity of harmonic oscillators and the rapid charging of two-level systems. Utilizing a harmonic oscillator charger and a three-level holder, we analyze the impact of linear and quadratic driving protocols within an open quantum system framework. Our results show that linear driving yields a highly efficient charging process with an ergotropy to energy ratio near unity. On the other hands, the quadratic driving significantly enhances stored energy and peak charging power but introduces increased state mixedness that limits the extractable work. Furthermore, these findings highlight the necessity of balancing coupling strengths and driving nonlinearities to maximize the thermodynamic efficiency of the quantum battery.
We discuss a one-dimensional coupled qubit-array quantum battery model under Born-Karman boundary conditions and investigate both the charging and discharging processes. Applying the stored energy, charging power, and ergotropy as the essential physical indicators of quantum battery, it is observed that minimizing the hopping interaction between the nearest-neighbor qubits in the qubit-array and increasing the number of qubits during battery setup are crucial. Additionally, we employ a classical driving field to optimize battery performance and explore the optimal quantum battery performance by adjusting the driving strength of the classical field. Finally, we have discovered that the initial energy in the charger no longer needs to be higher than the energy in the battery in our protocol, the charger will continue to supply energy to the battery even when there is limited initial available energy in the charger. And the conventional approach of preparing the battery's initial state in its ground state, as observed in previous studies, may not necessarily be the optimal choice. By introducing a strong classical driving field, it is possible to enhance energy storage by allowing for an initial presence of some energy within the battery.
We theoretically investigate a quantum battery architecture where two identical two-level atoms are charged by a cavity-magnomechanical system, which includes a microwave cavity, a magnon mode hosted in a YIG sphere, and phonon mode due to the deformation of the YIG sphere. The charging process relies on coherent energy exchange, where the atoms couple to the cavity, which in turn, it interacts with the magnon mode via a beam-splitter mechanism. By deriving the system Hamiltonian under the rotating-wave approximation and employing a Lindblad master equation to rigorously model dissipation, we analyze the complete dynamical evolution of the battery. Our study demonstrates that strong, resonant light-matter interactions are crucial for enhancing the key performance metrics: charging efficiency, stored energy, and ergotropy (extractable work). We systematically investigate the deleterious effects of detuning and decoherence, and critically, we uncover a non-trivial interplay between the system's coupling strengths. This reveals optimal operating regimes where constructive interference maximizes performance, while excessive coupling in specific channels can degrade it. Ultimately, our findings provide a quantitative framework for engineering high-efficiency quantum batteries in hybrid magnonic platforms, offering a design roadmap for future experimental realizations.
This paper discusses the evolving dynamics of a quantum battery (QB) model consisting of two qubits interacting with a cavity field via multi-photon transitions. Employing the Lindblad master equation to account for dissipative effects, we investigated energy charging, charging power, ergotropy, and energy fluctuations to ascertain optimal conditions for efficient energy storage and extraction. Our results elucidate that lower photon numbers and moderate coherent state result in higher energy peaks and more stable storage. The charging power underscores the significance of maximizing initial energy transfer rates while mitigating rapid power decay. Ergotropy, representing the maximum extractable energy, is highly sensitive to dissipation rates, with elevated photon numbers enhancing charging efficiency but reducing stability. Energy fluctuation reveals that systems with higher photon numbers exhibit greater instability, emphasizing the necessity for controlling dissipation to preserve energy stability.
We investigate a two-qubit quantum battery where coherent charger-battery coupling competes with non-Markovian environmental interactions. By tuning the coupling strengths and detuning, we identify regimes in which environmental memory enhances energy storage and charging power, while strong dissipation suppresses ergotropy by driving the battery into passive states. We show that detuning plays a dual role: reducing dissipation and inducing a phase shift in the memory kernel that controls the interference between coherent energy exchange and environment-induced backflow. As a result, although the stored energy varies smoothly, the extractable work exhibits a discontinuous onset at a critical detuning, signaling a first-order phase transition in ergotropy. The corresponding phase diagram in the coupling-detuning plane reveals a sharp boundary between thermodynamically inactive and work-producing regimes. Our results demonstrate that phase-controlled coherence and non-Markovianity provide a powerful mechanism for optimizing work extraction in open quantum batteries, offering practical strategies for noise-resilient quantum energy storage.