Ergotropy--a key figure of merit for quantum battery (QB) performance--plays a crucial role. However, the dynamics and physical mechanisms governing ergotropy evolution remain open challenges. Here, we investigate the ergotropy of a general QB model and find that the charging process is accompanied by the variation and inversion of the energy level populations. In the absence of population inversion, the ergotropy is fully consistent with coherent ergotropy; in local and global population inversion, it is determined by both coherent and incoherent ergotropy. Via random sampling of quantum states and Hamiltonians, we show that coherence and the participation ratio enhance coherent ergotropy, whereas incoherent ergotropy--whether enhanced, unchanged, or suppressed--depends on diagonal entropy, the participation ratio, and energy level population ordering. We demonstrate that the ergotropy lower bound is incoherent ergotropy, the upper bound is the QB stored energy, and enhanced QB purity suppresses locked energy and boosts charging efficiency. Furthermore, we use the Tavis-Cummings (TC) and Jaynes-Cummings (JC) batteries as paradigms to validate our findings. Our work elucidates ergotropy underlying mechanisms in general QBs and establishes a rigorous framework for optimizing ergotropy and charging efficiency, paving the way for high-performance quantum energy-storage devices.
Ergotropy--a key figure of merit for quantum battery (QB) performance--plays a crucial role. However, the dynamics and physical mechanisms governing ergotropy evolution remain open challenges. Here, we investigate the ergotropy of a general QB model and find that the charging process is accompanied by the variation and inversion of the energy level populations. In the absence of population inversion, the ergotropy is fully consistent with coherent ergotropy; in local and global population inversion, it is determined by both coherent and incoherent ergotropy. Via random sampling of quantum states and Hamiltonians, we show that coherence and the participation ratio enhance coherent ergotropy, whereas incoherent ergotropy--whether enhanced, unchanged, or suppressed--depends on diagonal entropy, the participation ratio, and energy level population ordering. We demonstrate that the ergotropy lower bound is incoherent ergotropy, the upper bound is the QB stored energy, and enhanced QB purity suppresses locked energy and boosts charging efficiency. Furthermore, we use the Tavis-Cummings (TC) and Jaynes-Cummings (JC) batteries as paradigms to validate our findings. Our work elucidates ergotropy underlying mechanisms in general QBs and establishes a rigorous framework for optimizing ergotropy and charging efficiency, paving the way for high-performance quantum energy-storage devices.
In recent years, quantum battery (QB) models have emerged as crucial platforms for exploring the connections between quantum effects and energy within the framework of quantum thermodynamics. Inspired by the physical implementation of quantum switch (QS), we, in this work, present a simple QB model in which a two-level system as battery, under a series of coherent chargers, performs the indefinite causal order (ICO) charging by introducing a control qubit as QS. Within the energy-preserving collision interaction framework, we analyze the charging ICO and conventional definite causal order (DCO) dynamics, respectively, and discover the underlying connection between the final charged states of battery in ICO and DCO charging modes. That is, the ICO charged state can be understood as a split of the DCO charged state, accompanied by an offset caused by the interference component characterizing the ICO effect. That provides direct theoretical evidence that the ICO effect positively influences the ergotropy (i.e., the maximum extractable work) of QB only when quantum coherence is present in the charging process, and it is independent of the average stored energy of the QB. By combining numerical simulations, we examine that quantum coherence in our model is a strong quantum resource contributing to the ergotropy of QB, while the ICO effect plays a catalyst-like role, assisting quantum coherence in further enhancing the ergotropy of the battery. In addition, we also demonstrate that increasing the number of chargers also benefits the optimal ergotropy of QB. Finally, we reveal that, when the coherent chargers are subject to the dephasing channel, the ICO charging mode is more robust against dephasing noise than the DCO charging mode. This investigation deepens our understanding of quantum coherence and the ICO effect in the context of quantum thermodynamics.
With intensive studies of quantum thermodynamics, quantum batteries (QBs) have been proposed to store and transfer energy via quantum effects. Despite many theoretical models, decoherence remains a severe challenge and practical platforms are still rare. Here, we propose a QB based on the coherent Ising machine, in which the signal field acts as the core energy-storage unit. To clarify the role of quantum coherence in resisting dissipation, we decompose the ergotropy, i.e., the maximum extractable work from the QB, into its coherent and incoherent components. We find that the coherent part decays at a rate roughly half that of the incoherent part, exhibiting much stronger robustness against decoherence. More importantly, the coherent ergotropy and the average charging power reach their respective maxima at essentially the same moment, which defines the optimal instant to switch off the pump field. Finally, by coupling the QB to a two-level system as the load, we demonstrate an efficient energy discharge process of the proposed QB. Our work establishes a realistic and immediately-implementable QB architecture on a mature optical platform, laying a foundation for experimental exploration of quantum energy storage.
Ergotropy provides a fundamental measure of the extractable work from a quantum system and, consequently, of the maximal useful energy, or charge, stored within it. Understanding how this quantity can be manipulated and transformed efficiently is crucial for advancing quantum energy management technologies. Here, we introduce and formalize the concepts of isoergotropic states and ergotropy-preserving operations, which reorganize the internal structure of ergotropy while keeping its total value unchanged. These ideas are illustrated for both discrete (two-level systems) and continuous-variable systems (single-mode Gaussian states). In each case, we show how ergotropy-preserving operations redistribute the respective coherent-incoherent and displacement-squeezing components. We further examine the thermodynamic exchanges accompanying ergotropy-preserving operations, including variations in energy and entropy, and demonstrate that these transformations can be dynamically implemented through standard beam-splitter-type interactions with an auxiliary system. Finally, we discuss the practical implications of isoergotropic states and operations in optimizing charging protocols and mitigating charge loss in open quantum batteries.
As a quantum thermodynamic device that utilizes quantum systems for energy storage and delivery, the quantum battery (QB) is expected to offer revolutionary advantages in terms of increasing the charging power and the extractable work by using quantum resources. However, the ubiquitous decoherence in the microscopic world inevitably forces the QB to spontaneously lose its stored energy. This is called the self-discharging of the QB and severely limits its realization. We propose a QB scheme based on the nitrogen-vacancy center in diamond, where the electronic spin serves as the QB. Inspired by our finding that the coherent ergotropy decays more slowly than the incoherent ergotropy, we reveal a mechanism to enhance the inherent robustness of the QB to the self-discharging by improving the ratio of coherent ergotropy to total ergotropy. The unique hyperfine interaction between the electron and the native ^{14}N nucleus in our scheme allows one to coherently optimize this ratio. Mitigating the self-discharging and optimizing the extractable work simultaneously, our results pave the way for the practical realization of the QB.
Nonstabilizerness plays an essential role in the efficient simulation of quantum systems on quantum computers. In this work, we investigate its role in the context of quantum batteries (QBs). To this end, we consider a system of N spin-1/2 particles, with the left half serving as the charger and the right half as the battery. By studying different classes of interactions between the charger and the battery, we quantify the amount of nonstabilizerness required to store work in the QB. Our results reveal a strong correlation between the ergotropy stored in the battery and the total nonstabilizerness of the composite system whenever the Hamiltonian preserves a U(1) symmetry. In contrast, this correspondence is generally lost for more generic interactions. A similar behavior is observed for unitary circuit dynamics. Finally, we examine the complementary scenario in which the battery is initialized in a nonstabilizer state and subsequently charged through Clifford evolution. In this case, we find that the maximum average charging power is nonmonotonic in the initial nonstabilizerness. Remarkably, the highest average power can be achieved even when the initial state carries no magic (nonstabilizerness), demonstrating that initial magic is not a necessary ingredient for generating optimal charging power.
The quantum battery (QB) is a conceptually new energy storage and conversion device, which consists usually of a quantum charger and an energy store (usually called the QB for simplicity). The demonstrated advantage of a QB, over its classical counterpart, is that its charging efficiency can be significantly enhanced by using quantum entanglement resources. In this paper, we investigate alternatively how to realize the switchable charging and the lossless power detection of the charged QB. With the proposed QB configuration we show that, by adjusting the eigenfrequency of the qubit-based charger, the cavity-based QB can be switched on between the charging and power-off states and its stored energy can be nondestructively monitored by probing the transmitted spectrum of the external electromagnetic waves scattered by the qubit-based charger. As the qubit-based charger has never been excited, the proposed cavity-based QB could directly store the coherent-state energy (rather than the single-photon one) and thus possess significantly large ergotropy. The physical realization of the proposed switchable QB configuration is demonstrated specifically with the experimental circuit quantum electrodynamical devices.