We reconsider the quantum energetics and quantum thermodynamics of the charging process of a simple, two-component quantum battery model made up of a charger qubit and a single--cell battery qubit. We allow for the initial quantum state of the charger to lie anywhere on the surface of the Bloch sphere, and find the generalized analytical expressions describing the stored energy, ergotropy and capacity of the battery, all of which depend upon the initial Bloch sphere polar angle in a manner evocative of the quantum area theorem. The origin of the ergotropy produced, as well as the genesis of the battery capacity, can be readily traced back to the quantum coherences and population inversions generated (and the balance between these two mechanisms is contingent upon the starting Bloch polar angle). Importantly, the ergotropic charging power and its associated optimal charging time display notable deviations from standard results which disregard thermodynamic considerations. Our theoretical groundwork may be useful for guiding forthcoming experiments in quantum energy science based upon coupled two-level systems.
We reconsider the quantum energetics and quantum thermodynamics of the charging process of a simple, two-component quantum battery model made up of a charger qubit and a single--cell battery qubit. We allow for the initial quantum state of the charger to lie anywhere on the surface of the Bloch sphere, and find the generalized analytical expressions describing the stored energy, ergotropy and capacity of the battery, all of which depend upon the initial Bloch sphere polar angle in a manner evocative of the quantum area theorem. The origin of the ergotropy produced, as well as the genesis of the battery capacity, can be readily traced back to the quantum coherences and population inversions generated (and the balance between these two mechanisms is contingent upon the starting Bloch polar angle). Importantly, the ergotropic charging power and its associated optimal charging time display notable deviations from standard results which disregard thermodynamic considerations. Our theoretical groundwork may be useful for guiding forthcoming experiments in quantum energy science based upon coupled two-level systems.
We derive a quantum speed limit for ergotropy charging in the N-qubit Dicke battery. With the qubits initially in their ground state and the charger in a coherent state of mean photon number nˉ, the charging time to a target fraction ε of the maximum extractable work obeys, in the classical-field limit, ΓNτ∗(ε)≥arcsinε, where ΓN=2λnˉ/N is a single rate combining the light-matter coupling, the charger amplitude and the system size. The bound is geometric: although the ergotropy is defined by an optimisation over unitaries, it reduces to a fixed function of the angle swept by the collective spin on the Bloch sphere, and the drive bounds the rate at which that angle can grow, so the charging time is at least the required arc divided by the maximum angular velocity. The reduction rests on an exact statement about work extraction: only the coherent component of the drive delivers extractable work, while its vacuum fluctuations deposit energy that remains locked in the passive state. This makes the short-time coefficient independent of the charger occupation, and it is what separates a bound on extractable work from a bound on stored energy, which no instantaneous-power argument can supply. At finite charger occupation the inequality is tested rather than proved: numerical integration of the full Dicke Hamiltonian, with a dynamical charger and a mixed battery state, finds the bound respected at every admitted charging time for two to five qubits, and approached most closely in the limit of small target work. The familiar square-root estimate is the chord to this arc, recovered in the small-angle limit and weaker whenever a large fraction of the maximum work is required.
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 propose a quantum charging scheme fueled by measurements on ancillary qubits serving as disposable chargers. A stream of identical qubits are sequentially coupled to a quantum battery of N+1 levels and measured by projective operations after joint unitary evolutions of optimized intervals. If charger qubits are prepared in excited state and measured on ground state, then their excitations (energy) can be near perfectly transferred to battery by iteratively updating the optimized measurement intervals. Starting from its ground state, the battery could be constantly charged to an even higher energy level. Starting from a thermal state, the battery could also achieve a near-unit ratio of ergotropy and energy through less than N measurements, when a population inversion is realized by measurements. If charger qubits are prepared in ground state and measured on excited state, useful work extracted by measurements alone could transform the battery from a thermal state to a high-ergotropy state before the success probability vanishes. Our operations in charging are more efficient than those without measurements and do not invoke the initial coherence in both battery and chargers. Particularly, our finding features quantum measurement in shaping nonequilibrium systems.
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.
We examine how a finite many-body system can function as an effective charger for a single-qubit quantum battery, using the Lipkin-Meshkov-Glick model as a paradigmatic setting. As our figure of merit, we consider the battery ergotropy while explicitly resolving the energetic flows across the composite system. In the absence of intra-charger interactions, we show that the generation of non-zero ergotropy is controlled by the competition between collective coupling and spectral mismatch. We further demonstrate that even passive positive-temperature charger states can generate finite battery ergotropy, provided the charger is sufficiently large and sufficiently hot. Intra-charger interactions restructure the charger spectrum and qualitatively modify the available energetic pathways. While they can enhance the amount of energy accessible for charging, they can simultaneously divert energy into internal many-body and battery-charger interaction channels, producing an energetic impedance to direct charger-to-battery transfer. Consequently, battery ergotropy alone is insufficient to characterize an effective many-body charger: the useful work generated and its energetic provenance must be assessed together.
In this work, we investigate the autonomous charging process of a quantum battery coupled to a structured reservoir composed of two qubits, each locally coupled to its own bosonic thermal bath. Moreover, the reservoir interacts with a charger-battery architecture through three configurations: (I) direct coupling between reservoir qubits and battery; (II) collective coupling among the reservoir qubits, charger, and battery; and (III) a collective coupling between the reservoir qubits and charger together with a local charger-battery interaction. However, by using incoherent and coherent initial states, we analyze the stored energy, ergotropy, and charging power of the battery, and derive upper and lower bounds on the extractable work in terms of the free energy of coherence and the correlations exchanged between subsystems. Our results show that global and local coherences, as well as total correlations, act as quantum resources that enhance autonomous charging. Additionally, we demonstrate that the free energy stored in the quantum battery splits into contributions from coherence and correlations, providing numerical evidence that supports the derived ergotropy bounds. Importantly, this work highlights how structured reservoirs enable autonomous and resource-enhanced quantum battery operation.