Abstract Quantum batteries (QBs)—small-scale energy storage devices based on quantum systems—offer the potential for enhanced charging performance through quantum effects such as coherence and collectivity. In this work, we study the collective charging of QBs consisting of N qubits, coupled to a driven qubit charger in a star configuration, with controlled pure dephasing acting on the charger. We investigate how an ‘asymptotic freedom’-like behavior—in which all the energy deposited into the battery can be extracted as work, resulting in the ergotropy-to-energy ratio approaching unity—can emerge in the steady state of the battery. We show that the ergotropy-to-energy ratio increases with the number of qubits and approaches unity asymptotically as 1 − O ( 1 / N ) . In the large- N limit, the emergence of approximate ground-state degeneracy of the collective battery system leads to this asymptotic freedom behavior, despite the battery state remaining mixed. We also discuss the scaling behavior of the charging time of the battery with N .
Abstract Quantum batteries (QBs)—small-scale energy storage devices based on quantum systems—offer the potential for enhanced charging performance through quantum effects such as coherence and collectivity. In this work, we study the collective charging of QBs consisting of N qubits, coupled to a driven qubit charger in a star configuration, with controlled pure dephasing acting on the charger. We investigate how an ‘asymptotic freedom’-like behavior—in which all the energy deposited into the battery can be extracted as work, resulting in the ergotropy-to-energy ratio approaching unity—can emerge in the steady state of the battery. We show that the ergotropy-to-energy ratio increases with the number of qubits and approaches unity asymptotically as 1 − O ( 1 / N ) . In the large- N limit, the emergence of approximate ground-state degeneracy of the collective battery system leads to this asymptotic freedom behavior, despite the battery state remaining mixed. We also discuss the scaling behavior of the charging time of the battery with N .
We establish a universal scaling law for collective charging of quantum batteries, independent of microscopic details. We prove that the ergotropy-to-energy ratio approaches unity at least as fast as ∼N−1 with the number of batteries N, implying generic asymptotic freedom. We further show how the universal 1/N scaling can be overcome: when the battery state becomes asymptotically pure, the convergence can be substantially faster, including ∼N−b with b>1 and even exponential scaling in N2. Rigorous finite-N upper and lower bounds on the ergotropy-to-energy ratio are further derived, providing nonasymptotic guarantees for the universal 1/N scaling.
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.
The performance of open quantum batteries (QBs) is severely limited by decoherence due to the interaction with the surrounding environment. So, protecting the charging processes against decoherence is of great importance for realizing QBs. In this work we address this issue by developing a charging process of a qubit-based open QB composed of a qubit-battery and a qubit-charger, where each qubit moves inside an independent cavity reservoir. Our results show that, in both the Markovian and non-Markovian dynamics, the charging characteristics, including the charging energy, efficiency and ergotropy, regularly increase with increasing the speed of charger and battery qubits. Interestingly, when the charger and battery move with higher velocities, the initial energy of the charger is completely transferred to the battery in the Markovian dynamics. In this situation, it is possible to extract the total stored energy as work for a long time. Our findings show that open moving-qubit systems are robust and reliable QBs, thus making them a promising candidate for experimental implementations.
As a model of so-called quantum battery (QB), quantum degrees of freedom as energy storage, we study a charging protocol of a many-body QB consisting of N two-level systems (TLSs) using quantum heat engines (QHEs). We focus on the collective enhancement effects in the charging performance of QBs in comparison to the individual charging. It is a challenging goal of QBs to achieve large collective enhancements in the charging power and the capacity while keeping the experimental feasibility, the stability, and the cheapness of the required control and resources. We show that our model actually exhibits these features. In fact, our protocol simultaneously achieves the asymptotically-perfect charge and almost N-order average power enhancement with only thermal energy resource and simple local interactions in a stable manner. The capacity is collectively enhanced due to the emergent bosonic quantum statistics caused by the symmetry of the interaction between the engine and the batteries, which results in asymptotically perfect excitation of all the TLSs. The charging speed, and hence the average power are collectively enhanced by the superradiance-like cooperative excitation in the effective negative temperature. Our results suggest that QHEs actually fit for a charger of QBs, efficiently exploiting the collective enhancements, not only converting the disordered thermal energy to the ordered energy stored in quantum degrees of freedom.
We propose a simple realization of an open quantum battery powered by local dephasing. The setup consists of a triple-quantum-dot chain coupled at one end to a thermal reservoir, with the dot at the opposite end strongly detuned to form a high-energy storage element. Local dephasing populates this highly excited state and autonomously drives the system into a nonequilibrium steady state with high ergotropic efficiency. We find a limit where the ergotropic efficiency approaches unity, while the ergotropy itself approaches one-third of the energy detuning. We characterize the battery through its energy-storage performance, charging time, and stability, showing that the charged state remains long-lived after the dephasing source is switched off. We then demonstrate two complementary protocols for extracting the stored energy. First, nearly all the available ergotropy can be recovered through a simple cyclic unitary protocol involving only modulation of the detuned-dot gate. Second, coupling the detuned dot to an electronic load allows the extraction of electrochemical work exceeding the initial ergotropy, thereby accessing part of the battery's passive energy. Our results establish local dephasing as an autonomous resource for charging open quantum batteries and demonstrate simple routes for extracting the resulting stored energy in experimentally accessible mesoscopic platforms.
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.