Enhancing the Charging Power of Quantum Batteries

Large Collective Power Enhancement in Dissipative Charging of a Quantum Battery

We consider a model for a quantum battery consisting of a collection of N two-level atoms driven by a classical field and decaying to a common reservoir. In the extensive regime, where the energy E scales as N and the fluctuations ΔE/E→0, our dissipative charging protocol yields a power proportional to N^{2}, a scaling that cannot be achieved in this regime by Hamiltonian protocols. The trade-off for this enhanced charging power is a relative inefficiency since a large fraction of the incoming energy is lost through spontaneous emission to the environment. Nevertheless, we find that the system can store a large amount of coherence and release the stored energy coherently through spontaneous emission, again with a power scaling as N^{2}.

Quantum Batteries: A Materials Science Perspective

In the context of quantum thermodynamics, quantum batteries have emerged as promising devices for energy storage and manipulation. Over the past decade, substantial progress is made in understanding the fundamental properties of quantum batteries, with several experimental implementations showing great promise. This perspective provides an overview of the solid-state materials platforms that can lead to fully operational quantum batteries. After briefly introducing the basic features of quantum batteries, organic microcavities are discussed, where superextensive charging is already demonstrated experimentally. Now, this explores other materials, including inorganic nanostructures (such as quantum wells and dots), perovskite systems, and (normal and high-temperature) superconductors. Key achievements in these areas, relevant to the experimental realization of quantum batteries, are highlighted. The challenges and future research directions are also addressed. Despite their enormous potential for energy storage devices, research into advanced materials for quantum batteries is still in its infancy. This paper aims to stimulate interdisciplinarity and convergence among different materials science research communities to accelerate the development of new materials and device architectures for quantum batteries.

Strong coupling non-Markovian quantum thermodynamics of a finite-bath system

The focus is on understanding the quantum thermodynamics of strongly coupled non-Markovian quantum systems. To this end, a non-trivial, non-Markovian model of a central spin surrounded by a spin bath is taken up, and its exact evolution is derived for arbitrary system-bath couplings. The fundamental quantum thermodynamic quantities, such as system and bath internal energies, work, heat, entropy production, and ergotropy, are calculated using the dynamics and the original system (bath) Hamiltonian. An explicit expression for the work, a mismatch between the system and bath internal energies, is derived. The thermodynamic entropy of the system at thermal equilibrium is studied using the Hamiltonian of mean force in the strong coupling regime. The role of a canonical Hamiltonian in calculating the above thermodynamic quantities, a recently developed technique, is also investigated. Furthermore, an interesting observation relevant to the spin bath acting as a charger is made in a scenario where the central spin is envisaged as a quantum battery.

Symmetry Induced Enhancement in Finite-Time Thermodynamic Trade-Off Relations

Symmetry imposes constraints on open quantum systems, affecting the dissipative properties in nonequilibrium processes. Superradiance is a typical example in which the decay rate of the system is enhanced via a collective system-bath coupling that respects permutation symmetry. Such a model has also been applied to heat engines. However, a generic framework that addresses the impact of symmetry in finite-time thermodynamics is not well established. Here, we show a symmetry-based framework that describes the fundamental limit of collective enhancement in finite-time thermodynamics. Specifically, we derive a general upper bound on the average jump rate, which quantifies the fundamental speed set by thermodynamic speed limits and trade-off relations. We identify the symmetry condition that achieves the obtained bound, and explicitly construct an open quantum system model that goes beyond the enhancement realized by the conventional superradiance model.

Observation of minimal and maximal speed limits for few and many-body states

Tracking the time evolution of a quantum state allows one to verify the thermalization rate or the propagation speed of correlations in generic quantum systems. Inspired by the energy-time uncertainty principle, bounds have been demonstrated on the maximal speed at which a quantum state can change, resulting in immediate and practical tasks. Based on a programmable superconducting quantum processor, we test the dynamics of various emulated quantum mechanical systems encompassing single- and many-body states. We show that one can test the known quantum speed limits and that modifying a single Hamiltonian parameter allows the observation of the crossover of the different bounds on the dynamics. We also unveil the observation of minimal quantum speed limits in addition to more common maximal ones, i.e., the lowest rate of change of a unitarily evolved quantum state. Our results show a comprehensive experimental characterization of quantum speed limits and enhance the understanding for their subsequent study in engineered non-unitary conditions.

Stable energy transfer of noninteracting quantum charger-battery via photonic band gap

We propose a stable charging scheme for a quantum battery in which the stable energy transfer of a noninteracting quantum charger-battery is induced by a common photonic band gap (PBG). By manipulating the transition frequency of the quantum battery to form multiple bound states, it is found that the capability of stable charging can be obtained without direct interaction between the quantum battery and the quantum charger. Among them, the formation of two bound states results in a lossless Rabi-like oscillatory behavior of the energy exchange. The formation of three bound states leads to a continuous collapse-revival process based on the oscillation of the stored energy. Particularly, the formation of three bound states also significantly enhances the energy extraction capability of the quantum battery. In addition, the stable charging scheme proposed in this paper can be further optimized from the perspective of environmental engineering. The expansion of the forbidden band gap width of the PBG environment not only enlarges the regulatory region for the formation of multiple bound states but also improves energy storage and extraction work.

Classical-driving-assisted qubit-array 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.

Reinforcement Learning Optimization of the Charging of a Dicke Quantum Battery

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.

Quantum Speed Limit in Quantum Sensing

Quantum sensors capitalize on advanced control sequences for maximizing sensitivity and precision. However, protocols are not usually optimized for temporal resolution. Here, we establish the limits for time-resolved sensing of dynamical signals using qubit probes. We show that the best possible time resolution is closely related to the quantum speed limit (QSL), which describes the minimum time needed to transform between basis states. We further show that a composite control sequence consisting of two phase-shifted pulses reaches the QSL. Practical implementation is discussed based on the example of the spin-1 qutrit of a nitrogen-vacancy center in diamond.

Controlling Energy Storage Crossing Quantum Phase Transitions in an Integrable Spin Quantum Battery

We investigate the performance of a one-dimensional dimerized XY chain as a spin quantum battery. Such integrable model shows a rich quantum phase diagram that emerges through a mapping of the spins onto auxiliary fermionic degrees of freedom. We consider a charging protocol relying on the double quench of an internal parameter, namely the strength of the dimerization, and address the energy stored in the systems. We observe three distinct regimes, depending on the timescale characterizing the duration of the charging: a short-time regime related to the dynamics of the single dimers, a long-time regime related to the recurrence time of the system at finite size, and a thermodynamic limit time regime. In the latter, the energy stored is almost unaffected by the charging time and the precise values of the charging parameters, provided the quench crosses a quantum phase transition. Finally, we analytically prove that the three-timescale behavior and the strong dependence of the energy stored on the quantum phase diagram also hold in the quantum Ising chain in a transverse field. Our results can play a relevant role in the design of stable solid-state quantum batteries.

Harnessing Nth Root Gates for Energy Storage

We explore the use of fractional controlled-not gates in quantum thermodynamics. The Nth-root gate allows for a paced application of two-qubit operations. We apply it in quantum thermodynamic protocols for charging a quantum battery. Circuits for three (and two) qubits are analysed by considering the generated ergotropy and other measures of performance. We also perform an optimisation of initial system parameters, e.g.,the initial quantum coherence of one of the qubits strongly affects the efficiency of protocols and the system's performance as a battery. Finally, we briefly discuss the feasibility for an experimental realization.

Work extraction from quantum coherence in non-equilibrium environment

Ergotropy, which represents the maximum amount of work that can be extracted from a quantum system, has become a focal point of interest in the fields of quantum thermodynamics and information processing. In practical scenarios, the interaction of quantum systems with their surrounding environment is unavoidable. Recent studies have increasingly focused on analyzing open quantum systems affected by non-stationary environmental fluctuations due to their significant impact on various physical scenarios. While much research has concentrated on work extraction from these systems, it often assumes that the environmental degrees of freedom are substantial and that the environment is effectively in equilibrium. This has led us to explore work extraction from quantum systems under non-stationary environmental conditions. In this work, the dynamics of ergotropy will be investigated in a non-equilibrium environment for both Markovian and non-Markovian regime. In this study, both the coherent and incoherent parts of the ergotropy will be considered. It will be shown that for a non-equilibrium environment, the extraction of work is more efficient compared to when the environment is in equilibrium.

Generalized Linear Response Theory for the Full Quantum Work Statistics

We consider a quantum system driven out of equilibrium via a small Hamiltonian perturbation. Building on the paradigmatic framework of linear response theory (LRT), we derive an expression for the full generating function of the dissipated work. Remarkably, we find that all information about the distribution can be encoded in a single quantity, the standard relaxation function in LRT, thus opening up new ways to use phenomenological models to study nonequilibrium fluctuations in complex quantum systems. Our results establish a number of refined quantum thermodynamic constraints on the work statistics that apply to regimes of perturbative but arbitrarily fast protocols, and do not rely on assumptions such as slow driving or weak coupling. Finally, our approach uncovers a distinctly quantum signature in the work statistics that originates from underlying zero-point energy fluctuations. This causes an increased dispersion of the probability distribution at short driving times, a feature that can be probed in efforts to witness nonclassical effects in quantum thermodynamics.

Noncompletely Positive Quantum Maps Enable Efficient Local Energy Extraction in Batteries

Energy extraction from quantum batteries by means of completely positive trace-preserving (CPTP) maps leads to the concept of CPTP-local passive states, which identify bipartite states from which no energy can be squeezed out by applying any CPTP map to a particular subsystem. We prove, for arbitrary dimension, that if a state is CPTP-local passive with respect to a Hamiltonian, then an arbitrary number of copies of the same state-including an asymptotically large one-is also CPTP-local passive. We show further that energy can be extracted efficiently from CPTP-local passive states employing noncompletely positive trace-preserving (NCPTP) but still physically realizable maps on the same part of the shared battery on which operation of CPTP maps were useless. Moreover, we provide the maximum extractable energy using local-CPTP operations, and then, we present an explicit class of states and corresponding Hamiltonians, for which the maximum can be outperformed using physical local NCPTP maps. We provide a necessary and sufficient condition and a separate necessary condition for an arbitrary bipartite state to be unable to supply any energy using NCPTP operations on one party with respect to an arbitrary but fixed Hamiltonian. We build an analogy between the relative status of CPTP and NCPTP operations for energy extraction in quantum batteries, and the association of distillable entanglement with entanglement cost for asymptotic local manipulations of entanglement. The surpassing of the maximum energy extractable by NCPTP maps for CPTP-passive as well as for CPTP-nonpassive battery states can act as detectors of non-CPTPness of quantum maps.

Quantum Speed Limit for States and Observables of Perturbed Open Systems

Quantum speed limits provide upper bounds on the rate with which a quantum system can move away from its initial state. Here, we provide a different kind of speed limit, describing the divergence of a perturbed open system from its unperturbed trajectory. In the case of weak coupling, we show that the divergence speed is bounded by the quantum Fisher information under a perturbing Hamiltonian, up to an error which can be estimated from system and bath timescales. We give three applications of our speed limit. First, it enables experimental estimation of quantum Fisher information in the presence of decoherence that is not fully characterized. Second, it implies that large quantum work fluctuations are necessary for a thermal system to be driven quickly out of equilibrium under a quench. Moreover, it can be used to bound the response to perturbations of expectation values of observables in open systems.

Evaluating extractable work of quantum batteries via entropic uncertainty relations

In this study, we investigate the effectiveness of entropic uncertainty relations (EURs) in discerning the energy variation in quantum batteries (QBs) modelled by battery-charger field in the presence of bosonic and fermionic reservoirs. Our results suggest that the extractable works (exergy and ergotropy) have versatile characteristics in different scenarios, resulting in a complex relationship between tightness and extractable work. It is worth noting that the tightness of the lower bound of entropic uncertainty can be a good indicator for energy conversion efficiency in charging QBs. Furthermore, we disclose how the EUR including uncertainty and lower bound contributes to energy conversion efficiency in the QB system. It is believed that these findings will be beneficial for better understanding the role of quantum uncertainty in evaluating quantum battery performance.

Nonreciprocal Quantum Batteries

Nonreciprocity, arising from the breaking of time-reversal symmetry, has become a fundamental tool in diverse quantum technology applications. It enables directional flow of signals and efficient noise suppression, constituting a key element in the architecture of current quantum information and computing systems. Here we explore its potential in optimizing the charging dynamics of a quantum battery. By introducing nonreciprocity through reservoir engineering during the charging process, we induce a directed energy flow from the quantum charger to the battery, resulting in a substantial increase in energy accumulation. Despite local dissipation, the nonreciprocal approach demonstrates a fourfold increase in battery energy compared to conventional charger-battery systems. This effect is observed in the stationary limit and remains applicable even in overdamped coupling regimes, eliminating the need for precise temporal control over evolution parameters. Our result can be extended to a chiral network of quantum nodes, serving as a multicell quantum battery system to enhance storage capacity. The proposed approach is straightforward to implement using current state-of-the-art quantum circuits, both in photonics and superconducting quantum systems. In a broader context, the concept of nonreciprocal charging has significant implications for sensing, energy capture, and storage technologies or studying quantum thermodynamics.

Inhibiting the self-discharging process of quantum batteries in non-Markovian noises

One of the main challenges in developing high-performance quantum batteries is the self-discharging process, where energy is dissipated from a quantum battery into the environment. In this work, we investigate the influence of non-Markovian noises on the performance of a quantum battery. Our results demonstrate that adding auxiliary qubits to a quantum battery system can effectively suppress the self-discharging process, leading to an improvement in both the steady-state energy and extractable work. We reveal that the physical mechanism inhibiting the self-discharging process is the formation of system-environment bound states, rather than an increase in non-Markovianity. Our results could be of both theoretical and experimental interest in exploring the ability of quantum batteries to maintain long stored energy in the environment.

Remote Charging and Degradation Suppression for the Quantum Battery

The quantum battery (QB) makes use of quantum effects to store and supply energy, which may outperform its classical counterpart. However, there are two challenges in this field. One is that the environment-induced decoherence causes the energy loss and aging of the QB, the other is that the decreasing of the charger-QB coupling strength with increasing their distance makes the charging of the QB become inefficient. Here, we propose a QB scheme to realize a remote charging via coupling the QB and the charger to a rectangular hollow metal waveguide. It is found that an ideal charging is realized as long as two bound states are formed in the energy spectrum of the total system consisting of the QB, the charger, and the electromagnetic environment in the waveguide. Using the constructive role of the decoherence, our QB is immune to the aging. Additionally, without resorting to the direct charger-QB interaction, our scheme works in a way of long-range and wireless-like charging. Effectively overcoming the two challenges, our result supplies an insightful guideline to the practical realization of the QB by reservoir engineering.

Population and Energy Transfer Dynamics in an Open Excitonic Quantum Battery

In a previous study, we proposed an open quantum network model of a quantum battery (QB) that possesses dark states owing to its structural exchange symmetries. While in a dark state, the QB is capable of storing an exciton without any environment-induced population losses. However, when the structural exchange symmetry is broken, the QB begins to discharge the exciton towards its exit site. In this article, we start by demonstrating that this QB is not only loss-free with respect to exciton population during the storage phase, but also with respect to the QB energy. We then explore the exciton population and energy transfer dynamics of the QB during the discharge phase over a wide range of site energies, bath temperatures, and bath reorganization energies. Our results shed light on how to optimize the QB's population and energy transfer dynamics for different purposes.

Trade-offs between precision and fluctuations in charging finite-dimensional quantum batteries

Within quantum thermodynamics, many tasks are modeled by processes that require work sources represented by out-of-equilibrium quantum systems, often dubbed quantum batteries, in which work can be deposited or from which work can be extracted. Here we consider quantum batteries modeled as finite-dimensional quantum systems initially in thermal equilibrium that are charged via cyclic Hamiltonian processes. We present optimal or near-optimal protocols for N identical two-level systems and individual d-level systems with equally spaced energy gaps in terms of the charging precision and work fluctuations during the charging process. We analyze the trade-off between these figures of merit as well as the performance of local and global operations.

Magnetically controlled quantum thermal devices via three nearest-neighbor coupled spin-1/2 systems

A quantum thermal device based on three nearest-neighbor coupled spin-1/2 systems controlled by the magnetic field is proposed. We systematically study the steady-state thermal behaviors of the system. When the two terminals of our system are in contact with two thermal reservoirs, respectively, the system behaves as a perfect thermal modulator that can manipulate heat current from zero to specific values by adjusting magnetic-field direction over different parameter ranges, since the longitudinal magnetic field can completely block the heat transport. Significantly, the modulator can also be achieved when a third thermal reservoir perturbs the middle spin. We also find that the transverse field can induce the system to separate into two subspaces in which neither steady-state heat current vanishes, thus providing an extra level of control over the heat current through the manipulation of the initial state. In addition, the performance of this device as a transistor can be enhanced by controlling the magnetic field, achieving versatile amplification behaviors, in particular substantial amplification factors.

Charging Quantum Batteries via Indefinite Causal Order: Theory and Experiment

In the standard quantum theory, the causal order of occurrence between events is prescribed, and must be definite. This has been maintained in all conventional scenarios of operation for quantum batteries. In this study we take a step further to allow the charging of quantum batteries in an indefinite causal order (ICO). We propose a nonunitary dynamics-based charging protocol and experimentally investigate this using a photonic quantum switch. Our results demonstrate that both the amount of energy charged and the thermal efficiency can be boosted simultaneously. Moreover, we reveal a counterintuitive effect that a relatively less powerful charger guarantees a charged battery with more energy at a higher efficiency. Through investigation of different charger configurations, we find that ICO protocol can outperform the conventional protocols and gives rise to the anomalous inverse interaction effect. Our findings highlight a fundamental difference between the novelties arising from ICO and other coherently controlled processes, providing new insights into ICO and its potential applications.

Localization effects in disordered quantum batteries

We investigate the effect of localization on the local charging of quantum batteries (QBs) modeled by disordered spin systems. Two distinct schemes based on the transverse-field random Ising model are considered, with Ising couplings defined on a Chimera graph and on a linear chain with up to next-to-nearest-neighbor interactions. By adopting a low-energy demanding charging process driven by local fields only, we obtain that the maximum extractable energy by unitary processes (ergotropy) is highly enhanced in the ergodic phase in comparison with the many-body localization (MBL) scenario. As we turn off the next-to-nearest-neighbor interactions in the Ising chain, we have the onset of the Anderson localization phase. We then show that the Anderson phase exhibits a hybrid behavior, interpolating between large and small ergotropy as the disorder strength is increased. We also consider the splitting of total ergotropy into its coherent and incoherent contributions. This incoherent part implies in a residual ergotropy that is fully robust against dephasing, which is a typical process leading to the self-discharging of the battery in a real setup. Our results are experimentally feasible in scalable systems, such as in superconducting integrated circuits.

Universal Scaling Bounds on a Quantum Heat Current

In this Letter, we derive new bounds on a heat current flowing into a quantum L-particle system coupled with a Markovian environment. By assuming that a system Hamiltonian and a system-environment interaction Hamiltonian are extensive in L, we prove that the absolute value of the heat current scales at most as Θ(L^{3}) in a limit of large L. Furthermore, we present an example of noninteracting particles globally coupled with a thermal bath, for which this bound is saturated in terms of scaling. However, the construction of such a system requires many-body interactions induced by the environment, which may be difficult to realize with the existing technology. To consider more feasible cases, we consider a class of the system where any nondiagonal elements of the noise operator (derived from the system-environment interaction Hamiltonian) become zero in the system energy basis, if the energy difference exceeds a certain value ΔE. Then, for ΔE=Θ(L^{0}), we derive another scaling bound Θ(L^{2}) on the absolute value of the heat current, and the so-called superradiance belongs to a class for which this bound is saturated. Our results are useful for evaluating the best achievable performance of quantum-enhanced thermodynamic devices, including far-reaching applications such as quantum heat engines, quantum refrigerators, and quantum batteries.

Battery Capacity of Energy-Storing Quantum Systems

The quantum battery capacity is introduced in this Letter as a figure of merit that expresses the potential of a quantum system to store and supply energy. It is defined as the difference between the highest and the lowest energy that can be reached by means of the unitary evolution of the system. This function is closely connected to the ergotropy, but it does not depend on the temporary level of energy of the system. The capacity of a quantum battery can be directly linked with the entropy of the battery state, as well as with measures of coherence and entanglement.

Study the charging process of moving quantum batteries inside cavity

In quantum mechanics, quantum batteries are devices that can store energy by utilizing the principles of quantum mechanics. While quantum batteries has been investigated largely theoretical, recent research indicates that it may be possible to implement such a device using existing technologies. The environment plays an important role in the charging of quantum batteries. If a strong coupling exists between the environment and the battery, then battery can be charged properly. It has also been demonstrated that quantum battery can be charged even in weak coupling regime just by choosing a suitable initial state for battery and charger. In this study, we investigate the charging process of open quantum batteries mediated by a common dissipative environment. We will consider a wireless-like charging scenario, where there is no external power and direct interaction between charger and battery. Moreover, we consider the case in which the battery and charger move inside the environment with a particular speed. Our results demonstrate that the movement of the quantum battery inside the environment has a negative effect on the performance of the quantum batteries during the charging process. It is also shown that the non-Markovian environment has a positive effect on improving battery performance.

Work Extraction from Unknown Quantum Sources

Energy extraction is a central task in thermodynamics. In quantum physics, ergotropy measures the amount of work extractable under cyclic Hamiltonian control. As its full extraction requires perfect knowledge of the initial state, however, it does not characterize the work value of unknown or untrusted quantum sources. Fully characterizing such sources would require quantum tomography, which is prohibitively costly in experiments due to the exponential growth of required measurements and operational limitations. Here, we therefore derive a new notion of ergotropy applicable when nothing is known about the quantum states produced by the source, apart from what can be learned by performing only a single type of coarse-grained measurement. We find that in this case the extracted work is defined by the Boltzmann and observational entropy in cases where the measurement outcomes are, or are not, used in the work extraction, respectively. This notion of ergotropy represents a realistic measure of extractable work, which can be used as the relevant figure of merit to characterize a quantum battery.

Analytically Solvable Model for Qubit-Mediated Energy Transfer between Quantum Batteries

The coherent energy transfer between two identical two-level systems is investigated. Here, the first quantum system plays the role of a charger, while the second can be seen as a quantum battery. Firstly, a direct energy transfer between the two objects is considered and then compared to a transfer mediated by an additional intermediate two-level system. In this latter case, it is possible to distinguish between a two-step process, where the energy is firstly transferred from the charger to the mediator and only after from the mediator to the battery, and a single-step in which the two transfers occurs simultaneously. The differences between these configurations are discussed in the framework of an analytically solvable model completing what recently discussed in literature.

Quantum battery based on dipole-dipole interaction and external driving field

The Dicke model is a fundamental model in quantum optics, which describes the interaction between quantum cavity field and a large ensemble of two-level atoms. In this work, we propose an efficient charging quantum battery achieved by considering an extension Dicke model with dipole-dipole interaction and an external driving field. We focus on the influence of the atomic interaction and the driving field on the performance of the quantum battery during the charging process and find that the maximum stored energy exhibits a critical phenomenon. The maximum stored energy and maximum charging power are investigated by varying the number of atoms. When the coupling between atoms and cavity is not very strong, compared to the Dicke quantum battery, such quantum battery can achieve more stable and faster charging. In addition, the maximum charging power approximately satisfies a superlinear scaling relation P_{max}∝βN^{α}, where the quantum advantage α=1.6 can be reached via optimizing the parameters.

Lossy Micromaser Battery: Almost Pure States in the Jaynes-Cummings Regime

We consider a micromaser model of a quantum battery, where the battery is a single mode of the electromagnetic field in a cavity, charged via repeated interactions with a stream of qubits, all prepared in the same non-equilibrium state, either incoherent or coherent, with the matter-field interaction modeled by the Jaynes-Cummings model. We show that the coherent protocol is superior to the incoherent one, in that an effective pure steady state is achieved for generic values of the model parameters. Finally, we supplement the above collision model with cavity losses, described by a Lindblad master equation. We show that battery performances, in terms of stored energy, charging power, and steady-state purity, are slightly degraded up to moderated dissipation rate. Our results show that micromasers are robust and reliable quantum batteries, thus making them a promising model for experimental implementations.

Thermodynamics of Quantum Spin-Bath Depolarization

We analyze here through exact calculations the thermodynamical effects in depolarizing a quantum spin-bath initially at zero temperature through a quantum probe coupled to an infinite temperature bath by evaluating the heat and entropy changes. We show that the correlations induced in the bath during the depolarizing process does not allow for the entropy of the bath to increase towards its maximal limit. On the contrary, the energy deposited in the bath can be completely extracted in a finite time. We explore these findings through an exactly solvable central spin model, wherein a central spin-1/2 system is homogeneously coupled to a bath of identical spins. Further, we show that, upon destroying these unwanted correlations, we boost the rate of both energy extraction and entropy towards their limiting values. We envisage that these studies are relevant for quantum battery research wherein both charging and discharging processes are key to characterizing the battery performance.

Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines

We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.

On the contribution of work or heat in exchanged energy via interaction in open bipartite quantum systems

The question of with what we associate work and heat in a quantum thermodynamic process has been extensively discussed, mostly for systems with time-dependent Hamiltonians. In this paper, we aim to investigate the energy exchanged between two quantum systems through interaction where the Hamiltonian of the system is time-independent. An entropy-based re-definitions of heat and work are presented for these quantum thermodynamic systems therefore an entropy-based formalism of both the first and the second laws of thermodynamics are introduced. We will use the genuine reasoning based on which Clausius originally defined work and heat. The change in the energy which is accompanied by a change in the entropy is identified as heat, while any change in the energy which does not lead to a change in the entropy is known as work. It will be seen that quantum coherence does not allow all the energy exchanged between two quantum systems to be only of the heat form. Several examples will also be discussed. Finally, we will examine irreversibility from our entropy-based formalism of quantum thermodynamics.

Quantum Battery Based on Hybrid Field Charging

A quantum battery consisting of an ensemble two-level atom is investigated. The battery is charged simultaneously by a harmonic field and an electrostatic field. The results show that the hybrid charging is superior to the previous case of only harmonic field charging in terms of battery capacity and charging power, regardless of whether the interaction between atoms is considered or not. In addition, the repulsive interaction between atoms will increase the battery capacity and charging power, while the attractive interaction between atoms will reduce the battery capacity and discharge power.

Quantum batteries in non-Markovian reservoirs

In this Letter, we propose schemes to improve the performance of quantum batteries and provide a new, to the best of our knowledge, quantum source for a quantum battery without an external driving field. We show that the memory effect of the non-Markovian reservoir can play a significant role in improving the performance of quantum batteries, which originates from a backflow on the ergotropy in the non-Markovian regime, while there is no counterpart in Markovian approximation. We find that the peak for the maximum average storing power in the non-Markovian regime can be enhanced by manipulating the coupling strength between the charger and the battery. Finally, we find that the battery can also be charged by non-rotating wave terms without driving fields.

Environment-mediated entropic uncertainty in charging quantum batteries

We studied the dynamics of entropic uncertainty in Markovian and non-Markovian systems during the charging of open quantum batteries (QBs) mediated by a common dissipation environment. In the non-Markovian regime, the battery is almost fully charged efficiently, and the strong non-Markovian property is beneficial for improving the charging power. In addition, the results show that the energy storage is closely related to the couplings of the charger-reservoir and battery-reservoir; that is, the stronger coupling of a charger reservoir improves energy storage. In particular, entanglement is required to obtain the most stored energy and is accompanied by the least tight entropic bound. Interestingly, it was found that the tightness of the entropic bound can be considered as a good indicator of the energy transfer in different charging processes, and the complete energy transfer always corresponds to the tightest entropic bound. Our results provide insight into the optimal charging efficiency of QBs during practical charging.

Quantum enhancement of a single quantum battery by repeated interactions with large spins

A generalized collision model is developed to investigate coherent charging a single quantum battery by repeated interactions with many-atom large spins, where collective atom operators are adopted and the battery is modeled by a uniform energy ladder. For an initially empty battery, we derive analytical results of the average number of excitations and hence the charging power in the short-time limit. Our analytical results show that a faster charging and an increased amount of the power in the coherent protocol uniquely arise from the phase coherence of the atoms. Finally, we show that the charging power defined by the so-called ergotropy almost follows our analytical result, due to a nearly pure state of the battery in the short-time limit.

Entanglement, Coherence, and Extractable Work in Quantum Batteries

We investigate the connection between quantum resources and extractable work in quantum batteries. We demonstrate that quantum coherence in the battery or the battery-charger entanglement is a necessary resource for generating nonzero extractable work during the charging process. At the end of the charging process, we also establish a tight link of coherence and entanglement with the final extractable work: coherence naturally promotes the coherent work while coherence and entanglement inhibit the incoherent work. We also show that obtaining maximally coherent work is faster than obtaining maximally incoherent work. Examples ranging from the central-spin battery and the Tavis-Cummings battery to the spin-chain battery are given to illustrate these results.

Energetics of a Single Qubit Gate

Qubits are physical, a quantum gate thus not only acts on the information carried by the qubit but also on its energy. What is then the corresponding flow of energy between the qubit and the controller that implements the gate? Here we exploit a superconducting platform to answer this question in the case of a quantum gate realized by a resonant drive field. During the gate, the superconducting qubit becomes entangled with the microwave drive pulse so that there is a quantum superposition between energy flows. We measure the energy change in the drive field conditioned on the outcome of a projective qubit measurement. We demonstrate that the drive's energy change associated with the measurement backaction can exceed by far the energy that can be extracted by the qubit. This can be understood by considering the qubit as a weak measurement apparatus of the driving field.

Boosting Quantum Battery-Based IoT Gadgets via RF-Enabled Energy Harvesting

The search for a highly portable and efficient supply of energy to run small-scale wireless gadgets has captivated the human race for the past few years. As a part of this quest, the idea of realizing a Quantum battery (QB) seems promising. Like any other practically tractable system, the design of QBs also involve several critical challenges. The main problem in this context is to ensure a lossless environment pertaining to the closed-system design of the QB, which is extremely difficult to realize in practice. Herein, we model and optimize various aspects of a Radio-Frequency (RF) Energy Harvesting (EH)-assisted, QB-enabled Internet-of-Things (IoT) system. Several RF-EH modules (in the form of micro- or nano-meter-sized integrated circuits (ICs)) are placed in parallel at the IoT receiver device, and the overall correspondingly harvested energy helps the involved Quantum sources achieve the so-called quasi-stable state. Concretely, the Quantum sources absorb the energy of photons that are emitted by a photon-emitting device controlled by a micro-controller, which also manages the overall harvested energy from the RF-EH ICs. To investigate the considered framework, we first minimize the total transmit power under the constraints on overall harvested energy and the number of RF-EH ICs at the QB-enabled wireless IoT device. Next, we optimize the number of RF-EH ICs, subject to the constraints on total transmit power and overall harvested energy. Correspondingly, we obtain suitable analytical solutions to the above-mentioned problems, respectively, and also cross-validate them using a non-linear program solver. The effectiveness of the proposed technique is reported in the form of numerical results, which are both theoretical and simulations based, by taking a range of operating system parameters into account.

Efficiency Fluctuations in a Quantum Battery Charged by a Repeated Interaction Process

A repeated interaction process assisted by auxiliary thermal systems charges a quantum battery. The charging energy is supplied by switching on and off the interaction between the battery and the thermal systems. The charged state is an equilibrium state for the repeated interaction process, and the ergotropy characterizes its charge. The working cycle consists in extracting the ergotropy and charging the battery again. We discuss the fluctuating efficiency of the process, among other fluctuating properties. These fluctuations are dominated by the equilibrium distribution and depend weakly on other process properties.

Collective enhancement in dissipative quantum batteries

We study a quantum battery made out of N nonmutually interacting qubits coupled to a dissipative single electromagnetic field mode in a resonator. We quantify the charging energy, ergotropy, transfer rate, and power of the system, showing that collective enhancements are still present despite losses, and can even increase with dissipation. Moreover, we observe that a performance deterioration due to dissipation can be reduced by scaling up the battery size. This is useful for experimental realizations when controlling the quality of the resonator and the number of qubits are limiting factors.

IBM Quantum Platforms: A Quantum Battery Perspective

We characterize for the first time the performances of IBM quantum chips as quantum batteries, specifically addressing the single-qubit Armonk processor. By exploiting the Pulse access enabled to some of the IBM Quantum processors via the Qiskit package, we investigate the advantages and limitations of different profiles for classical drives used to charge these miniaturized batteries, establishing the optimal compromise between charging time and stored energy. Moreover, we consider the role played by various possible initial conditions on the functioning of the quantum batteries. As the main result of our analysis, we observe that unavoidable errors occurring in the initialization phase of the qubit, which can be detrimental for quantum computing applications, only marginally affect energy transfer and storage. This can lead counter-intuitively to improvements of the performances. This is a strong indication of the fact that IBM quantum devices are already in the proper range of parameters to be considered as good and stable quantum batteries comparable to state-of-the-art devices recently discussed in the literature.

Enhancing self-discharging process with disordered quantum batteries

One of the most important devices emerging from quantum technology are quantum batteries. However, self-discharging, the process of charge wasting of quantum batteries due to decoherence phenomenon, limits their performance, measured by the concept of ergotropy and half-life time of the quantum battery. The effects of local field fluctuation, introduced by the disorder term in the Hamiltonian of the system, on the performance of the quantum batteries is investigated in this paper. The results reveal that the disorder term could compensate disruptive effects of the decoherence, i.e., self-discharging, and hence improve the performance of the quantum battery via "incoherent gain of ergotropy" procedure. Adjusting the strength of the disorder parameter to a proper value and choosing a suitable initial state of the quantum battery, the amount of free ergotropy, defined with respect to the free Hamiltonian, could exceed the amount of initial stored ergotropy. In addition harnessing the degree of the disorder parameter could help to enhance the half-life time of the quantum battery. This study opens perspective to further investigation of the performance of quantum batteries that explore disorder and many-body effects.

Quantum Charging Advantage Cannot Be Extensive without Global Operations

Quantum batteries are devices made from quantum states, which store and release energy in a fast and efficient manner, thus offering numerous possibilities in future technological applications. They offer a significant charging speedup when compared to classical batteries, due to the possibility of using entangling charging operations. We show that the maximal speedup that can be achieved is extensive in the number of cells, thus offering at most quadratic scaling in the charging power over the classically achievable linear scaling. To reach such a scaling, a global charging protocol, charging all the cells collectively, needs to be employed. This concludes the quest on the limits of charging power of quantum batteries and adds to other results in which quantum methods are known to provide at most quadratic scaling over their classical counterparts.

Periodically driven many-body quantum battery

We explore the charging of a quantum battery based on spin systems through periodic modulation of a transverse-field-like Ising Hamiltonian. In the integrable limit, we find that resonance tunneling can lead to a higher transfer of energy to the battery and better stability of the stored energy at specific drive frequencies. When the integrability is broken in the presence of an additional longitudinal field, we find that the effective Floquet Hamiltonian contains terms which may lead to a global charging of the battery. However, we do not find any quantum advantage in the charging power, thus demonstrating that global charging is only a necessary and not sufficient condition for achieving quantum advantage.

Superabsorption in an organic microcavity: Toward a quantum battery

The rate at which matter emits or absorbs light can be modified by its environment, as markedly exemplified by the widely studied phenomenon of superradiance. The reverse process, superabsorption, is harder to demonstrate because of the challenges of probing ultrafast processes and has only been seen for small numbers of atoms. Its central idea—superextensive scaling of absorption, meaning larger systems absorb faster—is also the key idea underpinning quantum batteries. Here, we implement experimentally a paradigmatic model of a quantum battery, constructed of a microcavity enclosing a molecular dye. Ultrafast optical spectroscopy allows us to observe charging dynamics at femtosecond resolution to demonstrate superextensive charging rates and storage capacity, in agreement with our theoretical modeling. We find that decoherence plays an important role in stabilizing energy storage. Our work opens future opportunities for harnessing collective effects in light-matter coupling for nanoscale energy capture, storage, and transport technologies.

Bounds on charging power of open quantum batteries

In general, quantum systems most likely undergo open-system dynamics due to their smallness and sensitivity. Energy storage devices, so-called quantum batteries, are not excluded from this phenomenon. Here, we study fundamental bounds on the power of open quantum batteries from the geometric point of view. By defining an activity operator, a tight upper bound on the charging power is derived for the open quantum batteries in terms of the fluctuations of the activity operator and the quantum Fisher information. The variance of the activity operator may be interpreted as a generalized thermodynamic force, while the quantum Fisher information describes the speed of evolution in the state space of the battery. The thermodynamic interpretation of the upper bound is discussed in detail. As an example, a model for the battery, taking into account the environmental effects, is proposed, and the effect of dissipation and decoherence during the charging process on both the stored work and the charging power is investigated. Our results show that the upper bound is saturated in some time intervals. Also, the maximum value of both the stored work and the corresponding power is achieved in the non-Markovian underdamped regime.

Observing crossover between quantum speed limits

Quantum mechanics sets fundamental limits on how fast quantum states can be transformed in time. Two well-known quantum speed limits are the Mandelstam-Tamm and the Margolus-Levitin bounds, which relate the maximum speed of evolution to the system’s energy uncertainty and mean energy, respectively. Here, we test concurrently both limits in a multilevel system by following the motion of a single atom in an optical trap using fast matter wave interferometry. We find two different regimes: one where the Mandelstam-Tamm limit constrains the evolution at all times, and a second where a crossover to the Margolus-Levitin limit occurs at longer times. We take a geometric approach to quantify the deviation from the speed limit, measuring how much the quantum evolution deviates from the geodesic path in the Hilbert space of the multilevel system. Our results are important to understand the ultimate performance of quantum computing devices and related advanced quantum technologies.