We study the problem of charging a quantum battery in finite time. We demonstrate an analytical optimal protocol for the case of a single qubit. Extending this analysis to an array of N qubits, we demonstrate that an N-fold advantage in power per qubit can be achieved when global operations are permitted. The exemplary analytic argument for this quantum advantage in the charging power is backed up by numerical analysis using optimal control techniques. It is demonstrated that the quantum advantage for power holds when, with cyclic operation in mind, initial and final states are required to be separable.
Can collective quantum effects make a difference in a meaningful thermodynamic operation? Focusing on energy storage and batteries, we demonstrate that quantum mechanics can lead to an enhancement in the amount of work deposited per unit time, i.e., the charging power, when $N$ batteries are charged collectively. We first derive analytic upper bounds for the collective \emph{quantum advantage} in charging power for two choices of constraints on the charging Hamiltonian. We then highlight the importance of entanglement by proving that the quantum advantage vanishes when the collective state of …
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…
We analyse the charging process of quantum batteries with general harmonic power. To describe the charge efficiency, we introduce the charge saturation and the charging power, and divide the charging mode into the saturated charging mode and the unsaturated charging mode. The relationships between the time-dependent charge saturation and the parameters of general driving field are discussed both analytically and numerically. And according to the Floquet theorem, we give the expressions of time-dependent charge saturation with the quasiengery and the Floquet states of the system. With both the …
We consider the dissipative charging process of quantum batteries in terms of a collisional model, where the batteries are coupled to a heat bath using non-energy preserving interactions. First, we show that for low temperatures the collective process can attain a charging power that increases polynomically with the number of batteries. The scaling we find is $N^3$ that, while being grater than the bound obtained for unitary processes, it has a lower efficiency. Then, we study the dissipative charging process of single battery using a time dependent Hamiltonian that generates coherences in the…
We consider a classical harmonic driving field as the energy charger for the quantum batteries, which consist of an ensemble of two-level atoms. The maximum stored energy and the final state are derived analytically with the optimal driving frequency. At the end of charging procedure, each of atoms is in the upper state and the batteries are charging completely, which exhibits a substantial improvement over the square-wave charger. Involving the interatomic correlations, we find that the repulsive couplings show an advantage in achieving fully charging with shorter charging period. However, th…
We present a scheme for the charging of a quantum battery based on the dynamics of an open quantum system undergoing coherent quantum squeezing and affected by an incoherent squeezed thermal bath. We show that quantum coherence, as instigated by the application of coherent squeezing, are key in the determination of the performance of the charging process, which is efficiency-enhanced at low environmental temperature and under a strong squeezed driving.
Quantum devices are systems that can explore quantum phenomena, like entanglement or coherence, for example, to provide some enhancement performance concerning their classical counterparts. In particular, quantum batteries are devices that use entanglement as main element in its high performance in the charging powerful. In this paper, we explore the quantum battery performance and its relationship with the amount of entanglement that arises during the charging process. By using a general approach to a two and three-cell battery, our results suggest that entanglement is not the main resource t…
The charging of a quantum battery by a four-stroke quantum machine that works either as an engine or a refrigerator is investigated. The presented analysis provides the energetic behavior of the combined system in terms of the heat and workflows of the machine, the average, and variance of the battery's energy as well as the coherent and incoherent parts of its ergotropy. To monitor the battery state its energy is measured either after the completion of any cycle or after a prescribed number of cycles is carried out. The resulting battery performances greatly differ for those two cases. During…
We study the charging process of open quantum batteries mediated by a common dissipative environment in two different scenarios. In the first case, we consider a quantum charger-battery model in the presence of a non-Markovian environment. Where the battery can be properly charged in a strong coupling regime, without any external power and any direct interaction with the charger, i.e., a wireless-like charging happens. The environment plays a major role in the charging of the battery, while this does not happen in a weak coupling regime. In the second scenario, we show the effect of individual…
Motivated by a recent disagreement about the claim that fluctuations in the free energy operator bound the charging power of a quantum battery, we present a critical analysis of the original derivation. The analysis shows that the above claim does not hold for both closed- and open-system dynamics. Our results indicate that the free energy operator is not a consistent quantifying operator for the work content of a charging quantum battery.
In an article by García-Pintos et al. [Rev. Lett. 125, 040601 (2020)] the connection between the charging power of a quantum battery and the fluctuations of a "free energy operator" whose expectation value characterizes the maximum extractable work of the battery is studied. The result of the closed-system analysis shows that for a general charging process the battery will have a nonzero charging power if and only if the state of the battery is not an eigenstate of the free energy operator. In this Comment, we point out a few mistakes in the analysis and obtain the correct bound on the chargin…
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 req…
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 \emph{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 the…
The storage and transfer of energy through quantum batteries are key elements in quantum networks. Here, we propose a charger design based on transitionless quantum driving (TQD), which allows for inherent control over the battery charging time, with the speed of charging coming at the cost of the internal energy available to implement the dynamics. Moreover, the TQD-based charger is also shown to be locally stable, which means that the charger can be disconnected from the quantum battery (QB) at any time after the energy transfer to the QB, with no fully energy backflow to the charger. This p…
Quantum batteries are energy storage devices that satisfy quantum mechanical principles. How to improve the battery's performance such as stored energy and power is a crucial element in the quantum battery. Here, we investigate the charging and discharging dynamics of a three-level counterdiabatic stimulated Raman adiabatic passage quantum battery via shortcuts to adiabaticity, which can compensate for undesired transitions to realize a fast adiabatic evolution through the application of an additional control field to an initial Hamiltonian. The scheme can significantly speed up the charging a…
The exactly-solvable Sachdev-Ye-Kitaev (SYK) model has recently received considerable attention in both condensed matter and high energy physics because it describes quantum matter without quasiparticles, while being at the same time the holographic dual of a quantum black hole. In this Letter, we examine SYK-based charging protocols of quantum batteries with N quantum cells. Extensive numerical calculations based on exact diagonalization for N up to 16 strongly suggest that the optimal charging power of our SYK quantum batteries displays a super-extensive scaling with N that stems from genuin…
In this article, in addition to the characterization of geometrical state spaces for the passive states, an operational approach has been introduced to distinguish them on their charging capabilities of a quantum battery. Unlike the thermal states, the structural instability of passive states assures the existence of a natural number $n$, for which $n+1$-copies of the state can charge a quantum battery while $n$-copies cannot. This phenomenon can be presented in a $n$-copy resource-theoretic approach, for which the free states are unable to charge the battery in $n$-copies. Here we have exhibi…
Fast charging of quantum batteries assisted by nonlinear couplings
National Tsing Hua University（国立清华大学）；Institute of Atomic and Molecular Sciences, Academia Sinica（中央研究院原子与分子科学研究所）；Georgia Institute of Technology（佐治亚理工学院）；National Central University（国立中央大学）；Molecular Science and Technology Program, Taiwan International Graduate Program, Academia Sinica（中央研究院台湾国际研究生分子科学与技术学程）；National Center for Theoretical Sciences（国家理论科学中心）
We study the problem of charging a dissipative one-dimensional $XXX$ spin-chain quantum battery using local magnetic fields in the presence of spin decay. The introduction of quantum feedback control based on homodyne measurement contributes to improve various performance of the quantum battery, such as energy storage, ergotropy, and effective space utilization rate. For the zero temperature environment, there is a set of optimal parameters to ensure that the spin-chain quantum battery can be fully charged and the energy stored in the battery can be fully extracted under the perfect measuremen…
The performance of quantum technologies that use entanglement and coherence as resource is highly limited by decohering effects due to their interaction with some environment. Particularly, it is important to take into account situations where such devices unavoidably interact with a surrounding. Here, we study memory effects on energy and ergotropy of quantum batteries in the framework of open system dynamics, where the battery and charger are individually allowed to access a bosonic environment. Our investigation shows that the battery can be fully charged and its energy can be preserved for…
We study the connection between the charging power of quantum batteries and the fluctuations of the extractable work. We prove that in order to have a non-zero rate of change of the extractable work, the state $ρ_\mathcal{W}$ of the battery cannot be an eigenstate of a `\emph{free energy operator}', defined by $\mathcal{F}~\equiv~H_\mathcal{W}~+~β^{-1}\log(ρ_\mathcal{W})$, where $H_\mathcal{W}$ is the Hamiltonian of the battery and $β$ is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the fr…
In the abstract of~[Phys. Rev. Lett. {\bf 125}, 040601 (2020)] one can read that: [...]{\it to have a nonzero rate of change of the extractable work, the state $ρ_\mathcal{W}$ of the battery cannot be an eigenstate of a "free energy operator", defined by $\mathcal{F}=H_\mathcal{W}+β^{-1}\log ρ_\mathcal{W}$, where $H_\mathcal{W}$ is the Hamiltonian of the battery and $β$ is the inverse temperature} [...]. Contrarily to what is presented below Eq.~(17) of the paper, we observe that the above conclusion does not hold when the battery is subject to nonunitary dynamics.
Spin-Squeezing-Enhanced Charging for Quantum Dicke Batteries
Fujian Key Laboratory of Quantum Information and Quantum Optics, Fuzhou University（福建量子信息与量子光学重点实验室，福州大学）；Department of Physics, Fuzhou University（福州大学物理系）；School of Physics and Electronic Engineering, Hubei University of Arts and Science（湖北文理学院物理与电子工程学院）；Quantum Information Physics Theory Research Team, Center for Quantum Computing, RIKEN（理化学研究所量子计算中心量子信息物理理论研究组）
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…
College of Physics and Electronic Science, Hubei Normal University（湖北师范大学物理与电子科学学院）；Hubei Engineering Institute（湖北工程学院）；State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University（山西大学量子光学与量子光学器件国家重点实验室激光光谱研究所）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
