Energy storage is a basic physical process with many applications. When considering this task at the quantum scale, it becomes important to optimise the non-equilibrium dynamics of energy transfer to the storage device or battery. Here, we tackle this problem using the methods of quantum feedback control. Specifically, we study the deposition of energy into a quantum battery via an auxiliary charger. The latter is a driven-dissipative two-level system subjected to a homodyne measurement whose output signal is fed back linearly into the driving field amplitude. We explore two different control strategies, aiming to stabilise either populations or quantum coherences in the state of the charger. In both cases, linear feedback is shown to counteract the randomising influence of environmental noise and allow for stable and effective battery charging. We analyse the effect of realistic control imprecisions, demonstrating that this good performance survives inefficient measurements and small feedback delays. Our results highlight the potential of continuous feedback for the control of energetic quantities in the quantum regime.
We consider a quantum battery modeled as a set of N independent two-level quantum systems driven by a time dependent classical source. Different figures of merit, such as stored energy, time of charging and energy quantum fluctuations during the charging process, are characterized in a wide range of parameters, by means of numerical approach and suitable analytical approximation scheme. Particular emphasis is put on the role of different initial conditions, describing the preparation state of the quantum battery, as well as on the sensitivity to the functional form of the external time-depende…
Achieving Identical Stored Energy in Cascaded Collisional Quantum Battery Charging: Analytical Result
College of Science, Nanjing University of Posts and Telecommunications（南京邮电大学理学院）；Jiangsu Provincial Engineering Research Center of Low Dimensional Physics and New Energy（江苏省低维物理与新能源工程研究中心）
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…
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 construct a collision model where measurements in the system, together with a Bayesian decision rule, are used to classify the incoming ancillas as having either high or low ergotropy (maximum extractable work). The former are allowed to leave, while the latter are redirected for further processing, aimed at increasing their ergotropy further. The ancillas play the role of a quantum battery, and the collision model therefore implements a Maxwell demon. To make the process autonomous, and with a well defined limit cycle, the information collected by the demon is reset after each collision by…
We present a collision model for the charging of a quantum battery by identical nonequilibrium qubit units. When the units are prepared in a mixture of energy eigenstates, the energy gain in the battery can be described by a classical random walk, where both average energy and variance grow linearly with time. Conversely, when the qubits contain quantum coherence, interference effects buildup in the battery and lead to a faster spreading of the energy distribution, reminiscent of a quantum random walk. This can be exploited for faster and more efficient charging of a battery initialized in the…
Charging efficiency bursts in a quantum battery with cyclic indefinite causal order
National Cheng Kung University（国立成功大学）；Center for Quantum Frontiers of Research and Technology, NCKU（国立成功大学量子前沿科技研究中心）；University of Rochester（罗切斯特大学）；National Center for Theoretical Sciences（国家理论科学中心）
Theoretical explorations have revealed that quantum batteries can exploit quantum correlation to achieve faster charging, thus promising exciting applications in future technologies. Using NMR architecture, here we experimentally investigate various aspects of quantum battery with the help of nuclear spin systems in star-topology configuration. We first carry out numerical analysis to study how charging a quantum battery depends on the relative purity factors of charger and battery spins. By experimentally measuring the polarization of the battery spin undergoing charging, we estimate the batt…
Quantum batteries are quantum systems that store energy which can then be used for quantum tasks. One relevant question about such systems concerns the differences and eventual advantages over their classical counterparts, whether in the efficiency of the energy transference, input power, total stored energy or other relevant physical quantities. Here, we show how a purely quantum effect related to the vacuum of the electromagnetic field can enhance the charging of a quantum battery. In particular, we demonstrate how an anti-Jaynes Cummings interaction derived from an off-resonant Raman config…
Quantum battery is one of the most prominent micro-devices in the rapid-developing quantum thermodynamics. We propose a quantum charging protocol in which both battery and charger are consisted of a many-spin system. The battery and charger are connected via the Kittle mode of the magnon system, that serves as a charging wire and then enables a long-range charging protocol. Counter-intuitively, we find that the spin-spin couplings insider both battery and charger can be used to promote the charging performance in comparison to the noninteracting condition. And a remarkable promotion is realize…
Charging power enhancement at the phase transition of a non-integrable quantum battery
Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）；INFN, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Università di Genova（热那亚大学）；CNR-SPIN（国家研究委员会自旋物理中心）
We consider a collection of two level systems, such as qubits, embedded into a microwave cavity as a promising candidate for the realization of high power quantum batteries. In this perspective, the possibility to design devices where the conventional single-photon coupling is suppressed and the dominant interaction is mediated by two-photon processes is investigated, opening the way to an even further enhancement of the charging performance. By solving a Dicke model with both single- and two-photon coupling we determine the range of parameters where the latter unconventional interaction domin…
Charging of a Quantum Battery by a Two-Photon Quantum Pulse
Institute for Physical Research, Armenian National Academy of Sciences（亚美尼亚国家科学院物理研究所）；Basic Sciences Group, Golpayegan College of Engineering, Isfahan University of Technology（伊斯法罕理工大学戈尔佩根工程学院基础科学组）
Coupling with an external environment inevitably affects the dynamics of a quantum system. Here, we consider how charging performances of a quantum battery, modelled as a two level system, are influenced by the presence of an Ohmic thermal reservoir. The latter is coupled to both longitudinal and transverse spin components of the quantum battery including decoherence and pure dephasing mechanisms. Charging and discharging dynamics of the quantum battery, subjected to a static driving, are obtained exploiting a proper mapping into the so-called spin-boson model. Analytic expressions for the tim…
One of the most fundamental tasks in quantum thermodynamics is extracting energy from one system and subsequently storing this energy in an appropriate battery. Both of these steps, work extraction and charging, can be viewed as cyclic Hamiltonian processes acting on individual quantum systems. Interestingly, so-called passive states exist, whose energy cannot be lowered by unitary operations, but it is safe to assume that the energy of any not fully charged battery may be increased unitarily. However, unitaries raising the average energy by the same amount may differ in qualities such as thei…
We show that a cyclic unitary process can extract work from the thermodynamic equilibrium state of an engineered quantum dissipative process. Systems in the equilibrium states of these processes serve as batteries, storing energy. The dissipative process that brings the battery to the active equilibrium state is driven by an agent that couples the battery to thermal systems. The second law of thermodynamics imposes a work cost for the process; however, no work is needed to keep the battery in that charged state. We consider simple examples of these batteries and discuss particular cases in whi…
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 …
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 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…
Quantum batteries are energy storage or extract devices in a quantum system. Here, we present a closed-loop quantum battery by utilizing a closed-loop three-state quantum system in which the population dynamics depends on the three control fields and associated phases. We investigate the charging process of the closed-loop three-level quantum battery. The charging performance is greatly improved due to existence of the third field in the system to form a closed-contour interaction. Through selecting an appropriate the third control field, the maximum average power can be increased, even far be…
Correlation Enhanced Autonomous Quantum Battery Charging via Structured Reservoirs
Abdelmalek Essaadi University（阿卜杜勒马利克·埃萨迪大学）；Mohammed VI Polytechnic University (UM6P)（穆罕默德六世polytechnic大学）；University of Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；Koç University（库奇大学）；TÜBİTAK Research Institute for Fundamental Sciences（土耳其科学与技术研究基金会基础科学研究所）
Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of quantum batteries (QBs) made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of $N$ two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model ("Dicke QB"), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode ("Rabi QB"). By …
A system in thermal equilibrium with a bath will generally be in an athermal state, if the system-bath coupling is strong. In some cases, it will be possible to extract work from that athermal state, after disconnecting the system from the bath. We use this observation to devise a battery charging and storing unit, simply consisting of a system, acting as the battery, and a bath. The charging cycle---connect, let thermalize, disconnect, extract work---requires very little external control and the charged state of the battery, being a part of global thermal equilibrium, can be maintained indefi…
Spectrally Selective Charging of an Interacting Quantum Battery via an Anharmonic Mediator
Ramakrishna Mission Vivekananda Educational and Research Institute（拉马克里希纳使命维韦卡南达教育与研究机构）；TCG CREST；Academy of Scientific and Innovative Research (AcSIR)（科学与创新研究学院）
We consider a central-spin battery where $N_b$ central spins serve as battery cells and $N_c$ bath spins serve as charging units. It is shown that the energy stored in the battery that can be extractable is quantified by the ergotropy, and that battery-charger entanglement is quantified via the Von Neumann entropy. By using an exact approach to a one-cell and two-cell battery, our analytical results suggest that, during the charging process, the extractable work slowly increases before the battery-charger entanglement reaches its maximum and then it will rapidly increase when the entanglement …
