Quantum Charging Advantage Cannot Be Extensive Without Global Operations
Ju-Yeon Gyhm, Dominik Šafránek, Dario Rosa
备注：
Main text: 5 pages, 1 figure. Supplemental material: 7 pages, 3 figures: v2: main: extended explanation of the source of the quantum advantage and comparison with parallel charging, references added, and other minor changes. Supplemental material: additional discussion of the scaling of the bandwidth of Fig. 1
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.
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…
We investigate the charging process of quantum battery (QB) systems in an extended Dicke model with both atomic interactions and an external driving field. We focus on the effects of the atomic interaction and the external driving field on the charging performance of QB and find that the maximum stored energy of QB has a critical phenomenon. We analyze the critical behavior and obtain the analytical expression of the critical atomic interaction. The dependence of the maximum stored energy, the energy quantum fluctuations and the maximum charging power on the number $N$ of the two-level systems…
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 …
Quantum advantage unlocked: Charging quantum batteries with K-regular graph stabilizers
Harish-Chandra Research Institute（哈立什-昌德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Mark Kac Complex Systems Research Center, Jagiellonian University in Kraków（雅盖隆大学马克·卡克复杂系统研究中心）；Dipartimento di Fisica e Astronomia, Università di Padova（帕多瓦大学物理与天文学系）；Department of Physics, Indian Institute of Technology Palakkad（印度理工学院帕拉卡德分校物理系）
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 …
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…
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…
Quantum battery works as a micro- or nano-device to store and redistribute energy at the quantum level. Here we propose a spin-charger protocol, in which the battery cells are charged by a finite number of spins through a general Heisenberg XY interaction. Under the isotropic interaction, the spin-charger protocol is endowed with a higher capacity in terms of the maximum stored energy than the conventional protocols, where the battery is charged by a continuous-variable system, e.g., a cavity mode. By tuning the charger size, a trade-off between the maximum stored energy and the average chargi…
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…
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…
The Su-Schrieffer-Heeger (SSH) model has recently received considerable attention in condensed matter because it describes a typical one-dimensional system with topological edge states. Here, we investigate SSH-based charging protocols of quantum batteries (QB) with N quantum cells. This SSH QB hopping interaction induced ground state splitting makes the different effects of the dimerize parameter to the QB in the different quantum phase region. In the non-splitting region, the dimerize parameter has little influence on the QB. Whereas the fully-splitting region, the dimerize parameter has a s…
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.
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…
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 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…
Collective dynamics versus entanglement in quantum battery performance
Bar-Ilan University（巴伊兰大学）；Indian Institute of Technology (Banaras Hindu University)（印度理工学院（贝拿勒斯印度教大学））；Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute（哈里什-钱德拉研究所，霍米·巴巴国立学院）
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…
To take quantum advantage of collective effects in many-body system, we design an elementary block for building multipartite quantum battery, which enables charging an atomic ensemble with optimal numbers in a common thermal bath. One achieves maximum free energy as the stored energy in the steady state, which is prior to each atom parallel charging independently. It ascribes to quantum collective effects in the ensemble of atoms induced by the competition between the coherent driving and decoherent dissipation. The corresponding thermodynamic efficiency of the energy storage is analyzed. The …
We investigate the performance of a quantum battery exposed to local Markovian and non-Markovian dephasing noises. The battery is initially prepared as the ground state of a one-dimensional transverse $XY$ model with open boundary condition and is charged (discharged) via interactions with local bosonic reservoirs. We show that in the transient regime, quantum battery (QB) can store energy faster and has a higher maximum extractable work, quantified via ergotropy, when it is affected by local phase-flip or bit-flip Markovian noise compared to the case when there is no noise in the system. In b…
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 …
Dual-use quantum hardware for quantum resource generation and energy storage
Smalley-Curl Institute, Rice University（斯莫利-柯尔研究所，莱斯大学）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文学系）；Extreme Quantum Materials Alliance, Rice University（极端量子材料联盟，莱斯大学）
