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arXiv:2205.05018 · Physical Review A

Catalysis in charging quantum batteries

Ricard Ravell Rodríguez, B. Ahmadi, Paweł Mazurek, Shabir Barzanjeh, Robert Alicki, Paweł Horodecki

Published Apr 17, 2023• 59 citations
arXivHTMLPDF

Abstract

We propose an approach for the optimization of the charging of harmonic oscillators (quantum batteries) coupled to a harmonic oscillator (charger), driven by a laser field. We demonstrate that energy transfer limitations can be significantly mitigated in the presence of catalyst systems, mediating between the charger and quantum batteries. We show that these catalyst systems, either qubits or harmonic oscillators, enhance the amount of energy transferred to quantum batteries, while they themselves store almost no energy. It eliminates the need for optimizing the frequency of the charging laser field whose optimal value in the bare setting depends on the coupling strengths between the charger and the batteries.

DOI
10.1103/physreva.107.042419

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We propose an approach for the optimization of the charging of harmonic oscillators (quantum batteries) coupled to a harmonic oscillator (charger), driven by a laser field. We demonstrate that energy transfer limitations can be significantly mitigated in the presence of catalyst systems, mediating between the charger and quantum batteries. We show that these catalyst systems, either qubits or harmonic oscillators, enhance the amount of energy transferred to quantum batteries, while they themselves store almost no energy. It eliminates the need for optimizing the frequency of the charging laser field whose optimal value in the bare setting depends on the coupling strengths between the charger and the batteries.
We investigate the optimal charging processes for several models of quantum batteries, finding how to maximize the energy stored in a given battery with a finite-time modulation of a set of external fields. We approach the problem using advanced tools of optimal control theory, highlighting the universality of some features of the optimal solutions, for instance the emergence of the well-known bang-bang behavior of time-dependent external fields. The technique presented here is general, and we apply it to specific cases in which the energy is either pumped into the battery by external forces (direct charging) or transferred into it from an external charger (mediated charging). In this paper we focus on particular systems that consist of coupled qubits and harmonic oscillators, for which the optimal charging problem can be explicitly solved using a combined analytical-numerical approach based on our optimal control techniques. However, our approach can be applied to more complex setups, thus fostering the study of many-body effects in the charging process.
Quantum batteries are quantum systems that potentially serve as fuel for other quantum devices by receiving and supplying energy. In this Letter, we investigate the charging processes of a state-of-the-art quantum battery made of a harmonic oscillator, which can store infinite amounts of energy in principle. We experimentally simulate the charging process using a high-dimensional photonic quantum system with multiple concatenated interferometers. Our experiments demonstrate that both the stored and extractable energy of the quantum battery can be significantly improved by introducing a catalyst system. This charging protocol has the same performance as optimized the frequency of the external field in the direct charging protocol but is more convenient without the requirement of probing the global frequency of the charge-battery system. From the viewpoint of experimental innovation, we propose a general method to deterministically implement an arbitrary trace-preserving nonunitary channel and realize it experimentally. Our work shows the potential of this interesting quantum battery and sheds light on experimental investigations of quantum batteries.
Coherent energy backflow and non-Markovian oscillations limit energy retention and degrade extractable work (ergotropy) in open many-body quantum batteries. Here, we present a catalyst-mediated charging protocol for a collective spin-array quantum battery coupled to a laser-driven charger. Using the open-system Lindblad master equation, we examine the energy transfer dynamics when both charger and battery are symmetrically coupled to an off-resonant auxiliary catalytic mode. Numerical simulations reveal that while unassisted bipartite setups exhibit pronounced backflow oscillations and poor energy retention, catalytic mediation quenches transient oscillations and accelerates energy injection. The auxiliary system operates as an energy-invariant conduit, maintaining a constant energy expectation value ⟨HC(t)⟩≈⟨HC(0)⟩\langle H_C(t)\rangle \approx \langle H_C(0)\rangle⟨HC​(t)⟩≈⟨HC​(0)⟩ and negligible transient population throughout the evolution. Microscopically, virtual excitations of the catalyst generate an effective complex inter-subsystem coupling JeffJ_{\text{eff}}Jeff​, which induces an underdamped-to-overdamped dynamical crossover and introduces selective coherence damping. This mechanism prevents population depletion in the battery, stabilizing the population inversion and significantly increasing the asymptotic steady-state ergotropy with increasing battery size NBN_BNB​. These findings clarify the dissipative dynamics of catalyst-mediated energy transfer and provide a practical scheme for improving storage stability in modern quantum hardware platforms.
We present a systematic analysis and classification of several models of quantum batteries involving different combinations of two-level systems and quantum harmonic oscillators. In particular, we study energy-transfer processes from a given quantum system, termed a ``charger,'' to another one, i.e., the proper ``battery.'' In this setting, we analyze different figures of merit, including the charging time, the maximum energy transfer, and the average charging power. The role of coupling Hamiltonians which do not preserve the number of local excitations in the charger-battery system is clarified by properly accounting for them in the global energy balance of the model.
We analyze the performance of a quantum battery in terms of energy storage and energy extraction, assisted by nonlinearities in a charger-battery system utilizing an open-system approach. In particular, we consider two types of nonlinearities in the system, viz. nonlinearity in the coupling between battery and charger, and the charger itself comprising an anharmonic oscillator. In both these scenarios, the charger is connected to an environment, and is driven by an external laser source. We derive the Markovian master equation for the dynamics of the combined charger-battery system in presence of the environment. When the charger is non-linearly coupled to a battery, we find an enhancement in the steady state ergotropy over the linearly-coupled case. We further see that the times at which steady state and maximum ergotopies are attained get decreased in presence of non-linear coupling. We also identify instances where no ergotropy is obtained in the linear case, but can be obtained in presence of any non-zero value of nonlinearity. We additionally find a complementarity between the non-linear interaction strength and the coherent-drive strength in the steady-state ergotropy values, i.e. the same ergotropy as that obtained using weak nonlinearity and strong coherent drive can be obtained utilizing an opposite order of their values. In case when the charger is modeled as a multi-level transmon with an inherent anharmonicity, we find an advantage in maximum ergotropy values over the harmonic instance. Unlike the non-linearly coupled batteries, the ones mediated by an anharmonic charger prove to be useful in the transient regime. We also determine values of the coherent drive for which the anharmonic battery is beneficial over the harmonic one at all timescales. Further, we observe a distinct region of the anharmonic strength and coherent drive where ergotropy values reach their maxima.
Abstract This study investigates the performance of a three-level quantum battery model, which aims to optimize the trade off between the high capacity of harmonic oscillators and the rapid charging of two-level systems. Utilizing a harmonic oscillator charger and a three-level holder, we analyze the impact of linear and quadratic driving protocols within an open quantum system framework. Our results show that linear driving yields a highly efficient charging process with an ergotropy to energy ratio near unity. On the other hands, the quadratic driving significantly enhances stored energy and peak charging power but introduces increased state mixedness that limits the extractable work. Furthermore, these findings highlight the necessity of balancing coupling strengths and driving nonlinearities to maximize the thermodynamic efficiency of the quantum battery.