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Journal of Physics Conference Series

Charger-Mediated Energy Transfer for Quantum Battery With Constant Time Dependent Step Function and Open System Approach

Putu Gede Agus Krisna Yogantara, Freddy Permana Zen

Published Mar 1, 2024• 1 citation
Publisher

Abstract

Abstract The energy charging of quantum battery is analysed by open quantum approach. The modelled of the charger and battery are described by harmonic oscillator model. We choose this model because the harmonic oscillator battery gives the largest maximum energy albeit having the longest maximum time. In this paper, the interaction as actual quantum system whose dynamic is determined by Lindblad Master Equation in terms of constant is a step function to set the time when energy flow and what time that energy stop to flow or the interaction between charger and battery has stopped. The energy equation was determined by solving the master equation with second order differential equation to find the first momenta from charger and battery. Based on the equation, the energy of charger will not be zero which mean after interaction in several times, the charger will not one hundred percent lose its energy when the energy storage in battery already done.

DOI
10.1088/1742-6596/2734/1/012070

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Abstract The energy charging of quantum battery is analysed by open quantum approach. The modelled of the charger and battery are described by harmonic oscillator model. We choose this model because the harmonic oscillator battery gives the largest maximum energy albeit having the longest maximum time. In this paper, the interaction as actual quantum system whose dynamic is determined by Lindblad Master Equation in terms of constant is a step function to set the time when energy flow and what time that energy stop to flow or the interaction between charger and battery has stopped. The energy equation was determined by solving the master equation with second order differential equation to find the first momenta from charger and battery. Based on the equation, the energy of charger will not be zero which mean after interaction in several times, the charger will not one hundred percent lose its energy when the energy storage in battery already done.
Abstract Quantum batteries are designed to outperform classical batteries by utilizing quantum effects, particularly in charging speed and energy storage efficiency. Quantum batteries based on chargers that interact periodically with an external energy source are analyzed within an open quantum system framework, with battery performance parameters such as charging time and total energy utilized for evaluation. In this paper, the charger and quantum battery are modeled as a quantum harmonic oscillator, and their interaction is governed by the Lindblad master equation. The energy function of the quantum battery is determined by the first momenta obtained by solving a system of coupled first-order linear differential equations formed from the master equation. Based on these results, we investigate the effect of periodic driving on energy charging, energy stability, and decoherence effects in the quantum battery.
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.
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.