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arXiv:2103.07828 · Physical Review A

Lower and upper bounds of quantum battery power in multiple central spin systems

Li Peng, Wenbin He, Stefano Chesi, Hai‐Qing Lin, Xi-Wen Guan

Published May 28, 2021• 63 citations
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Abstract

We study the energy-transfer process in quantum battery systems consisting of multiple central spins and bath spins. Here with ``quantum battery'' we refer to the central spins, whereas the bath serves as the ``charger.'' For the single-central-spin battery, we analytically derive the time evolutions of the energy transfer and the charging power with arbitrary number of bath spins. For the case of multiple central spins in the battery, we find the scaling-law relation between the maximum power ${P}_{\mathrm{max}}$ and the number of central spins ${N}_{B}$. It approximately satisfies a scaling law relation ${P}_{\mathrm{max}}\ensuremath{\propto}{N}_{B}^{\ensuremath{\alpha}}$, where scaling exponent $\ensuremath{\alpha}$ varies with the bath spin number $N$ from the lower bound $\ensuremath{\alpha}=1/2$ to the upper bound $\ensuremath{\alpha}=3/2$. The lower and upper bounds correspond to the limits $N\ensuremath{\rightarrow}1$ and $N\ensuremath{\gg}{N}_{B}$, respectively. In thermodynamic limit, by applying the Holstein-Primakoff transformation, we rigorously prove that the upper bound is ${P}_{\mathrm{max}}=0.72BA\sqrt{N}{N}_{B}^{3/2}$, which shows the same advantage in scaling of a recent charging protocol based on the Tavis-Cummings model. Here $B$ and $A$ are the external magnetic field and coupling constant between the battery and the charger.

DOI
10.1103/physreva.103.052220

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Abstract In this paper, we study the performance of a quantum battery composed of three non-interacting central qubits, which are charged through interactions with three distinct thermal baths, each bath consisting of interacting qubits. We utilize the Holstein-Primakoff transformation and thermodynamic limits to map the collective spin operators of the baths to bosonic modes. Additionally, we employ the finite trio coherent state as the initial state for the charging process to explore its impact on the overall system performance. The study focuses on evaluating the stored energy efficiency and the entropy of the charger modes to assess the overall charging performance. By examining the system parameters such as anisotropy, dimension and shift parameters, and the intensity of the trio coherent state, the optimal conditions for efficient energy storage are identified. Our results provided the role of thermodynamic processes and quantum correlations in enhancing the performance of our quantum battery model.
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