Quantum Batteries in Coherent Ising Machine

TL;DR

This work proposes a quantum battery built from a degenerate optical parametric oscillator, storing energy in the signal field while the pump provides charging. By decomposing ergotropy into coherent and incoherent parts, it shows the coherent component is more robust to decoherence and dominates early charging, with both the maximum coherent ergotropy and peak charging power occurring near γ_s t ≈ 10, guiding the optimal switch-off time. The authors derive a master-equation description, reveal exponential growth of steady-state ergotropy with pump strength, and demonstrate efficient discharge by coupling to a two-level load, with discharge efficiency limited by the available ergotropy. Together, these results outline a realistic, implementable QB architecture on a mature DOPO platform with tunable charging and reliable discharging capabilities.

Abstract

With intensive studies of quantum thermodynamics, the quantum batteries (QBs) have been proposed to store and transfer energy via quantum effects. Despite many theoretical models, decoherence remains a severe challenge and practical platforms are still rare. Here we propose the QB based on the degenerate optical parametric oscillator (DOPO), using the signal field as the energy-storage unit. We carefully separate the ergotropy into coherent and incoherent components and find that the coherent part decays roughly half as slowly as the incoherent part. More importantly, the coherent ergotropy and the average charging power reach their respective maxima at essentially the same moment, i.e., $γ_s t \approx 10$. This coincidence defines the optimal instant to switch off the pump. Finally, coupling the QB to a two-level system (TLS) as the load, we demonstrate an efficient discharge process of the QB. Our work establishes a realistic and immediately-implementable QB architecture on a mature optical platform.

Figures (8)

• Figure 1: (a) Schematic of a DOPO-based QB. The entire process is divided into two stages, i.e., charging and discharging. During the charging stage, a pump field with frequency $\omega_{p}$ is applied to charge the QB. In the discharging stage, after the QB is connected to the load, e.g. an atom, the QB transfers its stored energy to the atom, driving it into its excited state. (b) Schematic of a DOPO. A pump field with frequency $\omega_{p}$ is injected into an optical cavity, where it interacts with a second-order nonlinear medium, i.e., $\chi^{(2)}$ crystal, via a three-wave mixing process, generating signal photons at frequency $\omega_{p}/2$. The signal field is in resonance with the cavity, while loss is also present in the system.
• Figure 2: (a) The ergotropy of the QB for different truncation of the signal field. The blue dotted line, red short dashed line, yellow long dashed line, pink solid line correspond to $N_{s}=24,\,28,\,32,\,36$ and $N_{p}=9$, respectively. (b) The ergotropy of the QB for different truncation of the signal field. The blue dotted line, red short dashed line, yellow long dashed line, pink solid line correspond to $N_{p}=3,\,5,\,7,\,9$ and $N_{s}=32$, respectively.
• Figure 3: (a) Time evolution of the QB's ergotropy under different $F_{p}$s, where the yellow dotted line, the pink short-dashed line, the green long-dashed line, the blue dash-dotted line, and the red solid line correspond to $F_{p}/\sqrt{\gamma_{s}} = 1.00,\, 1.50,\, 2.00,\, 2.50,$ and $3.00$, respectively. (b) The steady-state ergotropy $W_{ss}$ of the QB for different $F_{p}/\sqrt{\gamma_{s}}$ is fitted linearly as $\ln W_{ss} = -5.330 + 2.742\times F_{p}/\sqrt{\gamma_{s}}$, yielding a correlation coefficient of $|r| = 0.9974$.
• Figure 4: The time evolution of the ergotropy $W(t)$, and its coherent part $W^{c}(t)$, and its incoherent part $W^{i}(t)$. The pink solid line, red dotted line, and blue dashed line correspond to $W(t)$, $W^{c}(t)$, and $W^{i}(t)$, respectively.
• Figure 5: (a) Time evolution of the ergotropy $W(t)$, and its coherent part $W^{c}(t)$, and its incoherent part $W^{i}(t)$ when $F_{p}=0$ since $\gamma_{s}t=40$. The pink solid, red dotted, and blue dashed lines correspond to $W(t)$, $W^{c}(t)$, and $W^{i}(t)$, respectively. (b) $W^{c}(t)$ by the red circles ($W^{i}(t)$ by the blue squares) are linearly fitted by $\ln W^{c}(t)=-1.127\gamma_{s}t+47.17$ ($\ln W^{i}(t)=-2.082\gamma_{s}t+85.48$) with the correlation coefficient $|r^{c}|=0.9996$ ($|r^{i}|=0.9881$).