A continuous variable quantum battery with wireless and remote charging

TL;DR

This work proposes a wireless, remote charging scheme for a continuous-variable quantum battery built from two coupled LC circuits and analyzes the charging dynamics across closed and open (Markovian) regimes. It demonstrates that quantum coherence, not entanglement, primarily enables ergotropy in several scenarios, and that nonzero ergotropy can be achieved even when the charger starts in a thermal state provided both rotating- and counter-rotating-wave couplings are present, yielding beat dynamics and parameter-dependent maxima. The study derives analytical and numerical results for energy components, ergotropy, and coherence, outlining regimes where coherence sustains ergotropy despite dissipation and offering practical experimental guidance for realizing long-range wireless charging. The findings indicate that the proposed continuous-variable battery can achieve substantial extractable work and extended charging distances relative to qubit-based schemes, with explicit design parameters for LC circuits and geometry.

Abstract

Quantum battery has become one of the hot issues at the research frontiers of quantum physics recently. Charging power, extractable work and wireless charging over long-distance are three important aspects of interest. Non-contact electromagnetic interaction provides an important avenue for wireless charging. In this paper, we design a wireless and remote charging scheme based on the quantized Hamiltonian of two coupled LC circuits, and focus on the charging dynamics of a continuous variable quantum battery. It is found that the quantum entanglement, which is regarded as a significant quantum resource, is not a prerequisite for charging the battery and extracting useful work. On the contrary, all of the energy in the battery could be converted into useful work in the absence of the entanglement for our model. The often overlooked counter-rotating wave coupling in the interacting Hamiltonian is helpful for extracting more useful work from the charger. If the coupling between the battery and the charger is designed to contain both the rotating and counter-rotating wave couplings, the extractable work can be obtained even if the charger is prepared in thermal states, while such effect cannot be achieved in the presence of a rotating or counter-rotating wave coupling alone. Finally, the effect of the system's parameters on the extractable work is discussed, which will provide a reference for full use of the thermal state energy.

Figures (6)

• Figure 1: (Color online) Scheme of a continuous variable quantum battery with wireless and remote charging based on two coupled LC circuits. $L_{1,2}$$(C_{1,2})$ denote the inductances (capacitances) of the two LC circuits. The $L_{m}$$(C_{m})$ is the coupling inductance (capacitance) between the circuits. The coupling strength is determined by the relative position and distance of the inductors and capacitors.
• Figure 2: (Color online) Change of the physical quantities with time for the closed system. (a, c) demonstrate the dynamics of $E_{e}(t)$, $E_{i}(t)$ and $E_{1}(t)$, while (b, d) give the dynamics of $S(t)$, $R(t)$ and $C(t)$. The system contains only the rotating wave coupling for $k_{L}=k_{C}=0.7$ in (a) and (b) and only the counter-rotating wave coupling for $k_{L}=-k_{C}=-0.7$ in (c) and (d). The coherent state $\hat{\varrho}_{1}(0)=\left\vert \alpha \right\rangle\left\langle\alpha\right\vert$ with $\alpha=2$ is chosen as the initial state of the charger and $\omega _{2}=1.3\omega _{1}$.
• Figure 3: (Color online) (a) Dynamics of $E_{e}(t)$, $E_{i}(t)$ and $E_{1}(t)$; (b) Dynamics of $R(t)$ and $C(t)$. The thermal state with an average thermal photon number $n_{p}=4$ is chosen as the initial state of the charger. The other parameters are $\omega _{2}=1.3\omega_{1}$, $k_{L}=-0.57$ and $k_{C}=0.7$.
• Figure 4: (Color online) Max$[E_{e}(t)]$ varies with $k_{L}$ and $k_{C}$ in (a), while Max$[R(t)]$ varies with $k_{L}$ and $k_{C}$ in (b). The thermal state with an average thermal photon number $n_{p}=4$ is chosen as the initial state of the charger. The other parameters are $\omega _{1}t\in \lbrack 0,20]$ and $\omega_{2}=1.3\omega_{1}$.
• Figure 5: (Color online) Change of Max$[E_{e}(t)]$ in (a) and Max$[R(t)]$ in (b) vary with the average thermal photon number $n_{p}$ at $\omega_{1}t\in \lbrack 0,20]$. The thermal state is chosen as the initial state of the charger. The other parameters are $\omega_{2}=1.3\omega_{1}$, $k_{L}=-0.37$ and $k_{C}=0.7$.