Magnetic Dipolar Quantum Battery with Spin-Orbit Coupling

TL;DR

The paper investigates a magnetic dipolar two-spin system with Zeeman splitting, DM, and KSEA interactions as a quantum battery medium, analyzing quantum resources under Gibbs thermal states and Pauli-$X$ dephasing via the Lindblad framework. It demonstrates that Zeeman fields suppress quantum resources in noise yet enhance ergotropy, capacity, and coherence during cyclic charging, while axial anisotropy, DM, and KSEA interactions provide distinct routes to boost energy storage and coherence, with KSEA showing particularly strong collective-coherence effects. The work introduces a NOT-like charging protocol and a rigorous framework of ergotropy, anti-ergotropy, and capacity to quantify work extraction and storage, linking spectral properties to performance and revealing regimes where incoherent ergotropy dominates. The authors propose NMR as a viable platform for experimental realization, offering concrete pulse-sequence strategies and tomography approaches, and outline future directions toward larger spin systems and improved charging protocols for practical quantum energy storage applications.

Abstract

We investigate a magnetic dipolar system influenced by the $z$-component of Zeeman splitting, Dzyaloshinsky--Moriya (DM) interaction, and Kaplan--Shekhtman--Entin-Wohlman--Aharony (KSEA) exchange interaction, with emphasis on the role of quantum resources in both closed and open settings. By analyzing the Gibbs thermal state and solving the Lindblad master equation, we study the behavior of quantum coherence, discord, and entanglement under thermal equilibrium and dephasing noise. After exploring these resources, we apply the model to a closed quantum battery (QB). Our results show that while Zeeman splitting degrades quantum resources in noisy and thermal regimes, it enhances QB performance by improving ergotropy, anti-ergotropy, storage capacity, and coherence during cyclic charging. The axial parameter further amplifies performance, leading to coherence saturation and persistent ergotropy growth, in line with the notion of incoherent ergotropy. KSEA interaction and the rhombic term consistently preserve coherence and entanglement under noise, thereby strengthening QB functionality. DM interaction mitigates thermal degradation of resources in the Gibbs state and improves performance, though its effect is limited under Pauli-$X$ dephasing. We reveal diverse behaviors, including increased ergotropy without coherence and the coexistence of coherence with zero extractable work. Finally, we propose Nuclear Magnetic Resonance (NMR) as a feasible platform for experimental implementation.

Figures (11)

• Figure 1: (a) Non-interacting quantum cell-based QB with a global charging from a common cavity field. (b) Interacting quantum cell-based QB with a local charging field stored in each cavity, including cell interactions.
• Figure 2: Two magnetic dipoles with moments $\vec{\mu}_1$ and $\vec{\mu}_2$ in 3D space, separated by distance $\vec{r}$. A Zeeman field $B$ is applied along the $z$-axis, and a time-dependent field $\Omega(t)$ is applied along the $x$-axis to charge the dipolar spins for QB.
• Figure 3: Time evolution of quantum discord $\mathcal{D}(\hat{\varrho})$, concurrence $\mathcal{E}(\hat{\varrho})$, and $l_1$-norm of $\mathcal{C}(\hat{\varrho})$ for varying parameters. Panels ($a$-$c$) illustrate the dynamics for $\epsilon = 0.1$ ($a$), $\epsilon = 0.5$ ($b$), and $\epsilon = 10$ ($c$), with $D = G = B =\Delta = 0$. Panels ($d$-$f$) present the effects of varying $B$, with $B=0.1$ ($d$), $B=1.0$ ($e$), and $B=10$ ($f$), under $D = G = 0$, $\Delta = 1$, and $\epsilon = 0.5$. Panels ($g$-$i$) examine the influence of $D$, showing results for $D = 0.1$ ($g$), $D = 1.0$ ($h$), and $D = 10$ ($i$), with $B=0$, $G = 0$, $\Delta = 1$, and $\epsilon = 0.5$. Panels ($j$-$l$) show the influence of $G$, revealing results for $G = 0.1$ ($j$), $G = 1.0$ ($k$), and $G = 10$ ($l$), with $B=0$, $D = 0$, $\Delta = 1$, and $\epsilon = 0.5$. Finally, panels ($m$-$o$) depict the mentioned behavior under varying $\Delta$, with $\Delta = 0.1$ ($m$), $\Delta = 1.0$ ($n$), and $\Delta = 10$ ($o$), keeping $B= G = 0$ and $\epsilon = 0.1$. Fixed parameter is $\gamma = 0.2$.
• Figure 5: Temporal evolution of QB performance metrics. (a) Ergotropy $\xi(t/\omega)$, (b) anti-ergotropy $\mathcal{P}(t/\omega)$, (c) capacity $\mathcal{Q}(t/\omega)$, and (d) $l_1$-norm of quantum coherence $\mathcal{C}(t/\omega)$ versus $t/\omega$ for different axial anisotropy values: $\Delta/\omega = 1$ (gray), 2 (red), 4 (black), 6 (green), and 12 (blue). Parameters: $G = D = B = 0$, $\epsilon/ \omega=0.1$, and $T/\omega = 1$.
• Figure 6: Magnetic field dependence of QB performance metrics. (a) Ergotropy $\xi(t/\omega)$, (b) anti-ergotropy $\mathcal{P}(t/\omega)$, (c) capacity $\mathcal{Q}(t/\omega)$, and (d) $l_1$-norm of quantum coherence $\mathcal{C}(t/\omega)$ versus $t/\omega$ for different magnetic field strengths: $B/\omega = 0.0$ (black), $0.5$ (red), $1.0$ (green), $1.5$ (blue), and $2.0$ (magenta). Parameters: $G = D = 0$, $\Delta/\omega = 1$, $T/\omega = 0.5$, and $\epsilon/\omega = 0.1$.