Boosting the Performance of a Lipkin-Meshkov-Glick Quantum Battery via Symmetry-Breaking Quenches and Bosonic Baths

Abstract

We explore the operation of quantum batteries in the Lipkin-Meshkov-Glick (LMG) model, when they are charged either through a sudden quench in the magnetic field strength or by coupling them to a bosonic oscillator bath. Through initializing the battery in either the symmetric or broken symmetry phases of the LMG model we analyze how the different spectral properties can affect the performance of both the charging and discharging of the battery. In particular, we show that by quenching the magnetic field strength from the symmetric phase to the broken phase, we can achieve a significant enhancement in stored energy, as well as stable and efficient ergotropy extraction. Similar observations can be made when introducing weak coupling between the battery with the bosonic bath, while the amount of stored work and ergotropy saturate at strong coupling. These findings emphasize the importance of the magnetic field dynamics and environmental coupling in optimizing charging performance, which could lead to practical applications in quantum energy storage.

Figures (9)

• Figure 1: An LMG-based QB featuring full-range interactions between spin-1/2 particles. The charging process is employed through (1) sudden quenching of the external magnetic field, (2) coupling to a bosonic oscillator environment.
• Figure 2: (a) Energy gap between the ground state and the first five excited states as a function of the magnetic field $h_{\rm i}$ for $N = 100$ particles in the anisotropic case $\gamma = 0$. (b) Phase diagram showing the boundary between the symmetric and broken phase, including cases of quenches within the same phase and across different phases. (c,d) Work probability distribution $\mathscr{P}(W)$ with different $h_{\rm c}$ for (c) $h_{\rm i} = 0.5$ and (d) $h_{\rm i} = 1.5$.
• Figure 3: Time evolution of the total stored work $\mathcal{W}(t)$ (a,e) and entropy (b,f). (c,d) Dependence of the maximum stored work, $\mathcal{W}_{\rm max}$, the long-time averaged work $\langle \mathcal{W} \rangle$ and its standard deviation ($\sqrt{\text{Var}(\mathcal{W})}$) on the quench parameter $h_{\rm c}$. (d,h) Variation of the peak power, $\mathcal{P}_{\rm max}$, and the optimal charging time, $t_{\rm opt}$, as functions of $h_{\rm c}$, illustrating contrasting dynamical behaviors. The first and second rows represent the initial state being in the broken phase ($h_{\rm i} = 0.5$) and the symmetric phase ($h_{\rm i} = 1.5$), respectively. The inset in panel (e) magnifies the interval $0 \leq t \leq 5$, highlighting short-time dynamics.
• Figure 4: The maximum ergotropy $\mathcal{E}_{\rm max}$ and the efficiency ratio $\mathcal{E}_{\rm max}/\mathcal{W}^M$ as a function of $h_{\rm c}$ for various values of $M$ (see the legends). Panels (a-b) show the results for $h_{\rm i} = 0.5$, whereas panels (c) and (d) illustrate those for $h_{\rm i} = 1.5$. Insets: zoom in from $h_{\rm c} = 0.3$ to 0.7. Numerically, we add a small offset $10^{-10}$ to $\mathcal{W}^M$ to avoid undefined values when $h_{\rm c} = h_{\rm i}$.
• Figure 5: Time evolution of the stored energy $\mathcal{W}(t)$, the average photon number $\langle n(t) \rangle$, the ergotropy $\mathcal{E}(t)$, and the ratio $\mathcal{E}(t)/\mathcal{W}(t)$, for two coupling strengths: $g = 0.25$ (left column) and $g = 2.0$ (right column).