Topological enhancement of a PT-symmetric Su-Schrieffer-Heeger quantum battery

TL;DR

We address how topology and non-Hermiticity can enhance charging in quantum batteries by studying a PT-symmetric SSH lattice with balanced gain and loss. The analysis reveals bulk and edge exceptional points, with an edge EP in the topological phase that triggers early PT-symmetry breaking and selective amplification of midgap states, boosting energy storage and speeding saturation. Quantitative metrics show the topological phase outperforms the trivial one across parameter regimes and system sizes, evidencing a genuine topological enhancement of charging dynamics. These results highlight topology as a physical resource for quantum energy storage and suggest experimental platforms in photonics, circuits, or cold-atom lattices to realize and test the predicted edge-induced benefits.

Abstract

We investigate a non-Hermitian quantum battery based on the Su-Schrieffer-Heeger (SSH) lattice, charged through a PT-symmetric protocol that alternates gain and loss between the two sublattices. The interplay between lattice topology and non-Hermiticity gives rise to both bulk and edge exceptional points (EPs), which govern the charging dynamics. In the topological regime, an edge-state EP emerges at an exponentially small non-Hermitian strength, resulting in early PT-symmetry breaking and rapid energy accumulation. This topological enhancement originates from the PT-symmetric non-Hermitian dynamics, in which the broken-symmetry edge mode with the largest imaginary part of the eigenvalue dominates the time evolution. Consequently, the topological phase consistently yields higher stored energy and faster saturation than the trivial configuration across all parameter regimes and system sizes. These findings demonstrate that topology constitutes a genuine physical resource for enhancing the performance of quantum batteries.

Figures (5)

• Figure 1: (a) SSH lattice with alternating couplings $J_{1}$ and $J_{2}$, serving as the basis for the $\mathcal{PT}$-symmetric SSH model with balanced gain and loss $\gamma$. (b) Bulk energy spectrum of the Hermitian SSH model. (c) Normalized energy spectrum, used to eliminate the trivial dependence on the overall energy scale and to enable consistent evaluation of charging performance.
• Figure 2: Spectral structure and phase diagram of the $\mathcal{PT}$-symmetric SSH model. (a,c) Real and imaginary parts of the eigenvalues in the topological phase ($J_{1}/J_{2}=0.5$); (b,d) corresponding spectra in the trivial phase ($J_{1}/J_{2}=1.5$). (e) Phase diagram in the $\gamma$--$J_{1}$ plane, showing unbroken, partially broken, and fully broken regimes. Dashed lines mark bulk thresholds $\gamma=|J_{1}\!\pm\!J_{2}|$ and the solid curve the edge EP $\gamma=\gamma_{e}$. The figures are generated with $N=6$.
• Figure 3: Time evolution of the stored energy $\Delta E(t)$ under different non-Hermitian parameters $\gamma$ and topological configurations. (a,b) Global maps of $\Delta E(t)$ for the topological ($J_{1}/J_{2}=0.5$) and trivial ($J_{1}/J_{2}=1.5$) phases, respectively. (c)--(f) Representative traces of $\Delta E(t)$ at $\gamma/J_{2}=0.01$, $0.45$, $1.0$, and $2.8$, corresponding to the unbroken, edge-state broken, partially broken, and fully broken $\mathcal{PT}$ regimes. Purple and red curves denote the topological and trivial phases, respectively. The topological phase exhibits faster energy growth and earlier saturation across all $\gamma$ values.
• Figure 4: Dependence of the charging performance on system parameters of the $\mathcal{PT}$-symmetric SSH quantum battery. (a) Amplitude of the first energy peak $\Delta E_{\mathrm{peak}}^{(1)}$ in the $\gamma$--$J_{1}$ plane. (b) Logarithmic saturation time $\log_{10}(t_{0.95})$ in the same parameter space. The phase boundaries $J_{1}=J_{2}$ and the $\mathcal{PT}$-symmetry-breaking thresholds $\gamma_{e}$, $|J_{1}-J_{2}|$, and $J_{1}+J_{2}$ are indicated for reference. (c) System-size dependence of $\Delta E_{\mathrm{peak}}^{(1)}$ for three representative values of the gain-loss strength $\gamma/J_{2}=0.45$, $1.0$, and $2.8$. (d) Corresponding system-size dependence of the saturation time, shown as $\log_{10}(t_{0.95})$. In panels (c) and (d), solid curves correspond to the topological configuration ($J_{1}/J_{2}=0.5$) and dashed curves correspond to the trivial configuration ($J_{1}/J_{2}=1.5$).
• Figure 5: Time-dependent populations of selected eigenstates $\phi_n$ of the SSH battery during $\mathcal{PT}$-symmetric charging. (a,e) Unbroken regime ($\gamma/J_{2}=0.01$); (b,f) edge-state broken regime ($\gamma/J_{2}=0.45$); (c,g) partially broken regime ($\gamma/J_{2}=1.0$); (d,h) fully broken regime ($\gamma/J_{2}=2.8$). Left and right panels correspond to the topological and trivial phases, respectively. The dominance of edge-related midgap states after the edge EP and the late-time flow toward central bulk modes in the fully broken regime are both consistent with growth-rate selection by $\operatorname{Im}E$.