Reservoir-Engineered Exceptional Points for Quantum Energy Storage

TL;DR

This work addresses fast, robust quantum energy storage by realizing exceptional-point physics in a fully passive open quantum system through reservoir engineering. A charger and a battery are coupled via a dissipative auxiliary mode that induces an effective complex interaction in the system's drift dynamics, enabling spectral coalescence without gain. Two dynamical regimes emerge: a stable phase with energy saturation and a broken phase with exponential energy growth under a bounded drive, offering rapid charging without external amplification. The approach is compatible with optomechanical, superconducting, and magnonic platforms, providing a practical route to scalable quantum batteries and broader implications for dissipative control in quantum thermodynamics.

Abstract

Exceptional points are spectral singularities where both eigenvalues and eigenvectors collapse onto a single mode, causing the system behavior to shift abruptly and making it highly responsive to even small perturbations. Although widely studied in optical and quantum systems, using them for energy storage in quantum systems has been difficult because existing approaches rely on gain, precise balanced loss, or explicitly non-Hermitian Hamiltonians. Here we introduce a quantum energy-storage mechanism that realizes exceptional-point physics in a fully passive, physically consistent open quantum system. Instead of amplification, we use trace-preserving reservoir engineering to create an effective complex interaction between a charging mode and a storage mode through a dissipative mediator, generating an exceptional point directly in the drift matrix of the Heisenberg-Langevin equations while preserving complete positivity. The resulting dynamics exhibit two regimes: a stable phase where the stored energy saturates, and a broken phase where energy grows exponentially under a bounded coherent drive. This rapid charging arises from dissipative interference that greatly boosts energy flow between the modes without gain media or nonlinear amplification. The mechanism is compatible with optomechanical devices, superconducting circuits, and magnonic systems, offering a practical route to fast, robust, and scalable quantum energy-storage technologies and new directions in quantum thermodynamics.

Figures (6)

• Figure 1: Schematic of the dissipative quantum battery. A harmonic oscillator with resonance frequency $\omega_a$ and damping rate $\kappa_a$ serves as the charger and is driven by a classical field of frequency $\omega_L$ and amplitude $\mathcal{E}$, which supplies energy to the system. The charger interacts dissipatively with a second mode, the battery, characterized by resonance frequency $\omega_b$ and damping rate $\kappa_b$, where the injected energy is ultimately stored. Their interaction is mediated by an auxiliary dissipative mode $c$, defined by resonance frequency $\omega_c$ and damping rate $\kappa_c$. When the charger and the battery both couple to mode $c$ via two nonlocal reservoirs with coupling rate $\Gamma$, a purely dissipative interaction between them is induced. By adiabatically eliminating mode $c$, this configuration effectively engineers a reservoir that mediates the dissipative coupling between the two modes.
• Figure 2: (a) Real and (b) imaginary parts of the eigenvalues $\lambda_+$ (dashed blue) and $\lambda_-$ (solid black) of $\mathbb{H}_{r}$ displaced by $i\gamma_{b}$ as a function of $\delta_r$ for symmetric damping rates $\alpha = 0$. The red diamond at $\delta_{r}=\pm1$ indicates the exceptional point (EP) where the eigenvalues coalesce.
• Figure 3: (a)-(c) Phase diagrams illustrating $\Re[-i\lambda_+]$ in terms of $\delta_r$ and $\alpha\geq-\gamma_{b}/2$ for fixed (a) $\gamma_b=0.5$, (b) $\gamma_b=1.0$ and (c) $\gamma_b=1.5$. The black dashed line indicates the transition boundary between the unbroken ($\mathcal{PT}$-symmetric) phase and the broken ($\mathcal{PT}$-broken) phase, the purple star highlights this point for $\delta_r=0$. The red diamonds mark the Exceptional Points (EPs), where the eigenvalues coalesce. The blue, black, green, and orange markers represent specific parameter points for which the dynamics are plotted in panels below. (d)-(f) present the energy dynamics assuming $\delta_r=0$ and distinct values of $\alpha$. The purple filling indicates the region with exponential energy growth. (g)-(i) Normalized rate of energy change in the battery $P_B(t)$, showing exponential growth in the broken regime and a bounded rate that decays to zero in the unbroken regime as the system approaches steady state.
• Figure 4: Schematic representation of the charging process. The charger $a$ is externally pumped by a laser field with amplitude $\varepsilon$ and frequency $\omega_L$. The battery $b$ charging is then mediated by a dissipative auxiliary mode $c$, individually connected to $a$ and $b$ through shared reservoirs $R_{ac}$ and $R_{bc}$ with coupling rate $\Gamma$. Each element has a local damping rate $\kappa_{a/b/c}$. The strongly overdamped auxiliary mode leads to an effective dissipative interaction between the charger and the battery.
• Figure 5: (a)-(c) Real and (b)-(d) imaginary parts of the eigenvalues $\lambda_\pm$ displaced by $i\gamma_{b}$ as a function of $\delta_{r}=\delta/\Gamma_{\textrm{eff}}$ and the coefficient of asymmetry $\alpha:=(\gamma_{a}-\gamma_{b})/2$. The black line in (a) and (c) highlights the discontinuity in the real components.