Coherence-Enhanced Quantum Battery Charging with Ergotropy Stabilization

Abstract: Quantum batteries utilize nonclassical resources to achieve charging speed and energy storage performances that surpass classical thermodynamic limits. However, the practical realization of quantum batteries is often constrained by the inevitable environment-induced dissipation of both stored ergotropy and coherence. To actively counteract these losses, we propose a dual-channel coherence framework that exploits dark-state protection to stabilize ergotropy. We conduct, for the first time, an investigation of the synergistic interplay between internal charger coherence and reservoir squeezing, the latter acting as a source of external coherence. In the resource-efficient regime where charger and battery sizes are comparable, our study shows that internal charger coherence and reservoir squeezing jointly enhance the transient charging power. Crucially, initial charger coherence is the fundamental resource for maximizing and stabilizing steady-state ergotropy through dark-state protection. Our analysis reveals that these advantages are driven by the buildup of local battery coherence, which emerges from the integration of both internal and external coherence sources. These results offer a robust pathway for high-power, stabilized energy storage in quantum architectures.

• The paper demonstrates that dual-channel coherence injection, combining internal charger coherence and external reservoir squeezing, enhances steady-state ergotropy in quantum batteries.
• The methodology uses analytical and numerical models to reveal superradiant scaling and optimal phase alignment under dark-state protection for efficient charging.
• The study identifies trade-offs between transient charging power and long-term stability, offering practical, resource-efficient protocols for quantum battery design.

Dual-Channel Coherence Framework for Quantum Battery Charging

Summary of Objectives and Contributions

The paper "Coherence-Enhanced Quantum Battery Charging with Ergotropy Stabilization" (2605.17700) establishes a rigorous framework for actively counteracting environmental dissipation in quantum batteries (QBs) by leveraging coherence from both the internal charger and an externally engineered squeezed reservoir. The authors demonstrate analytically and numerically that the synergistic use of two distinct coherence channels fundamentally modifies charging dynamics and steady-state ergotropy, enabling high-performance, resource-efficient quantum batteries. The primary claims are that internal charger coherence is indispensable for robust steady-state ergotropy under dark-state protection, while reservoir squeezing acts as a catalytic external coherence channel accelerating transient charging power.

Ergotropy, Coherence, and Resource Decomposition

The operational figure of merit is ergotropy—the maximum extractable work from a quantum state via cyclic unitary operations. The authors provide a formal decomposition: ergotropy comprises an incoherent, population-driven component and a purely coherent component. The latter is quantified via the $\ell_1$ norm of coherence, emphasizing the centrality of quantum coherence as a resource in battery charging protocols.

A fundamental challenge is environmental decoherence, which rapidly depletes both population inversion and quantum coherence, resulting in diminished ergotropy in practical, open-system QBs. Previous approaches for stabilization, such as encoding into decoherence-free subspaces or measurement-based feedback, incur prohibitive resource costs or operational trade-offs. This work circumvents such limitations via passive stabilization built on dark-state protection: the use of collective coupling to a shared reservoir, ensuring dissipative immunity for certain state manifolds.

Physical Model and Dual-Source Coherence Injection

The charger and battery are modeled as separate spin domains, each comprised of $N_C$ and $N_B$ spin-1/2 particles. Collective spin-coherent states serve as the charge carriers; such states are experimentally accessible across platforms (Cavity QED, BECs, NMR, NV centers). The shared reservoir is prepared as a squeezed vacuum generated from common microwave-domain hardware (e.g., Josephson or parametric amplifiers).

The dual-channel protocol comprises (1) internal coherence introduced via the charger's spin-coherent state (parameterized by a Bloch polar angle $\theta$ and azimuthal phase $\phi$) and (2) external coherence supplied by the squeezed vacuum reservoir (parameterized by squeezing strength $r$ and phase $\psi$). The resultant system is governed by a generalized Lindblad master equation where both population and coherence dynamics respond to the interplay of these injected resources. The critical control parameter is the relative alignment of internal and external coherence channels, characterized by the phase $\delta = \psi - 2\phi$.

Analytical and Numerical Results: Steady-State and Dynamical Charging

Minimal Two-Spin Limit

For $N_C = N_B = 1$, the steady-state solution under the dark-state condition yields two protected stationary configurations. Ergotropy here is entirely coherence-driven; population inversion does not arise due to the absence of inversion in the stationary population. Analytical expressions reveal that ergotropy is strictly non-negative only with finite charger coherence ($\theta > 0$) and is maximized with optimal phase alignment ($N_C$0). Squeezing alone, without internal charger coherence, cannot generate local battery coherence necessary for work extraction.

Multi-Spin Scaling and Collective Advantage

Extending to $N_C$1, the architecture demonstrates collective enhancement. The presence of dark-state cross-terms enables the buildup of local battery coherence, fundamentally absent in the single-spin regime. The ergotropy per spin exhibits non-monotonic dependence on charger coherence ($N_C$2): increased coherence enhances coherent ergotropy but reduces initial population energy, yielding an optimal trade-off. The relative phase condition ($N_C$3) remains universally optimal for total ergotropy across all system sizes. Numerical simulations confirm a quadratic (superradiant) scaling of maximum charging power with system size ($N_C$4), even in the comparable-size, resource-efficient regime.

Squeezing confers significant transient power advantage but its effect on steady-state ergotropy diminishes with system scaling. Internal charger coherence remains the dominant steady-state resource.

Entanglement Effects

The analysis examines the battery-charger entanglement using logarithmic negativity. Strong subsystem entanglement competes with local battery purity and suppresses extractable ergotropy, redistributing quantum resources into nonlocal correlations. The quantum advantage in this passive stabilization framework is thus more closely tied to locally-generated coherence than bipartite entanglement.

Time-Resolved Dynamics and Charging Power Optimization

Time evolution of ergotropy and local coherence reveals that both initial charger coherence and reservoir squeezing independently accelerate early-time charging. Their combination yields the fastest and largest transient build-up. Squeezing induces rapid but ultimately decaying coherence; only internal charger coherence stabilizes finite steady-state ergotropy under dark-state protection.

The maximum ergotropy charging power increases monotonically with squeezing strength $N_C$5, but its dependence on charger preparation is nonmonotonic; optimal values exist for coherent trade-off parameters. Superradiant scaling persists in both energy and ergotropy charging power, demonstrating collective quantum advantage.

Resource-Efficient Protocols and Experimental Considerations

A finite-time squeezing protocol is proposed: the squeezed reservoir operates briefly as a catalyst for battery coherence generation, then is quenched to vacuum, yielding substantial transient enhancement with low persistent resource cost. This protocol achieves rapid charging dynamics while avoiding continuous squeezing expense—a crucial consideration for scaling real-world QBs.

Both spin-coherent charger preparation and squeezed-vacuum reservoir engineering are achievable in diverse platforms, supporting near-term experimental implementation.

Implications and Outlook

The coherence-driven charging framework outlined establishes an experimentally feasible route to stabilized, high-power quantum batteries in open systems. The hierarchy of quantum resources is clarified: internal charger coherence is essential for robust steady-state performance, while reservoir squeezing amplifies power in transient regimes. The results suggest that combining these resources preserves collective quantum advantages, such as superradiant scaling, while minimizing resource overhead.

These findings indicate practical strategies for resource-efficient quantum battery design, inform future developments in quantum thermodynamics, and open avenues for dissipative generation of metrologically relevant states beyond battery applications, including quantum sensing platforms.

Conclusion

This study rigorously demonstrates that quantum batteries operating in the comparable-size regime can attain enhanced, stabilized ergotropy through dual-channel coherence injection under dark-state protection. Internal charger coherence is identified as the fundamental resource for maximizing and stabilizing steady-state work extraction, while external reservoir squeezing provides a catalytic channel for fast transient charging. These results establish a clear quantum resource hierarchy and support practical, scalable control protocols for energy storage in quantum architectures. Experimentally, coherence-assisted quantum batteries are viable across a wide range of platforms, promising further advances in quantum energy storage and related collective-spin technologies.