Loss-induced nonreciprocal quantum battery

Abstract: Nonreciprocal quantum batteries offer superior charging performance compared to reciprocal quantum batteries. We consider a charger-battery system comprising two optical cavities that interact independently with a third auxiliary cavity. We show that the nonzero dissipation of the auxiliary cavity induces a nonreciprocal exchange of excitations among the charger-battery system. Therefore, by engineering the loss in the auxiliary cavity, we induce a directional energy flow that enhances the charging efficiency. Using numerical and analytical calculations, we show that the steady-state energy stored in the battery significantly exceeds that in the charger. We compare our results with those of the reciprocal cases and demonstrate that our nonreciprocal quantum battery model exhibits a significant charging advantage. We believe that our proposed scheme represents a step forward in cavity-loss engineering, making it a viable approach for nonreciprocal quantum batteries with existing experimental techniques.

• The paper introduces a quantum battery model with three coupled cavities that achieves up to fourfold energy storage advantage via loss-induced nonreciprocity.
• The paper employs analytical and numerical simulations, including QuTiP, to demonstrate that controlled dissipation in an auxiliary cavity creates a directional energy flow.
• The paper shows that optimizing coherent coupling strengths and phase parameters significantly enhances energy transfer, offering scalable pathways for experimental realization.

Loss-Induced Nonreciprocal Quantum Battery: A Technical Perspective

Context and Motivation

Quantum batteries (QBs) exploit non-classical features for energy storage, with performance metrics linked to quantum speedup, enhanced capacity, and robustness against dissipation. While collective and coherent effects in models such as the Dicke battery have been pursued, consistent quantum advantage remains elusive. Recent attention has shifted toward nonreciprocal energy transfer mechanisms, where engineered asymmetry in excitation transfer rates facilitates preferential charging. However, implementation challenges—such as the necessity for a shared dissipative reservoir—hinder practical realization of such schemes.

The work under review addresses these limitations by proposing a charger–battery setup using three coupled optical cavities, wherein nonreciprocity is generated via controlled loss in an auxiliary cavity, sidestepping the requirement for collective coupling to a common bath. This approach enables locality in loss engineering while inducing directional energy flow, thus enhancing the charging properties of the quantum battery.

Model and Framework

The system comprises three single-mode bosonic cavities, labeled as charger (â), battery (ĉ), and auxiliary cavity (b), all mutually coupled with coherent coupling strengths $J_{ab}$, $J_{bc}$, and $J_{ac}e^{i\theta}$. The charger is externally driven, with drive amplitude $\Omega$ and detuning $\Delta$. The Hamiltonian is described in the rotating frame:

$$\hat{H} = \sum_{j=a,b,c} \omega_j \hat{j}^\dagger \hat{j} + (J_{ab} \hat{a}^\dagger \hat{b} + J_{bc} \hat{b}^\dagger \hat{c} + J_{ac}e^{i\theta} \hat{a}^\dagger \hat{c} + \text{H.c.}) + \Omega (\hat{a} + \hat{a}^\dagger)$$

Dissipation for each cavity is governed by decay rates $\kappa_a$, $\kappa_b$, and $\kappa_c$, with the master equation formulated in Lindblad form. Crucially, only the auxiliary cavity (b) is engineered for significant loss, introducing a directional energy current.

Nonreciprocity is characterized via the energy transfer gain $$\eta = \langle \hat{c}^\dagger \hat{c} \rangle / \langle \hat{a}^\dagger \hat{a} \rangle$$, a primary performance figure. Analytical steady-state solutions show that for $J_{bc}$0, $J_{bc}$1 emerges—signifying preferential energy accumulation in the battery cavity as compared to the charger.

Principal Results

The study reports both analytical and numerically-simulated results (with QuTiP) for time-dependent and steady-state energy storage and transfer metrics. The key findings are:

• Nonreciprocal Charging Performance: With optimized auxiliary cavity dissipation and coupling phase $J_{bc}$2, energy stored in the battery at steady state can exceed that in the charger by a factor approaching 4 for the three-cavity system. This transfer gain is unattainable in reciprocal setups, which otherwise converge to energy equipartition ($J_{bc}$3) between charger and battery.
• Comparison to Reciprocal Schemes: When benchmarked against both the equivalent reciprocal three-cavity battery (setting $J_{bc}$4) and a conventional two-cavity configuration (auxiliary cavity absent), the proposed nonreciprocal battery demonstrates a charging advantage by factors up to approximately fourfold and eightfold, respectively—substantiating the efficacy of loss-induced nonreciprocity.
• Parameter Dependence and Optimization: Charging enhancement achieves maximality at optimal values of the coherent coupling $J_{bc}$5 and controllable phase $J_{bc}$6. Beyond this regime, excessive $J_{bc}$7 diminishes the gain due to the inability of the dissipative path to suppress energy backflow, as analytically captured by the derived transfer gain expression. The energy advantage is robust across a broad range of system parameters, including cavity decay rates and coupling strengths.
• Physical Mechanism: Nonreciprocity arises from engineered destructive interference between direct ($J_{bc}$8) and indirect ($J_{bc}$9) energy transmission channels, where dissipation in the auxiliary cavity introduces an additional phase that suppresses backflow and thus establishes energy current directionality.

Implications and Future Perspectives

This work demonstrates that local loss engineering in auxiliary elements of coherent quantum systems offers a powerful strategy for inducing nonreciprocal energy dynamics. The findings suggest several broader implications:

• Scalability and Experimental Viability: The architecture is compatible with state-of-the-art cavity or circuit QED platforms, where cavity losses can be tuned with high precision (e.g., via nanofiber tips as absorbers). This facilitates experimental exploration of nonreciprocal quantum energy devices without reliance on collective dissipative channels.
• Theoretical Impact: By decoupling nonreciprocal behavior from the requirement of a shared reservoir, the proposed approach generalizes the class of quantum battery models with tunable, robust directional energy transfer. The framework provides a basis for further investigations into the interplay between coherence, dissipation, and non-Hermitian phenomena in quantum thermodynamics.
• Extensions and Open Problems: The model presumes Markovian dynamics, ensuring that the stored energy (ergotropy) is entirely extractable. Future directions may address non-Markovian environments, energy extraction protocols, and integration with solid-state architectures. Further, exploring scalability to networks or arrays, and tailoring auxiliary cavity spectral properties, could enable new regimes of performance and functionality.
• Quantum Information Processing: The ability to direct and localize energy in quantum devices without backflow may have implications for quantum communication and device initialization, serving as foundational elements for on-chip energy management in quantum circuits.

Conclusion

The presented study establishes a realistic and analytically tractable model for loss-induced nonreciprocal quantum batteries, confirming a significant and tunable charging advantage over conventional reciprocal architectures. The approach's compatibility with current experimental technology and its robust performance across relevant parameters highlight its immediate relevance for advancing quantum energy storage protocols. By leveraging engineered dissipation, the results open a pathway for further theoretical and practical advancements in nonreciprocal quantum thermodynamic devices.