Extractability of steady-state energy with one bound state

Determine whether a steady-state quantum battery energy can be made extractable when the coupled charger–battery system embedded in a three-dimensional anisotropic photonic-crystal environment supports exactly one system–environment bound state, including by increasing the atomic eigenfrequency and charger–battery coupling strength.

Background

The paper analyzes a quantum battery formed by one two-level atom coupled to a two-level-atom charger, with the charger interacting with a three-dimensional anisotropic photonic-crystal environment. The number of system–environment bound states determines the long-time battery behavior: no bound state leads to complete energy decay, one bound state produces persistent battery energy at a constant value, and two bound states produce persistent periodic energy oscillations.

For the single-bound-state regime during the charging process, the authors report that they have not found a steady-state battery whose stored energy is extractable, even after increasing the atomic eigenfrequency and the charger–battery coupling strength. They identify the two-bound-state regime as the preferred regime for long-term storage and extraction, leaving unresolved whether extractable steady-state energy is possible in the single-bound-state charging scenario.

References

However, we have not yet found a steady-state battery that can be extracted in the presence of a bound state, even with the increment of ${\omega _0}$ and $\kappa $.

— Bound-State Engineered Quantum Batteries Against Decoherence  (2609.17367 - Li et al., 15 Sep 2026) in Section 3.1, subsection “Steady-State Battery Energy and Ergotropy”