The Tight Charging

Quantum batteries — quantum systems charged by unitary operations to store extractable work (ergotropy) — exhibit collective speedups when N qubits interact through a common bosonic mode (Dicke model). But how fast can charging proceed? Quantum speed limits bound the minimum time, but generic bounds are loose.

The tight bound collapses to a single parameter (arXiv:2603.10415). The composite quantity Γ_N = 2λ√(n̄/N) — coupling strength times root of photon-to-qubit ratio — uniquely governs charging speed. All protocols satisfy Γ_N · τ ≥ √ε, tight to within 1%. The collective enhancement scales as √N, not linearly.

The structural observation: the optimization landscape, which could have depended on coupling strength, photon number, qubit count, and protocol details independently, collapses to one dimensionless number. This is a universality result: the speed limit doesn’t depend on how you charge, only on Γ_N. The √N scaling (not linear N) means the superradiant advantage is real but sublinear — the battery charges faster collectively, but not as fast as naive counting would suggest. The single-parameter collapse means there are no clever protocols that beat the bound; the physics is fully characterized by one number.