Tight Quantum Speed Limit for Ergotropy Charging in the N-Qubit Dicke Battery

• URL: http://arxiv.org/abs/2603.10415v2
• Date: Tue, 17 Mar 2026 01:37:30 GMT
• Title: Tight Quantum Speed Limit for Ergotropy Charging in the N-Qubit Dicke Battery
• Abstract summary: We derive and analytically prove a tight quantum speed limit (QSL) for ergotropy charging in the $N$-qubit Dicke quantum battery.<n>All protocols collapse onto $_N * geq sqrt$, with the bound saturated to within 1% at small $$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive and analytically prove a tight quantum speed limit (QSL) for ergotropy charging in the $N$-qubit Dicke quantum battery: the first-passage time to normalised ergotropy $ε$ satisfies $τ^{*}(ε) \geq \sqrt{Nε}/(2λ\sqrt{\bar{n}})$, where $λ$ is the coupling and $\bar{n}$ is the mean charger photon number. The bound follows from an exact perturbative identity $ε(t) = Aλ^2\bar{n}t^2 + \mathcal{O}((λt)^4)$, where $A=4/N$ is the short-time ergotropy coefficient, combined with a global upper bound proved analytically for all $N$. The composite parameter $Γ_N = 2λ\sqrt{\bar{n}/N}$ is the unique figure of merit for charging speed; all protocols collapse onto $Γ_N τ^{*} \geq \sqrtε$, with the bound saturated to within 1% at small $ε$.

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