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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.10415 |
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| _version_ | 1866918391643635712 |
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| author | Jad, Anass Allati, Abderrahim El |
| author_facet | Jad, Anass Allati, Abderrahim El |
| contents | 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 $ε$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10415 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tight Quantum Speed Limit for Ergotropy Charging in the N-Qubit Dicke Battery Jad, Anass Allati, Abderrahim El Quantum Physics Mathematical Physics 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 $ε$. |
| title | Tight Quantum Speed Limit for Ergotropy Charging in the N-Qubit Dicke Battery |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2603.10415 |