Exact $1/4$ mean-rung population and $\sqrt{2}$ continuum revival-time ratio in the anti-Jaynes--Cummings vertex at $f_\star=\sqrt{\bar n+1}$

• URL: http://arxiv.org/abs/2609.14563v1
• Date: Sun, 13 Sep 2026 14:48:40 GMT
• Title: Exact $1/4$ mean-rung population and $\sqrt{2}$ continuum revival-time ratio in the anti-Jaynes--Cummings vertex at $f_\star=\sqrt{\bar n+1}$
• Abstract summary: We show that the mean-rung excited population of the AJC block equals exactly $1/4$ at $f_star=sqrtbar n+1$, while the JC population at the same point is $1/2$.<n>At $f_star$ the modulation of the AJC inversion is $1/2$ and the relative sensitivity of the revival-time ratio $r=t_Rrm AJC/t_Rrm JC$ is maximal with value $1/(2sqrtbar n+1)$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: At atomic resonance the Jaynes--Cummings (JC) vertex of a single bosonic mode coupled to a two-level emitter is blind to $f=ω/λ$ at zero detuning and Kerr; the anti-Jaynes--Cummings (AJC) vertex is not. We show that the mean-rung excited population of the AJC block equals exactly $1/4$ at $f_\star=\sqrt{\bar n+1}$, while the JC population at the same point is $1/2$. The Poisson-averaged packet value at $\bar n=16$ is $0.24650$, within $3.5\times 10^{-3}$ of the exact value, with the deviation reproduced by $-\bar n/[16(\bar n+1)^2]$. At $f_\star$ the modulation depth of the AJC inversion is $1/2$ and the relative sensitivity of the continuum revival-time ratio $r=t_R^{\rm AJC}/t_R^{\rm JC}$ is maximal with value $1/(2\sqrt{\bar n+1})$. Full diagonalization on $2(n_{\max}{+}1)$ states confirms the analytic values. The $1/4$ value can be generated by Floquet-engineered counter-rotating coupling provided that the static transverse rate satisfies $g_0\ll g_1$. Parameter translations for an ideal trapped-ion blue sideband and a flux-tunable circuit-QED coupler are reported.

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