Exact 1/4 mean-rung population and √2 continuum revival-time ratio in the anti-Jaynes--Cummings vertex at f_⋆=√(n̅+1)

@misc{okeyo2026exact,
  title = {{Exact $1/4$ mean-rung population and $\sqrt2$ continuum revival-time ratio in the anti-Jaynes--Cummings vertex at $f_\star=\sqrt\bar n+1$}},
  author = {Onyango Stephen Okeyo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14563},
  eprint = {2609.14563},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14563},
}

TY  - UNPB
TI  - Exact 1/4 mean-rung population and √2 continuum revival-time ratio in the anti-Jaynes--Cummings vertex at f_⋆=√(n̅+1)
AU  - Onyango Stephen Okeyo
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14563
UR  - https://arxiv.org/abs/2609.14563
AB  - 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_⋆=√(n̅+1), while the JC population at the same point is 1/2. The Poisson-averaged packet value at n̅=16 is $0.24650$, within 3.5× 10^−3 of the exact value, with the deviation reproduced by −n̅/[16(n̅+1)^2]. At f_⋆ the modulation depth of the AJC inversion is 1/2 and the relative sensitivity of the continuum revival-time ratio r=t_R^AJC/t_R^JC is maximal with value 1/(2√(n̅+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≪ g_1. Parameter translations for an ideal trapped-ion blue sideband and a flux-tunable circuit-QED coupler are reported.
ER  -