Residual detuning in the laboratory-frame anti-Jaynes--Cummings model with a squeezed vacuum
Abstract
The laboratory-frame anti-Jaynes--Cummings (AJC) interaction retains a residual detuning 2fλ that is absent from the rotating-frame model. We map two proposed remedies---a Kerr shift χ(â†â)2 and collective Dicke coupling of N two-level emitters---for a squeezed vacuum on that ladder (r=1, ⟨ n⟩=sinh2 r≃ 1.38). All quoted contrasts are the amplitude of the first turning point of the atomic ground-state population, which coincides with the two-level formula 𝒞=1/[1+(2f+χ)2] at r=0 to 10−9. Three results follow. (i)~A single Kerr strength never restores unit contrast at r=1; the r=0 n-dependent shift χ(2n+1) cannot cancel 2fλ on every occupied Fock component. (ii)~The exact r=1 contrast at χ=0 is not reproduced by an incoherent sum ∑n Pn(r) 𝒞n built from the r=0 two-level formula; pointwise deviations are several tenths. (iii)~Collective coupling raises the contrast systematically. At f=5 one finds 𝒞=0.140 (N=1) and 𝒞=0.575 (N=8), above the unsqueezed value 8/[8+(2f)2]=0.074. The N=16 point at this f remains truncation-limited and is not quoted to three digits. The same N∼(2f)2 estimate for 𝒞=1/2 places trapped-ion values f∼ 102--103 outside the present construction. The relevant platform is ultrastrong circuit QED with f∼ 1--$10$. The calculation is a numerical control landscape, not a new solvable limit.
Related
- Quantum Optics of harmonic generation in the strongly driven Jaynes-Cummings-type system
- Pöschl-Teller type of Jaynes-Cummings Hamiltonians: SUSY transformations
- Dynamical protection of quantum steering and fidelity dynamics in the double Jaynes-Cummings model
- Supersymmetry of dissipative Bose-Fermi systems with application to Jaynes-Cummings and Dicke models
- Jaynes--Cummings dynamics of fermionic heteronuclear dimers in the Mott regime
BibTeX
@misc{okeyo2026residual,
title = {{Residual detuning in the laboratory-frame anti-Jaynes--Cummings model with a squeezed vacuum}},
author = {Onyango Stephen Okeyo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04580},
eprint = {2609.04580},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04580},
}
RIS
TY - UNPB
TI - Residual detuning in the laboratory-frame anti-Jaynes--Cummings model with a squeezed vacuum
AU - Onyango Stephen Okeyo
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04580
UR - https://arxiv.org/abs/2609.04580
AB - The laboratory-frame anti-Jaynes--Cummings (AJC) interaction retains a residual detuning 2fλ that is absent from the rotating-frame model. We map two proposed remedies---a Kerr shift χ(â^†â)^2 and collective Dicke coupling of N two-level emitters---for a squeezed vacuum on that ladder (r=1, ⟨ n⟩=sinh^2 r≃ 1.38). All quoted contrasts are the amplitude of the first turning point of the atomic ground-state population, which coincides with the two-level formula 𝒞=1/[1+(2f+χ)^2] at r=0 to 10^−9. Three results follow. (i)~A single Kerr strength never restores unit contrast at r=1; the r=0 n-dependent shift χ(2n+1) cannot cancel 2fλ on every occupied Fock component. (ii)~The exact r=1 contrast at χ=0 is not reproduced by an incoherent sum ∑_n P_n(r) 𝒞_n built from the r=0 two-level formula; pointwise deviations are several tenths. (iii)~Collective coupling raises the contrast systematically. At f=5 one finds 𝒞=0.140 (N=1) and 𝒞=0.575 (N=8), above the unsqueezed value 8/[8+(2f)^2]=0.074. The N=16 point at this f remains truncation-limited and is not quoted to three digits. The same N∼(2f)^2 estimate for 𝒞=1/2 places trapped-ion values f∼ 10^2--10^3 outside the present construction. The relevant platform is ultrastrong circuit QED with f∼ 1--$10$. The calculation is a numerical control landscape, not a new solvable limit.
ER -