含压缩真空的实验室框架反Jaynes-Cummings模型中的剩余失谐
Residual detuning in the laboratory-frame anti-Jaynes--Cummings model with a squeezed vacuum
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- Maseno University（马塞诺大学）
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中文总结 AI 辅助
该研究针对含压缩真空的实验室框架反Jaynes-Cummings模型的剩余失谐，分析Kerr位移、集体Dicke耦合两种校正方案，发现集体耦合可系统性提升对比度，适用于超强电路QED平台。
中文摘要 AI 辅助
实验室框架下的反Jaynes-Cummings（AJC）相互作用存在旋转框架模型中不存在的剩余失谐2fλ。我们针对该梯子上的压缩真空（压缩参数r=1，平均光子数⟨n⟩=sinh²r≈1.38），分析两种已提出的校正方案：Kerr位移χ(â†â)²和N个两能级发射体的集体Dicke耦合。所有引用的对比度均为原子基态布居第一个转折点的振幅，在r=0时与两能级公式𝒞=1/[1+(2f+χ)²]的偏差达10⁻⁹量级。得到三个结果：(i) 单一Kerr强度无法在r=1时恢复单位对比度；r=0时与n相关的位移χ(2n+1)无法抵消所有占据Fock分量上的2fλ；(ii) χ=0时r=1的精确对比度无法通过r=0两能级公式的非相干求和∑ₙPₙ(r)𝒞ₙ复现，逐点偏差达十分之几；(iii) 集体耦合可系统性提升对比度，当f=5时，N=1对应𝒞=0.140，N=8对应𝒞=0.575，高于未压缩值8/[8+(2f)²]=0.074；该f值下N=16的点受截断限制，未给出三位有效数字；对于𝒞=1/2，N~(2f)²的估计表明，囚禁离子的f~10²–10³超出当前构造范围，相关平台为f~1–10的超强电路QED；该计算为数值控制景观，非新的可解极限。
英文摘要
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 $χ(\hat a^\dagger\hat a)^2$ and collective Dicke coupling of $N$ two-level emitters---for a squeezed vacuum on that ladder ($r=1$, $\langle n\rangle=\sinh^2 r\simeq 1.38$). All quoted contrasts are the amplitude of the first turning point of the atomic ground-state population, which coincides with the two-level formula $\mathcal{C}=1/[1+(2f+χ)^2]$ 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 $\sum_n P_n(r)\,\mathcal{C}_n$ 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 $\mathcal{C}=0.140$ ($N=1$) and $\mathcal{C}=0.575$ ($N=8$), 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 $N\sim(2f)^2$ estimate for $\mathcal{C}=1/2$ places trapped-ion values $f\sim 10^{2}$--$10^{3}$ outside the present construction. The relevant platform is ultrastrong circuit QED with $f\sim 1$--$10$. The calculation is a numerical control landscape, not a new solvable limit.
