用原子干涉术探测修正引力：一种数值方法
Probing Modified Gravity with Atom-Interferometry: a Numerical Approach
摘要：
精化约束变色龙理论计算原子干涉实验，使用数值方法，包括在解决一个四区域模型的静态和球对称克莱因-戈登方程的变色龙字段。该方法不仅模拟了试验质量和真空室，而且模拟了真空室的壁面和外部环境，从而可以探测到新的效应对原子的标量场分布和诱导加速度的影响。在弱扰动试验质量的情况下，壁的作用是增强场分布，并将室内的加速度降低一个数量级。在薄壳制度，结果被发现是在良好的协议与分析估计，当测量实现在紧邻的测试质量。靠近真空室壁时，加速度变为负值并且可能是可测量的。通过在真空室内的几个关键位置进行实验，这种预测可以用来区分第五力效应和系统实验的不确定性。对于变色龙势$V(ϕ) = Λ^{4+α} / ϕ^α$和耦合函数$A(ϕ) = \exp(ϕ/M)$，我们发现$M \gtrsim 7 \times 10^{16} \mathrm{GeV}$与幂律指数无关。对于$V(ϕ) = Λ^4 (1+ Λ/ ϕ)$，可以找到$M \gtrsim 10^{14} \mathrm{GeV}$。$a\sim 10^{-11} \mathrm{m/s^2} $的灵敏度将探测到普朗克尺度的模型。最后，第二个实验设置，在真空室，提出了一个建议。在这种情况下，只要$a \sim 10^{-10} \mathrm{m/s^2}$（未来实验可达到的极限），就可以探测$M$的普朗克值。我们的方法可以很容易地扩展到约束其他模型的筛选机制，如Escherichon，Escherichon和f（R）理论。
英文摘要：
Refined constraints on chameleon theories are calculated for atom-interferometry experiments, using a numerical approach consisting in solving for a four-region model the static and spherically symmetric Klein-Gordon equation for the chameleon field. By modeling not only the test mass and the vacuum chamber but also its walls and the exterior environment, the method allows to probe new effects on the scalar field profile and the induced acceleration of atoms. In the case of a weakly perturbing test mass, the effect of the wall is to enhance the field profile and to lower the acceleration inside the chamber by up to one order of magnitude. In the thin-shell regime, results are found to be in good agreement with the analytical estimations, when measurements are realized in the immediate vicinity of the test mass. Close to the vacuum chamber wall, the acceleration becomes negative and potentially measurable. This prediction could be used to discriminate between fifth-force effects and systematic experimental uncertainties, by doing the experiment at several key positions inside the vacuum chamber. For the chameleon potential $V(ϕ) = Λ^{4+α} / ϕ^α$ and a coupling function $A(ϕ) = \exp(ϕ/M)$, one finds $M \gtrsim 7 \times 10^{16} \mathrm{GeV}$, independently of the power-law index. For $V(ϕ) = Λ^4 (1+ Λ/ ϕ)$, one finds $M \gtrsim 10^{14} \mathrm{GeV}$. A sensitivity of $a\sim 10^{-11} \mathrm{m/s^2} $ would probe the model up to the Planck scale. Finally, a proposal for a second experimental set-up, in a vacuum room, is presented. In this case, Planckian values of $M$ could be probed provided that $a \sim 10^{-10} \mathrm{m/s^2}$, a limit reachable by future experiments. Our method can easily be extended to constrain other models with a screening mechanism, such as symmetron, dilaton and f(R) theories.
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