测量牛顿引力常数时圆柱形源质量组产生的原子干涉仪相位的优化
Optimization of the atom interferometer phase produced by the set of cylindrical source masses to measure the Newtonian gravity constant
摘要：
本文导出了均匀圆柱体的引力场的解析表达式。本文计算了由圆柱组的重力场产生的原子干涉仪的相位。得到了原子云的初始位置和初始速度的最佳值。结果表明，当原子云在垂直和横向上的尺寸相等，以及原子垂直和横向的温度相等时，由有限的原子云尺寸和温度引起的系统误差消失。为了克服地球引力场对相位双差测量精度的影响，提出了消除重力梯度项的方法。在消除之后，可以使用原子位置和速度的极值。在这些极端值附近，原子位置和速度的不确定性的相位的非线性依赖性要求我们修改标准相位偏差的表达式。此外，这种依赖性导致相移，这也被计算。对于24个和630个圆柱体的测量，牛顿引力常量的相对测量精度分别为10^-4和2*10^-5。
英文摘要：
An analytical expression for the gravitational field of a homogeneous cylinder is derived. The phase of the atom interferometer produced by the gravity field of the set of cylinders has been calculated. The optimal values of the initial positions and velocities of atomic clouds were obtained. It is shown that at equal sizes of the atomic cloud in the vertical and transverse directions, as well as at equal atomic vertical and transverse temperatures, systematic errors due to the finite size and temperature of the cloud disappear. To overcome the influence of the Earth gravitational field on the accuracy of the phase double difference measurement, it is proposed to use the technique of eliminating gravity-gradient terms. After eliminating, one can use extreme values of the atomic positions and velocities. Nonlinear dependences of the phase on the uncertainties of atomic positions and velocities near those extreme values required us to modify the expression for the standard phase deviation. Moreover, such dependences lead to a phase shift, which was also calculated. The relative accuracy of measurements of Newtonian gravitational constant 10^-4 and 2*10^-5 is predicted for sets of 24 and 630 cylinders, respectively.
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