从原子波包所满足的薛定谔方程出发,从理论上巧妙地推导出了原子干涉仪在重力的影响下所产生的相位差与重力加速度的关系表达式。提出了一种3×3阶的矩阵方法,以此来分析多个元件情况下原子干涉仪中的相位差,可以大大简化计算。利用这种方法不但能得到原子束在重力的影响下在自由空间中的传输矩阵,也可以得到原子束与π/2和π脉冲的相互作用矩阵。作为例子,用3×3阶矩阵方法计算了三脉冲原子干涉仪中的相位差,得出的结果与Wolf等对经典轨迹进行拉格朗日积分所得出的结果完全相符。进一步分析了五脉冲的原子干涉仪中的相位差,以说明3×3阶矩阵方法的简便性。

Based on the Schrdinger equation for atomic waves, the relation between the gravity and the phase difference of atom interferometer is derived. A new 3×3 matrix method was introduced to calculate the phase difference for complicated system of the multiloop interferometers, which simplifies the calculation greatly. By use of this method, not only the propagation matrix of atom beam in free space under the influence of gravity can be, but also the interaction matrix of atom beam with π/2 and π pulse can be obtained. As an example, the phase difference for the three-pulse atom gravimeter by using the 3×3 matrix is derived, and the results obtained coincide precisely with those obtained by Wolf et al. through the integration of the Lagrangian over the classical trajectory. Finally, the phase difference of five-pulse atom gravimeter is analyzed to illustrate the convenience of the 3×3 matrix method.