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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。
Starting from the Schrödinger equation satisfied by the atomic wave packet, a theoretically ingenious expression of the relation between the phase difference and the gravitational acceleration generated by the atomic interferometer under the influence of gravity is deduced. A 3 × 3 matrix method is proposed to analyze the phase difference in the atomic interferometer with multiple elements, which can greatly simplify the calculation. By using this method, not only the transfer matrix in free space of the atomic beam under the influence of gravity but also the interaction matrix between the atomic beam and π / 2 and π pulse can be obtained. As an example, the phase difference in a three-pulse atomic interferometer is calculated by a 3 × 3 matrix method, and the result is in good agreement with Wolf’s result of Lagrange’s integralization of the classical trajectory. Further analysis of the phase difference in the five-pulse atomic interferometer to illustrate the simplicity of 3 × 3 matrix method.