Double-diffraction Raman interference is a novel interference scheme developed in recent years. It has a potentially high measurement precision due to the symmetric interference loop with identical internal states. In this paper, we analyze the high-order diffraction process in double-diffraction Raman interference and derive state evolution equations that include multiple diffraction processes. The population evolution of the states and the Mach-Zehnder interference fringe are calculated under the action of a Raman laser. The thermal momentum distribution averaging and state grouping methods are employed to solve the problem of decoherence at different interference exit ports. We compare the phase shifts calculated by integrating the sensitivity function and the two-photon frequency shift and by numerically solving the state evolution equations with high-order diffraction states. The good agreement between the results of the two methods shows that the two-photon frequency shift is the main reason for the phase shift induced by the higher-order diffraction states. Finally, the test error of an equivalent principle test experiment due to this effect is analyzed. This paper may be helpful for the analysis and suppression of the systemic error in such experiments.

中文翻译：

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由于高阶衍射状态引起的双衍射拉曼干涉的相移

双衍射拉曼干涉是近年来发展起来的一种新型干涉方案。由于具有相同内部状态的对称干扰回路，它具有潜在的高测量精度。在本文中，我们分析了双衍射拉曼干涉中的高阶衍射过程，并推导出包含多个衍射过程的状态演化方程。在拉曼激光的作用下计算了态的种群演化和马赫-曾德干涉条纹。采用热动量分布平均和状态分组的方法来解决不同干扰出口处的退相干问题。我们比较了通过积分灵敏度函数和双光子频移以及通过数值求解具有高阶衍射状态的状态演化方程计算出的相移。两种方法的结果之间的良好一致性表明，双光子频移是高阶衍射态引起相移的主要原因。最后，分析了等效原理试验实验中由于这种效应引起的试验误差。本文可能有助于分析和抑制此类实验中的系统误差。分析了等效原理试验实验中由于这种效应引起的试验误差。本文可能有助于分析和抑制此类实验中的系统误差。分析了等效原理试验实验中由于这种效应引起的试验误差。本文可能有助于分析和抑制此类实验中的系统误差。