High-fidelity Bragg pulses are an indispensable tool for state-of-the-art atom interferometry experiments. In this work, we introduce an analytic theory for such pulses. Our theory is based on the pivotal insight that the physics of Bragg pulses can be accurately described by the adiabatic theorem. We show that efficient Bragg diffraction is possible with any smooth and adiabatic pulse shape and that high-fidelity Gaussian pulses are exclusively adiabatic. Our results give strong evidence, that adiabaticity according to the adiabatic theorem is a necessary requirement for high-performance Bragg pulses. Our model provides an intuitive understanding of the Bragg condition, also referred to as condition on the “pulse area”. It includes corrections to the adiabatic evolution due to Landau-Zener processes as well as the effects of a finite atomic velocity distribution. We verify our model by comparing it to an exact numerical integration of the Schr"odinger equation for Gaussian pulses diffracting $4,6,8$ and $10$ photon recoils. Our formalism provides an analytic framework to study systematic effects as well as limitations to the accuracy of atom interferometers employing Bragg optics that arise due to the diffraction process.

中文翻译：

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基于绝热定理的布拉格原子干涉分析理论

高保真布拉格脉冲是先进的原子干涉实验不可或缺的工具。在这项工作中，我们介绍了这种脉冲的分析理论。我们的理论基于关键见解，即可以通过绝热定理准确描述布拉格脉冲的物理原理。我们表明，有效的布拉格衍射对于任何光滑绝热的脉冲形状都是可行的，而高保真高斯脉冲完全是绝热的。我们的结果提供了有力的证据，根据绝热定理的绝热性是高性能布拉格脉冲的必要条件。我们的模型可以直观地了解布拉格条件，也称为“脉冲区域”上的条件。它包括对由于Landau-Zener过程引起的绝热演化以及有限原子速度分布的影响的校正。我们通过与高斯脉冲衍射的Schr“ odinger方程的精确数值积分进行比较来验证我们的模型$4，6，8$ 和 $10$光子后坐力。我们的形式主义为研究系统效应以及由于衍射过程而产生的采用布拉格光学的原子干涉仪的精度限制提供了一个分析框架。