Analytic theory for Bragg atom interferometry based on the adiabatic theorem
High fidelity Bragg pulses are an indispensable tool for state of the art atom interferometry experiments. In this paper, 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 the 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 four, six, eight and ten 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.