The Raman Pulse Duration Effect In High-precision Atom Interferometry Gravimeters

With the development of cold atomic interferometry gravimeter, people pursuit theaccuracy of the measurement result more and more strictly. To evaluate a high-precisionatom interferometry measurement, some systematic effects need to be reconsidered, suchas effects of wave distortion, Stark effect, gravity gradient, Zeeman effect, etc. areimportant factors to the performance of the interferometer. Therefore, in order to achievehigh-precision atom interferometry, we need to have a theoretical investigation of somesystematic effects in atom interferometers that have been used to measure the accelerationof gravity, which has important guiding significance for the experiment.The influence of Raman laser duration is an important factor to the performance ofthe interferometer. Pervious works studied this influence in uniform gravitational field.Unfortunately, in realistic situation, Earth’s gravitational field is inhomogeneous, so for ahigh-precision atom interferometry gravimeters it is necessary to consider this effect.However, if the methods presented in previous works are extended to include the effect ofthe gravitational gradient field, the calculation precess is too complicated to consider.In this paper, we present analytical frameworks. Using the analytical method, wehave respectively obtained an explicit expression for the interferometer phase shift in theabsence of a gravitational field, in an uniform Earth’s gravitational field and in a lineargravitational gradient field. If a homogeneous Earth’s gravitational field is supposed, ourresults are the same with the previous results. If the effect of the Raman pulse duration isneglected, our results also can return to previous results including terms characterizing theeffect of the gravity gradient. More importantly, this method provides a feasible way toconsider the effect of the Raman pulse duration in the gravitational gradient field, whichprovide theoretical support for the high-precision atomic interferometers. Evaluating ourresult, we find that the effect of Raman pulse durations need to be taken into account at atargeted measurement accuracy of10-11.