Gravimetry using atom interferometers: Some systematic effects

We present a theoretical investigation of some systematic effects in atom i nterferometers that have been used to measure the acceleration of gravity, g, We derive an explicit expression for the interferometer phase difference that differs from previously obtained results by a number of correction te rms. These terms result from a rigorous treatment of the variation of the l aser frequencies necessary to compensate for the first order Doppler shift of the freely falling atoms on one hand, and characterise systematic effect s due to the quadratic term in the expansion of the Earth's gravitational f ield (effect of the gravity gradient) on the other hand, Evaluating the mag nitude of these terms we find that, depending on the precise experimental c onditions, they could contribute systematic errors in the gravimetric measu rement of Delta g/g less than or equal to 5 x 10(-8). They are therefore no n-negligible in recent gravimetric measurements using atom interferometers which reach uncertainties of a few parts in 10(9). (C) 1999 Published by El sevier Science B.V.