Fringe contrast in three grating Mach-Zehnder atomic interferometers

Several three-grating Mach-Zehnder atomic interferometers have been built a nd operated in recent years but no general theory of the contrast of the fr inges produced by these apparatus is available. The purpose of this paper i s to develop this theory, based on the Fresnel-Kirchoff approximate treatme nt of diffraction.. Such a theory has been developed by Turchette et al. [J OSA B 9, 1601 (1992)] but because the necessary multiple integrals were eva luated in a purely numerical way, this treatment was not fully general. We show here how to reduce the computation by analytic means and we are thus a ble to calculate the contrast with a modest numerical effort. Moreover; we get a simple insight of the contrast reduction related to several defects o f a real apparatus. We apply our calculations to existing interferometers a s well as to an apparatus working with lithium which is under construction in our laboratory.