The atomic interferometry by Kasevich and Chu (Phys. Rev. Lett. 67, 181(1991)) has been the beginning of a range of very sensitive measurement techniques. We present a complete density matrix analysis of this technique. Although there has been several attempts to provide a theoretical analysis for this technique, the models used are incomplete. The density matrix method allows investigation of all the decoherence effects that are present in the real experimental system. This allows better understanding of how decoherences affect the resolution of the measurement of atom intereferometer, either as a gyroscope, magnetometer or a gravimeter.
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