Phase shift due to atom-atom interactions in a light-pulse atom interferometer

We present a theoretical model allowing precise calculation of the phase shift induced by atom-atom interactions in a light-pulse atom interferometer based on two-photon Raman atom optics. This model is in good agreement with numerical simulations based on solving the Gross-Pitaevskii equation. The atom interferometer exhibits an atom-atom-interaction-induced phase shift when there is asymmetry between the two arms of the interferometer. In the case of a Ramsey-Bordé atom interferometer ({π/2-π/2}-{π/2-π/2} pulse configuration), the asymmetry comes from the fact that the number of atoms in each arm of the interferometer is not constant. In the case of a Mach-Zehnder ({π/2-π-π/2} pulse sequence), if the pulses are perfect, the number of atoms is constant in the interferometer. We study the effect due to imperfections of the light pulses as well as the effect due to the expansion of the cloud. Our model leads to precise and simple formulas of the mean-field phase shift as a function of the experimental parameters.