Effect of trap symmetry and atom-atom interactions on a trapped-atom interferometer with internal state labeling

In this paper, we study the dynamics of a trapped atom interferometer with internal state labelling in presence interactions. We consider two situations: an atomic clock which states remain superposed, and inertial sensor configuration they are separated. From average spin evolution, deduce fringe contrast phase-shift. configuration, recover well-known identical rotation effect (ISRE) can significantly increase coherence time. also find that magnitude depends on trap geometry way is consistent our recent experimental results [M. Dupont-Nivet, al., New J. Phys., 20, 043051 (2018)], where ISRE was not observed. case sensor, show despite spatial separation it still possible to time by using mean field interactions counteract asymmetries trapping potential.