Multimode Kapitza-Dirac interferometer on Bose-Einstein condensates with atomic interactions

The dynamics of multimode interferometers for Bose Einstein condensation (BEC) with atomic interactions confined to a harmonic trap is investigated. At the initial time t=0, several spatially addressable wave packets (modes) with different momenta are created by the first Kapitza-Dirac pulse. These modes are coherently recombined by the harmonic potential with atomic interactions. The second Kapitza-Dirac pulse splits the evolved modes a second time and separates them along different paths for a second time. The signal to noise ratio is numerically calculated by the Fisher information and the Cramér-Rao lower bound. We find that the small atomic interactions decrease the measurement accuracy for current atom interferometers when measuring the gravitational acceleration. Its impact on measurement precision can be reduced by improving the Kapitza-Dirac strength.