Effects of anharmonicity in a dual-Sagnac interferometer rotation sensor*

A recent experiment implemented a dual Sagnac atom interferometer (AI) for rotation sensing using a Bose-Einstein condensate (BEC) confined in a TOP-trap potential. The BEC is split twice by laser light to create two pairs of counter-orbiting clouds in a lowest-order harmonic potential with each pair acting as a separate Sagnac interferometer. After one orbit the two overlapping cloud pairs are split again and the interference patterns are inferred from the population of atoms in the zero-momentum state. We have simulated the impact of the presence of anharmonic terms in the potential on the performance of the AI as measured in a recent experiment by using a variational approximation of the Gross-Pitaevskii equation (GPE) model. This model based on the Lagrangian Variational Method where the condensate pieces are represented by Gaussian clouds. We have compared the phase differences between the dual interferometers as computed in the model with that predicted by the action computed over the classical path for various types of anharmonic terms and for condensates of different sizes to assess the impact of these on interferometer performance.