Quantum perturbation theory for atom interferometers in anharmonic traps

Atom interferometers using trapped atoms offer potential advantages in interrogation time and system volume compared to interferometers with free atoms. Recent advances in this area have led to interferometers with millimeter-scale trajectories and second-scale durations. Even if interactions between atoms are ignored, numerical modelling of the wave function evolution is impractical at these scales. A semi-classical approximation can be used, which is exact for a harmonic trapping potential but may lead to errors in the case of anharmonic traps. We have developed a perturbation theory approach to determine the leading order quantum corrections to the semi-classical theory. The method is based on representing the interfering wave packets as generalized coherent states, which leads to a simple diagramatic calculation method and relatively compact analytical expressions.