GS4 Student Scholars Symposium

We have studied 1D and 3D atom interferometry (AI) sequences carried out with Bose-Einstein condensates (BECs) in the presence of external potentials consisting of harmonic plus anharmonic terms. The process where a BEC is split into multiple clouds and then recombined to form an interference pattern was numerically simulated by solving the Gross-Pitaevskii equation (GPE). Approximate solutions to this equation were generated using the Lagrangian Variational Method (LVM) whose trial wave function consisted of a sum of Gaussian functions, one for each cloud. We derive the LVM equations of motion as well as a formula for the phase of the trial wave function. The variational result is compared to the numerical solution of the GPE. We will also compare these results with those given by time-dependent perturbation theory.