Estimation of phase diffusion rates in a condensate interferometer using the Gross–Pitaevskii equation

Atom interferometers using Bose–Einstein condensates are fundamentally limited by a phase diffusion process that arises from atomic interactions. Numerical solution of the Gross–Pitaevskii equation is here used to accurately calculate the diffusion rate for a Bragg interferometer. It is seen to agree with a Thomas–Fermi approximation at large atom numbers and a perturbative approximation at low atom numbers. Most experiments to date operate in the crossover region between these two regimes. Even in this case, it is found that that the diffusion time is governed in a simple way by the ratio of the healing length to the size of the condensate. (paper)