Generalized wave-packet model for studying coherence of matter-wave interferometers

Abstract

We present a generalized model for the evolution of atomic wave-packets in matter-wave interferometers. This method provides an efficient tool for analyzing the performance of atomic interferometers using atom clouds prepared in a trap as a Bose-Einstein condensate (BEC) or as a thermal ensemble. Predictions of the model for dynamic properties such as wave-packet size and phase are in excellent agreement with explicit numerical solutions of the non-linear Gross-Pitaevskii equations and enable fast calculations of interferometric performance in regimes where full numerical solutions become impractical. As a starting point, the static Thomas-Fermi (TF) approximation for a BEC in a harmonic trap is generalized to the whole range of atom-atom interaction strengths: from non-interacting atoms (low densities) to the standard TF limit (high atomic densities, as long as the condensate approximation still holds). In particular, this generalization allows a good estimation of atomic cloud properties along the transition from a three-dimensional to a quasi-one-dimensional BEC in an elongated trap. We then develop a theoretical model of wave-packet evolution in time-dependent conditions. The model is applicable for a wide range of dynamical problems involving evolution in time-dependent potentials and in a changing mean-field atomic repulsion due to splitting and separation of wave-packets. We use the model for studying two effects that influence interferometric coherence: imperfect spatial recombination in a two-state interferometer (the so-called "Humpty-Dumpty effect") and phase diffusion due to number uncertainty in the two interferometer arms, which was previously studied thoroughly only for interferometric schemes where the BECs in the two arms stay trapped (for example, in a double-well potential).