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Physical Review A

Expansion of a Bose-Einstein condensate from a microtrap into a waveguide

James Stickney, Alex A. Zozulya

Published May 8, 2002• 13 citations
Publisher

Abstract

Coherence properties of atomic Bose-Einstein condensates determine the performance of waveguide atom interferometers. We analyze the expansion of a Bose-Einstein condensate from a magnetic microtrap into a waveguide. We derive analytical expressions to describe the expansion, show how the expanded cloud maps onto transverse linear eigenfunctions of the guide, and calculate the dependence of the modal decomposition coefficients on the chemical potential of the cloud and the anisotropy of the trap. Analytical results are compared with three-dimensional numerical simulations of the expansion.

DOI
10.1103/physreva.65.053612

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Coherence properties of atomic Bose-Einstein condensates determine the performance of waveguide atom interferometers. We analyze the expansion of a Bose-Einstein condensate from a magnetic microtrap into a waveguide. We derive analytical expressions to describe the expansion, show how the expanded cloud maps onto transverse linear eigenfunctions of the guide, and calculate the dependence of the modal decomposition coefficients on the chemical potential of the cloud and the anisotropy of the trap. Analytical results are compared with three-dimensional numerical simulations of the expansion.
An atom interferometer is a sensitive device that has potential for many useful applications. Atoms are sensitive to electromagnetic fields due to their electric and magnetic moments and their mass allows them to be deflected in a gravitational field, thereby making them attractive for measuring inertial forces. The narrow momentum distribution of Bose-Einstein condensate (BEC) is a great asset in realizing portable atom interferometers. An example is a guided-wave atom interferometer that uses a confining potential to guide the motion of the condensate. Despite the promise of guided-wave atom interferometry with BEC, spatial phase and phase diffusion limit the contrast of the interference fringes. The control of these phases is required for successful development of a BEC-based guided-wave atom interferometer. This thesis analyses the guided-wave atom interferometer, where an atomic BEC cloud at the center of a confining potential is split into two clouds that move along different arms of the interferometer. The clouds accumulate relative phase due to the environment, spatially inhomogeneous trapping potential and atom-atom interactions within the condensate. At the end of the interferometric cycle, the clouds are recombined producing a cloud at rest and moving clouds. The number of atoms in the clouds that emerge depends on the relative phase accumulated by the clouds during propagation. This is investigated by deriving an expression for the probability of finding any given number of atoms in the clouds that emerge after recombination. Characteristic features like mean, standard deviation and cross-correlation function of the probability density distribution are calculated and the contrast of the interference fringes is optimized. This thesis found that optimum contrast is achieved through the control of total population of atoms in the condensate, trap frequencies, s-wave scattering length, and the duration of the interferometric cycle.
[EN] In this work, we have studied a dilute and ultracold bosonic gas of weakly interacting atoms, \ni.e. a Bose-Einstein Condensate (BEC) by means of the Modi ed Gross-Pitaevskii equation \n(MGPE) taking into account beyond-mean- eld corrections due to quantum \nuctuations. We \nhave considered the case where the cloud of atoms is strongly con ned transversally (within a \ncigar-shaped trap) and therefore, the three-dimensional (3D) MGPE is reduced to an e ective \none-dimensional (1D) form by averaging over the transverse coordinates. Based on this approach, \nwe have performed numerical simulations for analyzing the behavior of the BEC under the \nin \nuence of quantum \nuctuations, which give rise to an additional nonlinear quartic term. After \nreviewing the mathematical theory of Bose-Einstein condensation based on the GPE and the \nnumerical methods used to integrate it we discuss the computation of the ground state and the \nsimulation of its dynamic evolution in a waveguide (free expansion).
We report on the creation of Bose-Einstein condensates of 87Rb{}^{87}\mathrm{Rb}87Rb in a specially designed hybrid, optical dipole and magnetic trap. This trap naturally allows the coherent transfer of matter waves into a pure optical dipole potential waveguide based on a doughnut beam. Specifically, we present studies of the coherence of the ensemble in the hybrid trap and during the evolution in the waveguide by means of an autocorrelation interferometer scheme. We observe a mean-field dominated acceleration in the waveguide on a much longer time scale than in the free three-dimensional expansion.
We have experimentally investigated the free expansion of a Bose-Einstein condensate in an array of two-dimensional traps created by a one-dimensional optical lattice. If the condensate held in a magnetic trap is loaded adiabatically into the lattice, the increase in chemical potential due to the additional periodic potential is reflected in the expansion of the condensate after switching off the magnetic trap. We have calculated the chemical potential from measurements of the transverse expansion of the condensate as a function of the lattice parameters.
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).