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arXiv:0805.1817 · Physical Review A

Atom-chip diffraction of Bose-Einstein condensates: The role of interatomic interactions

T. E. Judd, R. G. Scott, T. M. Fromhold

Published Nov 17, 2008• 14 citations
arXivHTMLPDF

Abstract

We use supercomputer simulations to show that interatomic interactions can strongly affect the phase evolution of Bose-Einstein condensates that are diffracted from atom chips, thereby explaining recent experiments. Interactions broaden and depopulate noncentral diffraction orders and so, counterintuitively, they actually reduce the spatial width of the diffracted cloud. This means that the experiments cannot be fully described by noninteracting theories and, consequently, interferometers that use many interacting atoms to enhance sensitivity require complex calibration. We identify device geometries required to approximate noninteracting behavior.

DOI
10.1103/physreva.78.053623

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We use supercomputer simulations to show that interatomic interactions can strongly affect the phase evolution of Bose-Einstein condensates that are diffracted from atom chips, thereby explaining recent experiments. Interactions broaden and depopulate noncentral diffraction orders and so, counterintuitively, they actually reduce the spatial width of the diffracted cloud. This means that the experiments cannot be fully described by noninteracting theories and, consequently, interferometers that use many interacting atoms to enhance sensitivity require complex calibration. We identify device geometries required to approximate noninteracting behavior.
In recent years, atom interferometry has become established as an indispensable tool in both fundamental and applied physics. With present state-of-the-art devices based on thermal atoms reaching limits imposed by the momentum spread of the initial atomic wavepacket, it seems natural to ask whether colder sources such as Bose-Einstein condensates may prove beneficial in advancing the precision of interferometric measurements. The thesis at hand aims to inform this question, specifically by examining the role played by atomic interactions in interferometers based on Bose-condensed atoms. Interactions can have both advantageous and deleterious consequences in the context of atom interferometry. They provide a means to control the momentum width of the condensate, and facilitate the generation of nonclassical squeezed states which may enhance the phase sensitivity beyond the shot noise limit. Conversely, the condensate self-interaction causes mean-field shifts, multimode excitations and phase diffusion which can erode both the precision and the accuracy of an interferometric measurement. The question of when and in which systems the detrimental effects of interactions outweigh the advantages of using Bose-Einstein condensates is an important one, and warrants investigation. This thesis presents experimental studies into the role of interactions in both internal- and external-state atom interferometers. As a foundation for these investigations, we describe the design and construction of an apparatus for creating Bose-Einstein condensates of the two stable rubidium isotopes in an optical trap. By sympathetic cooling with a rubidium-87 reservoir, we are able to produce condensates of rubidium-85 in which the interactions may be adjusted by means of a magnetic Feshbach resonance. The tunability afforded by the Feshbach resonance is used to study inelastic losses in ultracold rubidium-85 clouds, as well as the effect of interactions on condensate stability and on the ground state of dual-species mixtures. In particular, we offer new experimental data on the dynamics of collapsing condensates with attractive interactions, over which some controversy has existed since the first experiments more than a decade ago. Good agreement is found between the measured collapse times and a simple mean-field model. Proceeding to interferometry, we present results from Ramsey interferometers operating on the clock transition of rubidium-87 Bose-Einstein condensates. In free-space operation with Raman beamsplitters, we demonstrate projection-noise-limited performance, an important prerequisite for the realisation of squeezing-enhanced sensitivity. Using large condensates of up to 10⁶ atoms and microwave coupling, we study the effect of interactions on the Ramsey fringe contrast. The dominant source of decoherence is found to be spatial dynamics driven by the difference in interparticle interaction strengths, which are analysed using the spin-echo technique and numerical simulations of the Gross-Pitaevskii equation. Finally, we turn our attention to external-state interferometry, implementing a Mach-Zehnder gravimeter using Bragg transitions in a freely falling rubidium-87 condensate. Large-momentum-transfer beamsplitters composed of higher-order Bragg diffraction and Bloch oscillations are used to increase the accumulated phase and thus the sensitivity of the interferometer. The role of interactions in this system is examined, and we canvass methods for achieving further increases in sensitivity.
A Mach-Zehnder-type atom interferometer with a Bose-Einstein condensate has been investigated on an atom chip by using optical Bragg diffraction. A phase shift and a contrast degradation, which depend on the atomic density and the trapping frequency of the magnetic-guide potential, have been observed. Also, the output wave packets were found to exhibit a spatial interference pattern. The atom-atom interaction and the guide potential induce the spatially inhomogeneous phase evolution of the wave packets in each arm of the interferometer. The observed contrast degradation can be quantitatively explained as a dephasing due to this inhomogeneous phase evolution.
We study spatial coherence near a classical environment by loading a Bose-Einstein condensate into a magnetic lattice potential and observing diffraction. Even very close to a surface ($5\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$), and even when the surface is at room temperature, spatial coherence persists for a relatively long time ($\ensuremath{\ge}\phantom{\rule{0.16em}{0ex}}500\phantom{\rule{0.16em}{0ex}}\mathrm{ms}$). In addition, the observed spatial coherence extends over several lattice sites, a significantly greater distance than the atom-surface separation. This opens the door for atomic circuits, and may help elucidate the interplay between spatial dephasing, interatomic interactions, and external noise.
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.
We develop a theoretical model to investigate the Bragg diffraction of an elongated interacting Bose-Einstein condensate which is illuminated by a pair of laser beams. We find that the mean-field effect resulting from the atomic interaction plays an important role in modifying the atomic coherence. Our results show that both the repulsive and attractive interactions would dampen the momentum oscillation of the condensate; they establish surprisingly distinguishable equilibria for the atomic occupations among different diffraction orders. We also give an experimental proposal to observe this phenomenon.