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Physical Review A

Transverse mode imaging of guided matter waves

R. G. Dall, Sean S. Hodgman, Mattias Johnsson, K. G. H. Baldwin, Andrew G. Truscott

Published Jan 7, 2010• 20 citations
Publisher

Abstract

Ultracold atoms whose de Broglie wavelength is of the same order as an extended confining potential can experience waveguiding along the potential. When the transverse kinetic energy of the atoms is sufficiently low, they can be guided in the lowest order mode of the confining potential by analogy with light guided by a single mode optical fiber. We have obtained the first images of the transverse mode structure of guided matter waves in a confining potential with up to $65%$ of atoms in the lowest order mode. The coherence of the guided atomic de Broglie waves is demonstrated by the diffraction pattern produced when incident upon a two dimensional periodic structure. Such coherent waveguides will be important atom optic components in devices with applications such as atom holography and atom interferometry.

DOI
10.1103/physreva.81.011602

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Ultracold atoms whose de Broglie wavelength is of the same order as an extended confining potential can experience waveguiding along the potential. When the transverse kinetic energy of the atoms is sufficiently low, they can be guided in the lowest order mode of the confining potential by analogy with light guided by a single mode optical fiber. We have obtained the first images of the transverse mode structure of guided matter waves in a confining potential with up to 6565%65 of atoms in the lowest order mode. The coherence of the guided atomic de Broglie waves is demonstrated by the diffraction pattern produced when incident upon a two dimensional periodic structure. Such coherent waveguides will be important atom optic components in devices with applications such as atom holography and atom interferometry.
In direct analogy to the textbook example of light guided in a few-mode fiber (FMF), we report the observation of the first excited mode of an optically guided atomic beam. We selectively excite the atomic analog of the LP₀₁ optical mode by controlling the energy distribution of ultracold atoms loaded into the guide, resulting in a modal structure dominated by a 47(2)% population in the first excited transverse mode. The ability to guide lower-order modes has been essential to demonstrating optical effects such as multimode interferometry, slow light, and entanglement, and an atomic analog to a FMF may lead to similarly useful applications.
Atom optical analoga exist for many light-optical elements like mirrors, lenses and beam splitters. Light - or generally electromagnetic fields - and matter virtually exchange roles: Optical elements correspond to electromagnetic fields and light fields to matter waves. The goal of this thesis was to realize a de Broglie waveguide: A standing wave was generated by reflecting a laser beam on a gold coated prism surface. Near the resonance frequency of an atomic transition in metastable argon the light field exercises a dipole force, which can be described by a potential proportional to the intensity distribution of the interferece patterns of the light field. Atoms with small enough kinetic energy can be stored in the potential minima. In longitudinal direction to the standing wave the center of mass motion of these atoms is strongly confined. It is characterised by a discreet quantum mechanical mode structure where the energy distance of the indivdual motional states is big compared to their uncertainty. Transversally the atoms can virtually move freely, i.e. their mode spectrum is continual. Therefore one single potential minimum can be considered a resonator for atomic de Broglie waves and can be regarded as the atom optical analogon of a two-dimensial waveguide in light optics. A de Broglie waveguide provides a possiblity of examining a nearly two-dimensional gas of ultracold atoms in front of a surface. Moreover a continuous laser-like source of atoms may be realized on this basis.
Here we utilize the single-atom detection capability of metastable helium to measure the second-order and third-order correlation functions for ensembles of ultracold atoms. We then extend these measurements to characterize the quantum statistics of atoms guided in a dipole potential. By appropriately loading atoms into the guide we are able to populate a selected number of guided modes, ranging from the majority of atoms in the lowest order mode (a BEC), to multi-mode guiding (equivalent to a thermal source). The guided BEC was characterised by a smooth gaussian transverse spatial profile, and a second-order correlation value of unity consistent with a coherent source. For multi-mode guiding, the matter-wave equivalent of speckle was observed. Furthermore, at short arrival times, the second-order correlation function was greater than unity, corresponding to atom bunching characteristic of an incoherent (thermal) source.
We report the first realization of a guided quasicontinuous atom laser by rf outcoupling a Bose-Einstein condensate from a hybrid optomagnetic trap into a horizontal atomic waveguide. This configuration allows us to cancel the acceleration due to gravity and keep the de Broglie wavelength constant at 0.5 microm during 0.1 s of propagation. We also show that our configuration, equivalent to pigtailing an optical fiber to a (photon) semiconductor laser, ensures an intrinsically good transverse mode matching.
We study modal propagation of cold atomic gases in a straight magnetic waveguide consisting of a current wire and a uniform magnetic field. This configuration is known to generate a transverse confining potential for atoms with magnetic dipole moment oriented anti-parallel to the magnetic field. The potential has azimuthal symmetry to first order in powers of the atomic distance to the waveguide axis. We obtain the modal dispersion curves by means of the WKB quantization method, and introduce a parameter Q that characterizes symmetric atomic waveguides as the parameter V does in optical fibers. We simulate propagation of cold atomic beams by means of the BPM (Beam Propagation Method) and show the spatial evolution of transverse monomode and multimode profiles obtained for different values of Q and arbitrary input beam profiles. We demonstrate, analytically and numerically, the existence of a threshold Q-value for guidance of matter waves analogous to the V-threshold for propagation in a TE00 mode in optical fibers and obtain that, under the experimental conditions reported in the literature, the already observed Gaussian profile of guided atomic beams corresponds to multimode propagation. RIAO/OPTILAS'04.
We have developed a nozzle source that delivers a continuous beam of atomic helium or molecular hydrogen having a high degree of transverse coherence and with adequate optical brightness to enable new kinds of experiments. Using this source we have measured single slit diffraction patterns and the first ever speckle-diffraction patterns using atomic and molecular de Broglie waves. Our results suggest fruitful application of coherent matter beams in dynamic scattering and diffractive imaging at short wavelength and with extreme surface sensitivity.