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A Planar de Broglie Waveguide

Michael Hartl

Published Jan 1, 2000• 0 citations

Abstract

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.

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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.

We prepare a quasi-2D gas of argon atoms confined in a planar matter waveguide in close vicinity ( $<1\ensuremath{\mu}\mathrm{m}$) of a reflecting surface. The (anti-)nodes of a far off resonant standing light wave in front of the surface provide a confining potential for the atomic motion normal to the surface. A cloud of cold atoms that approaches the surface is compressed by deceleration in an evanescent field and loaded predominantly into one single potential well close to the surface by optical pumping. The spatial density achieved is more than 100 times higher than the density of the approaching atoms.

Two-dimensional systems are of great interest in physics as the celebrated quantum-Hall effects show, which are based on a 2D electron gas. Neutral systems involve thin He films and spin polarized atomic hydrogen in a cryogenic environment, where the successful creation of a 2D quasi-condensate was recently reported. Over the last years, with laser cooling and trapping techniques at hand, several schemes for the preparation of laser cooled atomic 2D gases have been proposed. Low dimensional gases are discussed as keys to achieve high density samples of purely optically cooled atoms, since the reabsorption of scattered photons is greatly suppressed compared to the situation in 3D. On the other hand, by structuring 2D waveguide light fields laterally, very versatile "integrated atom optical" elements can be realized. We have prepared a quasi-2D gas of argon atoms confined in a planar matter waveguide less than 1 /spl mu/m away from a reflecting surface. We trap metastable Ar/sup +/ atoms in the ls/sub 5/(J=2) state in a magneto-optical trap. Upon release, they fall towards a gold coated prism surface where an evanescent light field is generated by resonant excitation of surface plasmons in the gold layer. This light field is blue detuned from the 1s/sub 5//spl hArr/2p/sub 9/(J=3) transition and hence creates a repulsive potential which slows down the falling atoms.

Matter–wave interferometry dates from the inception of quantum mechanics, i.e., the early electron diffraction experiments. More recent neutron interferometry experiments have yielded new insights into many fundamental aspects of quantum mechanics. Presently, atom interferometry has been demonstrated and holds promise as a new field of optics – matter–wave optics. This field is particularly interesting since the potential sensitivity of matter–wave interferometers far exceeds that of their light-wave or ‘photon’ antecedents. In this chapter we consider the physics of light-induced forces on the center-of-mass motion of atoms and their application to atom optics (Fig. 17.1). The most obvious being the recoil associated with the emission and absorption of light. This ‘radiation pressure’ is the basis for laser induced cooling. Another very important mechanical effect is the gradient force due to, e.g., transverse variation in the laser beam. These, essentially semiclassical, forces are useful in guiding and trapping neutral atoms. After considering the basic forces which allow us to cool, guide, and trap atoms, we turn to the optics of atomic center-of-mass de Broglie waves, i.e., atom optics. In keeping with the spirit of the present text, we will focus on the quantum limits to matter–wave interferometry. An analysis of a matter–wave gyro in an obvious extension of the laser gyro and the similarity and relative merits of the two will be compared and contrasted. Finally we derive the “recoil limit” to laser cooling; and show that it is possible to supersede this limit via atomic coherence effects.

Realization of the analogues of optical components for the manipulation of atomic de Broglie waves has recently become possible through the use of laser-based techniques. The strong fields generated by laser light have already been used to reflect atoms using travelling evanescent waves, and to diffract atomic beams through small angles using transmission gratings formed by a standing laser light wave in vacuo. Present experiments aim to combine these techniques to produce a reflection diffraction grating formed by a standing evanescent laser-light field, and to exploit the larger diffraction angles made possible theoretically by such a scheme.

We prepare a quasi 2D gas of ultracold argon atoms confined in a planar matter waveguide in close vicinity (< 1µm) of a reflecting surface. The (anti-)nodes of a far off resonant standing light wave in front of the surface provide a confining potential for the atomic motion normal to the surface. A cloud of cold atom that approaches the surface is compressed by deceleration in an evanescent field and loaded predominantly into one single potential well close to the surface by optical pumping. The spatial density achieved is more than 100 times higher than the density of the approaching atoms.

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.