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Physical Review Letters

Two-dimesional atomic crystal bound by light

Andreas Hemmerich, Theodor W. Hänsch

Published Jan 25, 1993• 226 citations
Publisher

Abstract

We have observed the vibrational levels of rubidium atoms spatially confined in two dimensions by two crossed optical standing waves (oriented along the x and y axes) with mutually orthogonal linear polarization (in the x-y plane). When the two standing waves oscillate with a 90\ifmmode^\circ\else\textdegree\fi{} time phase delay, the atoms are confined by dipole forces to the intensity maxima forming a two-dimensional collimated array of linear de Broglie waveguides, spaced by half an optical wavelength. When the standing waves oscillate in phase no vibrational energy structure can be observed.

DOI
10.1103/physrevlett.70.410

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We have observed the vibrational levels of rubidium atoms spatially confined in two dimensions by two crossed optical standing waves (oriented along the x and y axes) with mutually orthogonal linear polarization (in the x-y plane). When the two standing waves oscillate with a 90\ifmmode^\circ\else\textdegree\fi{} time phase delay, the atoms are confined by dipole forces to the intensity maxima forming a two-dimensional collimated array of linear de Broglie waveguides, spaced by half an optical wavelength. When the standing waves oscillate in phase no vibrational energy structure can be observed.
We have observed quantized motion of rubidium atoms spatially confined by dipole forces inside microscopic light traps. A cubic lattice of such traps is formed by three mutually orthogonal standing waves. We compare 2D and 3D confinement in the same experiment by observing the absorption of a weak probe laser beam. In both cases we observe Raman transitions between vibrational levels and a central Rayleigh resonance. When we switch to 3D confinement the line width of this Rayleigh resonance dramatically decreases to values below 1 kHz.
We have experimentally studied the interaction of a collimated thermal rubidium beam with a two-dimensional intense standing wave generated in the intersection area of the TEM00{\mathrm{TEM}}_{00}TEM00​ modes of two mutually orthogonal linear optical resonators. The relative time-phase difference of the two resonator modes was controlled. We observe transverse confinement of the atoms in the node or antinode structure of the standing wave and a deflection of the atoms after their passage through the light field. In both cases the time-phase difference can be identified as an important parameter for the kinematics of the interaction process between atoms and standing waves. Our experimental data are in qualitative agreement with the results of a Monte Carlo simulation based on a two-level atom.
We have studied Raman transitions between vibrational levels of atoms confined in the antinodes of a two-dimensional (2D) optical standing wave by means of dipole forces. These transitions are excited by the cooperation of the confining 2D field, with a weak probe laser beam directed through the atomic sample. We experimentally find that the relative line strengths corresponding to transitions from the vibrational ground state to the first and second excited states depend on the polarization of the probe beam. The excitation mechanism is based on a time-modulated distortion of the potential wells. We discuss how the spatial geometry of this distortion depends on the probe polarization, thus qualitatively explaining the experimental observations.
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.