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Bulletin of the American Physical Society

Matter-wave diffraction at the natural limit

Christian Brand, Michele Sclafani, Christian Knobloch, Yigal Lilach, Thomas Juffmann, Jani Kotakoski, Clemens Mangler, Andreas Winter, Andrey Turchanin, Jannik C. Meyer, Ori Cheshnovsky, Markus Arndt

Published May 26, 2016• 0 citations
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We report adjustable magnetic `bouncing' and focusing of a dilute 87^{87}87Rb Bose gas. Both the condensate production and manipulation are realised using a particularly straight-forward apparatus. The bouncing region is comprised of approximately concentric ellipsoidal magnetic equipotentials with a centre that can be adjusted vertically. We extend, and discuss the limitations of, simple Thomas-Fermi and Monte-Carlo theoretical models for the bouncing, which at present find close agreement with the condensate's evolution. Very strong focusing has been inferred and the observation of atomic matter-wave diffraction should be possible. Prospects look bright for applications in matter-wave atom-optics, due to the very smooth nature of the mirror.
Diffraction of a de Broglie matter wave by a system of two pinholes on an optical axis exhibits the multifocal focusing effect of matter waves in the near-field (Fresnel zone). The focusing, defocusing and refocusing phenomenon results from periodic phase changes at singular points, which are observed for the even Fresnel numbers, where the intensity is zero and the phase is undefined. As an on-axis observation point passes through a singular point, the nature of the wave in the neighborhood of the axis changes from that of a diverging wave to that of a converging wave, i.e., the wave refocuses. The amplitudes of the oscillations in the intensity and phase of the de Broglie wave depend on the ratio of the radii of the two apertures in the system. This effect of diffractive multifocal focusing of de Broglie waves can be used for designing a diffractive lens for matter-wave beams.
De Broglie proposed the matter wave in 1924. The de Broglie wave is neither a mechanical wave nor an electromagnetic wave and has a very short wavelength. The Davisson-Germer electron diffraction experiment performed in 1925 involved bombarding the surface of a nickel crystal with a narrow beam of electrons. When the accelerating voltage V was maintained at 54 V, the wavelength of the incident electron was λ=h/ 2 m e V = 0.167 nm [Y. S. Chen and Z. Z. Li, College Physics (Tianjin University, Tianjin, 1999)] demonstrating the existence of the matter wave. We introduce a type of electron wave with a very long wavelength in this study that is different from the matter wave. For example, the wavelength of the electron wave can reach 0.43 mm in the double-slit interference of electrons. Experiments demonstrate that this long-wavelength electron wave can produce both double-slit interference and electron diffraction. A comparative analysis of matter and electron waves reveals the physical natures of these waves and wave‐particle duality.