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Miroirs de Bragg pour ondes de matière et apport de la supersymétrie aux potentiels exponentiels

Charlotte Fabre 1 
1 Atomes Froids (LCAR)
LCAR - Laboratoire Collisions Agrégats Réactivité
Abstract : This manuscript contains two parts, both of them dealing with the scattering of guided matter waves on engineered potentials. The first part demonstrates the experimental realization of a Bragg mirror for matter waves. We describe the experimental setup that produces Bose-Einstein condensates (BECs) in a crossed optical dipole trap. We explain how the BEC is outcoupled in an optical wave guide and set in motion. The optical lattice on which the BEC scatters and its characteristics are subsequently detailed. We discuss the processes involved in a scattering event and the role played by the envelope of the lattice. Depending on the lattice depth, we observe the reflection of different velocity classes of the incoming wave packet. These phenomena are reminiscent of the physics involved in optical dielectric mirrors. In the second part, we report the theoretical study of matter wave scattering on potentials having exponential shapes. The spectrum and the scattering states are derived analytically. We then apply the formalism of the supersymmetry in quantum mechanics in order to generate the corresponding family of isospectral potentials. Furthermore, we use those the exact solutions to test the accuracy of different approximations schemes used in quantum mechanics (semi-classical approximations and variational method).
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Submitted on : Wednesday, November 7, 2012 - 8:01:41 PM
Last modification on : Monday, July 4, 2022 - 9:03:37 AM
Long-term archiving on: : Saturday, December 17, 2016 - 8:22:53 AM


  • HAL Id : tel-00749622, version 1


Charlotte Fabre. Miroirs de Bragg pour ondes de matière et apport de la supersymétrie aux potentiels exponentiels. Physique Atomique [physics.atom-ph]. Université Paul Sabatier - Toulouse III, 2012. Français. ⟨tel-00749622⟩



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