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Related Experiment Videos

Levinson-like theorem for scattering from a Bose-Einstein condensate.

J Brand1, I Häring, J-M Rost

  • 1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.

Physical Review Letters
|August 26, 2003
PubMed
Summary

This study derives an exact relation between bound excitations in atomic Bose-Einstein condensates and atom scattering phase shifts. This finding generalizes Levinson

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Area of Science:

  • Atomic, Molecular, and Optical Physics
  • Quantum Many-Body Systems
  • Condensed Matter Theory

Background:

  • Bose-Einstein condensates (BECs) are quantum states of matter.
  • Understanding elementary excitations is key to BEC properties.
  • Scattering phase shifts reveal interaction details.

Purpose of the Study:

  • To derive a quantitative relation between bound excitations and scattering phase shifts in atomic BECs.
  • To generalize Levinson's theorem to the context of weakly interacting Bose gases.
  • To explore the implications of the Bogoliubov model for these phenomena.

Main Methods:

  • Derivation of a theoretical relation within the Bogoliubov model.
  • Analysis of elastic scattering of atoms.

Related Experiment Videos

  • Application to weakly interacting Bose gases.

    • Main Results:

    • An exact relation is established between the number of bound elementary excitations and the phase shift of elastically scattered atoms.
    • The derived relation is shown to be a generalization of Levinson's theorem for the Bogoliubov model.
    • Specific features of the Bogoliubov model, including complex energy and continuum bound states, are discussed.

    Conclusions:

    • The established relation provides a new tool for analyzing excitations in BECs.
    • The generalization of Levinson's theorem offers deeper insights into scattering properties.
    • The study highlights the utility of the Bogoliubov model for describing these quantum phenomena.