Abstract

Classically, rigid objects with elongated shapes can fit through apertures only when properly aligned. Quantum-mechanical particles which have internal structure (e.g. a diatomic molecule) also are affected during attempts to pass through small apertures, but there are interesting differences with classical structured particles. We illustrate here some of these differences for ultra-slow particles. Notably, we predict resonances that correspond to prolonged delays of the rotor within the aperture—a trapping phenomenon not found classically.

Highlights

  • Continued advances in cold-atom technology have opened new opportunities for studying the influence of internal structure upon the scattering of particles

  • Three such advances come to mind here: The formation of cold molecules from a Bose–Einstein condensate [33] or Fermi gas [36], the observation of the eclipse effect [23] in the scattering of helium clusters by a grating [37], and the creation of an Efimov state [8] in collisions between cold atoms of cesium [39] and potassium [19, 61]

  • In the present paper we investigate the scattering of slow structured particles from an aperture in a thin screen

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Summary

27 January 2015

11, D-89069 Ulm, Germany and Texas A&M University Institute for Advanced Study (TIAS), Institute for Quantum Science and may be used under the Engineering (IQSE) and Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA terms of the Creative. Quantum-mechanical particles which have internal structure (e.g. a diatomic molecule) are affected during attempts to pass through small apertures, but there are interesting differences with classical structured particles. We illustrate here some of these differences for ultra-slow particles. We predict resonances that correspond to prolonged delays of the rotor within the aperture—a trapping phenomenon not found classically

Introduction
Classical elongated particles
Classical constraints
Quantum particles with internal structure
The quantum Hamiltonian
Mode-decoupling approximation
The scattering equations
Energies below the barrier height: trapping and resonances
Outlook and conclusions
Energy requirements
Entanglement between rotation and translation
Transformation to algebraic equations

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