Generalized Kronig-Penney model for ultracold atomic quantum systems

A. Negretti, R. Gerritsma, Z. Idziaszek, F. Schmidt-Kaler, and T. Calarco
Phys. Rev. B 90, 155426 – Published 15 October 2014

Abstract

We study the properties of a quantum particle interacting with a one-dimensional structure of equidistant scattering centers. We derive an analytical expression for the dispersion relation and for the Bloch functions in the presence of both even and odd scattering waves within the pseudopotential approximation. This generalizes the well-known solid-state physics textbook result known as the Kronig-Penney model. Our generalized model can be used to describe systems such as degenerate Fermi gases interacting with ions or with another neutral atomic species confined in an optical lattice, thus enabling the investigation of polaron or Kondo physics within a simple formalism. We focus our attention on the specific atom-ion system and compare our findings with quantum defect theory. Excellent agreement is obtained within the regime of validity of the pseudopotential approximation. This enables us to derive a Bose-Hubbard Hamiltonian for a degenerate quantum Bose gas in a linear chain of ions.

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  • Received 24 June 2014
  • Revised 30 September 2014

DOI:https://doi.org/10.1103/PhysRevB.90.155426

©2014 American Physical Society

Authors & Affiliations

A. Negretti1, R. Gerritsma2, Z. Idziaszek3, F. Schmidt-Kaler2, and T. Calarco4

  • 1Zentrum für Optische Quantentechnologien and The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg
  • 2QUANTUM, Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
  • 3Faculty of Physics, University of Warsaw, PL-00-681 Warsaw, Poland
  • 4Center for Integrated Quantum Science and Technology, Institute for Complex Quantum Systems, University of Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany

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Issue

Vol. 90, Iss. 15 — 15 October 2014

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