One-dimensional Fermi gas with a single impurity in a harmonic trap: Perturbative description of the upper branch

POSTER

Abstract

The transition from ``few to many'' has recently been probed experimentally in an ultracold harmonically confined one-dimensional lithium gas, in which a single impurity atom interacts with a background gas consisting of one, two, or more identical fermions [A. N. Wenz {\em{et al.}}, Science {\bf{342}}, 457 (2013)]. For repulsive interactions between the background or majority atoms and the impurity, the interaction energy for relatively moderate system sizes was analyzed and found to converge toward the corresponding expression for an infinitely large Fermi gas. Motivated by these experimental results, we apply perturbative techniques to determine the interaction energy for weak and strong coupling strengths and derive approximate descriptions for the interaction energy for repulsive interactions with varying strength between the impurity and the majority atoms and any number of majority atoms.

Authors

  • Seyed Ebrahim Gharashi

    Washington State University

  • Bethany Mathews

    International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore, India, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam-Golm, Germany, Univ of Idaho, Washington State University, University of California Berkeley, University of British Columbia, Max Planck Institute for Solid State Research and Ecole Polytechnique F\'ed\'erale de Lausanne, Max Planck Institute for Solid State Research, University of British Columbia and Max Planck Institute for Solid State Research, Physikalisches Institut, Ruprecht-Karls-Universitaet Heidelberg, Univ of Oregon, Whitman College, The University of British Columbia, Durham University, Universit\"at Freiburg, Institute for Nuclear Theory, University of Washington, National Renewable Energy Laboratory, Golden, CO 80401, Los Alamos National Laboratory, Oregon State University

  • Bethany Mathews

    International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore, India, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam-Golm, Germany, Univ of Idaho, Washington State University, University of California Berkeley, University of British Columbia, Max Planck Institute for Solid State Research and Ecole Polytechnique F\'ed\'erale de Lausanne, Max Planck Institute for Solid State Research, University of British Columbia and Max Planck Institute for Solid State Research, Physikalisches Institut, Ruprecht-Karls-Universitaet Heidelberg, Univ of Oregon, Whitman College, The University of British Columbia, Durham University, Universit\"at Freiburg, Institute for Nuclear Theory, University of Washington, National Renewable Energy Laboratory, Golden, CO 80401, Los Alamos National Laboratory, Oregon State University

  • Bethany Mathews

    International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore, India, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam-Golm, Germany, Univ of Idaho, Washington State University, University of California Berkeley, University of British Columbia, Max Planck Institute for Solid State Research and Ecole Polytechnique F\'ed\'erale de Lausanne, Max Planck Institute for Solid State Research, University of British Columbia and Max Planck Institute for Solid State Research, Physikalisches Institut, Ruprecht-Karls-Universitaet Heidelberg, Univ of Oregon, Whitman College, The University of British Columbia, Durham University, Universit\"at Freiburg, Institute for Nuclear Theory, University of Washington, National Renewable Energy Laboratory, Golden, CO 80401, Los Alamos National Laboratory, Oregon State University