Harmonically trapped two-atom systems: Interplay of short-range $s$-wave interaction and spin-orbit coupling

POSTER

Abstract

We investigate the interplay between the single-particle spin-orbit coupling term of Rashba type and the short-range two-body $s$-wave interaction for cold atoms under external confinement. Treating the spin-orbit term with strength $k_{so}$ perturbatively, we determine the correction to the ground state energy for various parameter combinations. We find that the interplay between the spin-orbit coupling term and the $s$-wave interaction enters, depending on the exact parameter combinations of the $s$-wave scattering lengths, at order $k_{so}^2$ or $k_{so}^4$ for the ground state and leads to a shift of the energy of either sign. Additionally, we find that, for certain parameter combinations, the spin-orbit coupling term turns sharp crossings into avoided crossings with an energy splitting proportional to $k_{so}$. Our perturbative results are confirmed by numerical calculations that expand the eigenfunctions of the two-particle Hamiltonian in terms of basis functions that contain explicitly correlated Gaussians.

Authors

  • X.Y. Yin

    Washington State University

  • William H. Dowd

    Oregon State University, University of Washington, University of Hong Kong, University of Tennessee, Oak Ridge National Laboratory, University of British Columbia, Univ of Washington, Univ of Cambridge, Michigan State University, Universit\'e de Caen, Argonne National Laboratory, Texas A\&M University -Commerce, Texas A\&M University, Department of Physics, University of Idaho, Moscow, Idaho 83844, USA, Universidad de Salamanca, E-37008 Salamanca, Spain, Department of Physics, Florida State University, Tallahassee, Florida 32306, USA, University of Cambridge, Institute of Astronomy, University of Cambridge, Canadian Institute for Theoretical Astrophysics, University of Toronto, Seoul National University, Chungnam National University, Department of Physics, Oregon State University, TRIUMF, Roosevelt High School, Department of Physics, University of Washington, Oregon State Department of Chemistry, Oregon State School of Electrical Engineering and Computer Science, Oregon State Department of Physics, University of Idaho, Lawrence Livermore National Laboratory, Idaho National Laboratory, Pacific Northwest National Laboratory, Carnegie Institution of Washington, Department of Chemistry, Oregon State University, School of Electrical Engineering and Computer Science, Oregon State University, Washington State University, Harvard University, Idaho Accelerator Center, Idaho Accelerator Center, Idaho State University, 1500 Alvin Ricken drive, Pocatello, ID 83201, USA, CENPA, University of Washington, Physics Division, ANL, NSCL, Michigan State University, Division, ANL, LPC, CAEN, France, Paul Scherrer Institute, US Geological Survey, 12201 Sunrise Valley Drive, Reston, VA, 20192, USA, University of Calgary Department of Physics and Astronomy, University of Calgary Department of Geoscience, None, University of the Fraser Valley, Univ of California, Berkeley, Simon Fraser University, Los Alamos Natl. Lab., University of Science and Technology of China, Hefei, U of Washington, Georgia Institute of Technology, Washington State Univ, National Institute of Standards and Technology and University of Maryland, American University

  • William H. Dowd

    Oregon State University, University of Washington, University of Hong Kong, University of Tennessee, Oak Ridge National Laboratory, University of British Columbia, Univ of Washington, Univ of Cambridge, Michigan State University, Universit\'e de Caen, Argonne National Laboratory, Texas A\&M University -Commerce, Texas A\&M University, Department of Physics, University of Idaho, Moscow, Idaho 83844, USA, Universidad de Salamanca, E-37008 Salamanca, Spain, Department of Physics, Florida State University, Tallahassee, Florida 32306, USA, University of Cambridge, Institute of Astronomy, University of Cambridge, Canadian Institute for Theoretical Astrophysics, University of Toronto, Seoul National University, Chungnam National University, Department of Physics, Oregon State University, TRIUMF, Roosevelt High School, Department of Physics, University of Washington, Oregon State Department of Chemistry, Oregon State School of Electrical Engineering and Computer Science, Oregon State Department of Physics, University of Idaho, Lawrence Livermore National Laboratory, Idaho National Laboratory, Pacific Northwest National Laboratory, Carnegie Institution of Washington, Department of Chemistry, Oregon State University, School of Electrical Engineering and Computer Science, Oregon State University, Washington State University, Harvard University, Idaho Accelerator Center, Idaho Accelerator Center, Idaho State University, 1500 Alvin Ricken drive, Pocatello, ID 83201, USA, CENPA, University of Washington, Physics Division, ANL, NSCL, Michigan State University, Division, ANL, LPC, CAEN, France, Paul Scherrer Institute, US Geological Survey, 12201 Sunrise Valley Drive, Reston, VA, 20192, USA, University of Calgary Department of Physics and Astronomy, University of Calgary Department of Geoscience, None, University of the Fraser Valley, Univ of California, Berkeley, Simon Fraser University, Los Alamos Natl. Lab., University of Science and Technology of China, Hefei, U of Washington, Georgia Institute of Technology, Washington State Univ, National Institute of Standards and Technology and University of Maryland, American University