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Title: Stability of spinor Fermi gases in tight waveguides

Abstract

The two- and three-body correlation functions of the ground state of an optically trapped ultracold spin-(1/2) Fermi gas (SFG) in a tight waveguide [one-dimensional (1D) regime] are calculated in the plane of even- and odd-wave coupling constants, assuming a 1D attractive zero-range odd-wave interaction induced by a 3D p-wave Feshbach resonance, as well as the usual repulsive zero-range even-wave interaction stemming from 3D s-wave scattering. The calculations are based on the exact mapping from the SFG to a 'Lieb-Liniger-Heisenberg' model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, and indicate that the SFG should be stable against three-body recombination in a large region of the coupling constant plane encompassing parts of both the ferromagnetic and antiferromagnetic phases. However, the limiting case of the fermionic Tonks-Girardeau gas, a spin-aligned 1D Fermi gas with infinitely attractive p-wave interactions, is unstable in this sense. Effects due to the dipolar interaction and a Zeeman term due to a resonance-generating magnetic field do not lead to shrinkage of the region of stability of the SFG.

Authors:
;  [1];  [2]
  1. Departamento de Quimica-Fisica, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao (Spain)
  2. College of Optical Sciences, University of Arizona, Tucson, Arizona 85721 (United States)
Publication Date:
OSTI Identifier:
21011284
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 76; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.76.013615; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANTIFERROMAGNETISM; CORRELATION FUNCTIONS; COUPLING CONSTANTS; FERMI GAS; FERMIONS; GROUND STATES; HEISENBERG MODEL; J-J COUPLING; MAGNETIC FIELDS; MESONS; P WAVES; S WAVES; SPIN; STABILITY; TEMPERATURE RANGE 0000-0013 K; THREE-BODY PROBLEM; WAVEGUIDES; ZEEMAN EFFECT

Citation Formats

Campo, A. del, Muga, J. G., and Girardeau, M. D. Stability of spinor Fermi gases in tight waveguides. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.76.013615.
Campo, A. del, Muga, J. G., & Girardeau, M. D. Stability of spinor Fermi gases in tight waveguides. United States. doi:10.1103/PHYSREVA.76.013615.
Campo, A. del, Muga, J. G., and Girardeau, M. D. 2007. "Stability of spinor Fermi gases in tight waveguides". United States. doi:10.1103/PHYSREVA.76.013615.
@article{osti_21011284,
title = {Stability of spinor Fermi gases in tight waveguides},
author = {Campo, A. del and Muga, J. G. and Girardeau, M. D.},
abstractNote = {The two- and three-body correlation functions of the ground state of an optically trapped ultracold spin-(1/2) Fermi gas (SFG) in a tight waveguide [one-dimensional (1D) regime] are calculated in the plane of even- and odd-wave coupling constants, assuming a 1D attractive zero-range odd-wave interaction induced by a 3D p-wave Feshbach resonance, as well as the usual repulsive zero-range even-wave interaction stemming from 3D s-wave scattering. The calculations are based on the exact mapping from the SFG to a 'Lieb-Liniger-Heisenberg' model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, and indicate that the SFG should be stable against three-body recombination in a large region of the coupling constant plane encompassing parts of both the ferromagnetic and antiferromagnetic phases. However, the limiting case of the fermionic Tonks-Girardeau gas, a spin-aligned 1D Fermi gas with infinitely attractive p-wave interactions, is unstable in this sense. Effects due to the dipolar interaction and a Zeeman term due to a resonance-generating magnetic field do not lead to shrinkage of the region of stability of the SFG.},
doi = {10.1103/PHYSREVA.76.013615},
journal = {Physical Review. A},
number = 1,
volume = 76,
place = {United States},
year = 2007,
month = 7
}
  • Divergence-free pseudo-potentials for spatially even- and odd-wave interactions in spinor Fermi gases in tight atom waveguides are derived. The Fermi-Bose mapping method is used to relate the effectively one-dimensional fermionic many-body problem to that of a spinor Bose gas. Depending on the relative magnitudes of the even- and odd-wave interactions, the N-atom ground state may have total spin S=0, S=N/2, and possibly also intermediate values, the case S=N/2 applying near a p-wave Feshbach resonance, where the N-fermion ground state is space-antisymmetric and spin-symmetric. In this case the fermionic ground state maps to the spinless bosonic Lieb-Liniger gas. An external magneticmore » field with a longitudinal gradient causes a Stern-Gerlach spatial separation of the corresponding trapped Fermi gas with respect to various values of S{sub z}.« less
  • The ground and excited states of a one-dimensional (1D) spin-(1/2) Fermi gas (SFG) with both attractive zero-range odd-wave interactions and repulsive zero-range even-wave interactions are mapped exactly to a 1D Lieb-Liniger-Heisenberg (LLH) model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, such that the complete SFG and LLH energy spectra are identical. The ground state in the ferromagnetic phase is given exactly by the Lieb-Liniger (LL) Bethe ansatz, and that in the antiferromagnetic phase by a variational method combining Bethe ansatz solutions of the LL and 1D Heisenberg models. There are excitation branches corresponding to LL type I andmore » II phonons and spin waves, the latter behaving quadratically for small wave numbers in the ferromagnetic phase and linearly in the antiferromagnetic phase.« less
  • We present an exact analytical solution of the fundamental systems of quasi-one-dimensional spin-1/2 fermions with infinite repulsion for an arbitrary confining potential. The eigenfunctions are constructed by the combination of Girardeau's hard-core contacting boundary condition and group theoretical method, which guarantees the obtained states to be simultaneously the eigenstates of S and S{sub z} and satisfy antisymmetry under odd permutation. We show that the total ground-state density profile behaves like the polarized noninteracting fermions, whereas the spin-dependent densities display different properties for different spin configurations. We also discuss the splitting of the ground states for large but finite repulsion.
  • The Fermi-Bose mapping method for one-dimensional Bose and Fermi gases with zero-range interactions is generalized to an anyon-fermion mapping and applied to exact solution of several models of ultracold gases with anyonic exchange symmetry in tight waveguides: anyonic Calogero-Sutherland model, anyons with point hard-core interaction (anyonic Tonks-Girardeau gas), and spin-aligned anyon gas with infinite zero-range odd-wave attractions (attractive anyonic Tonks-Girardeau, or AATG, gas). It is proved that for even N{>=}4 there are states of the AATG gas on A, with anyonic phase slips which are odd integral multiples of {pi}/(N-1), of energy lower than that of the corresponding fermionic groundmore » state. A generalization to a spinor Fermi gas state with anyonic symmetry under purely spatial exchange enables energy lowering by the same mechanism.« less
  • The compensation of quadratic Zeeman effect and trap energy in high-spin fermions is shown to lead to resonances in the spin-changing collisions that are typically absent in spinor condensates and spin-1/2 fermions. We study these resonances in lattice fermions, showing that they permit the targeting of a particular spin-changing channel while suppressing the rest and the creation of magnetically insensitive superpositions of many-body states with entangled spin and trap degrees of freedom. Finally, the intersite tunneling may lead to a quantum phase transition described by a quantum Ising model.