# 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:

- Departamento de Quimica-Fisica, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao (Spain)
- 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. Sun .
"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 = {Sun Jul 15 00:00:00 EDT 2007},

month = {Sun Jul 15 00:00:00 EDT 2007}

}