Fulde-Ferrell-Larkin-Ovchinnikov states in one-dimensional spin-polarized ultracold atomic Fermi gases

Xia-Ji Liu, Hui Hu, and Peter D. Drummond
Phys. Rev. A 76, 043605 – Published 4 October 2007

Abstract

We present a systematic study of quantum phases in a one-dimensional spin-polarized Fermi gas. Three comparative theoretical methods are used to explore the phase diagram at zero temperature: the mean-field theory with either an order parameter in a single-plane-wave form or a self-consistently determined order parameter using the Bogoliubov–de Gennes equations, as well as the exact Bethe ansatz method. We find that a spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase, which lies between the fully paired Bardeen-Cooper-Schrieffer (BCS) state and the fully polarized normal state, dominates most of the phase diagram of a uniform gas. The phase transition from the BCS state to the Fulde-Ferrell-Larkin-Ovchinnikov phase is of second order, and therefore there are no phase separation states in one-dimensional homogeneous polarized gases. This is in sharp contrast to the three-dimensional situation, where a phase separation regime is predicted to occupy a very large space in the phase diagram. We conjecture that the prediction of the dominance of the phase separation phases in three dimension could be an artifact of the non-self-consistent mean-field approximation, which is heavily used in the study of three-dimensional polarized Fermi gases. We consider also the effect of a harmonic trapping potential on the phase diagram, and find that in this case the trap generally leads to phase separation, in accord with the experimental observations for a trapped gas in three dimensions. We finally investigate the local fermionic density of states of the Fulde-Ferrell-Larkin-Ovchinnikov ansatz. A two-energy-gap structure appears, which could be used as an experimental probe of the Fulde-Ferrell-Larkin-Ovchinnikov states.

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  • Received 27 July 2007

DOI:https://doi.org/10.1103/PhysRevA.76.043605

©2007 American Physical Society

Authors & Affiliations

Xia-Ji Liu1,2, Hui Hu1,2, and Peter D. Drummond1

  • 1ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Queensland 4072, Australia
  • 2Department of Physics, Renmin University of China, Beijing 100872, China

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Vol. 76, Iss. 4 — October 2007

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