An Effective Field Theory for One-dimensional Polarized Fermi Gases

Brandon Anderson, Chien‐Te Wu, Rufus Boyack +1 more

Xia-Ji Liu, Hui Hu, P. D. Drummond

Stefan K. Baur, Erich J. Mueller

Ya-Dong Song, Cunxi Zhang, Yun-Qing Zhou

Erhai Zhao, W. Vincent Liu

We present a theory for a lattice array of weakly coupled one-dimensional ultracold attractive Fermi gases (1D tubes) with spin imbalance, where strong intratube quantum fluctuations invalidate mean-field theory. We first construct an effective field theory, which treats spin-charge mixing exactly, based on the Bethe ansatz solution of the 1D single tube problem. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a two-component Luttinger liquid, and its elementary excitations are fractional states carrying both charge and spin. We analyze the instability of the 1D FFLO state against intertube tunneling by renormalization group analysis, and find that it flows into either a polarized Fermi liquid or a FFLO superfluid, depending on the magnitude of interaction strength and spin imbalance. We obtain the phase diagram of the quasi-1D system and further determine the scaling of the superfluid transition temperature with intertube coupling.

Xia-Ji Liu, Hui Hu, P. D. Drummond

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.