Theory of quasi-one dimensional imbalanced Fermi gases

Details Theory of quasi-one dimensional imbalanced Fermi gases Theory of quasi-one dimensional imbalanced Fermi gases

2008-04-28

arxiv.org/abs/0804.4461v2

Phys. Rev. A 78, 063605 (2008)

Physics

Condensed Matter

Other Condensed Matter

new expanded version, 8 pages, updated references

Scientific paper

10.1103/PhysRevA.78.063605

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 inter-tube 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.

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