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arXiv:1011.2944

Fractionalization in Three-Components Fermionic Atomic Gases in a One-Dimensional Optical Lattice

P. Azaria

Published Nov 12, 2010• 0 citations
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Abstract

We study a three-components fermionic gas loaded in a one-dimensional optical trap at half-filling. We find that the system is fully gapped and may order into 8 possible phases: four 2$k_F$ atomic density wave and spin-Peierls phases with all possible relative $π$ phases shifts between the three species. We find that trionic excitations are unstable toward the decay into pairs of kinks carrying a {\it fractional} number, $Q=3/2$, of atoms. These sesquions eventually condense upon small doping and are described by a Luttinger liquid. We finally discuss the phase diagram of a three component mixture made of three hyperfine level of $^6$Li as a function of magnetic field.

DOI
10.48550/arxiv.1011.2944

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We investigate the effect of the anisotropy between the sss-wave scattering lengths of a three-component atomic Fermi gas loaded into a one-dimensional optical lattice. We find four different phases which support trionic instabilities made of bound states of three fermions. These phases distinguish themselves by the relative phases between the 2kF2{k}_{F}2kF​ atomic density wave fluctuations of the three species. At small enough densities and strong anisotropies we give further evidences for a decoupling and the stabilization of more conventional BCS phases. Finally, our results are discussed in light of a recent experiment on 6Li^{6}\text{L}\text{i}6Li atoms.
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The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard model is studied in the canonical ensemble using a quantum Monte Carlo method. We focus on the case where both species have half filling in order to maximize the pairing correlations between the bosons and the fermions. In case of equal hopping we distinguish among phase separation, a Luttinger liquid phase, and a phase characterized by strong singlet pairing between the species. True long-range density waves exist with unequal hopping amplitudes.
We present a detailed study of the population imbalanced three-component Hubbard chain with attractive interactions. Such a system can be realized experimentally with three different hyperfine states of ultra cold 6^66Li atoms in an optical lattice. We find that there are different phases that compete with each other in this system: A molecular superfluid phase in which the three fermion species pair up to form molecules (trions), a usual pairing phase involving two species with exactly opposite momenta, and a more exotic generalized Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase consisting of three competing pairing tendencies with different non-zero center-of-mass momenta. At large attractive interactions the system exhibits strong tendencies towards collapse and phase separation. Employing the density-matrix-renormalization-group-method (DMRG) to determine the decay exponents of the various correlators we establish the phase diagram of this model for different fillings and interactions. We also discuss the experimentally relevant situation in a trap and report the existence of an additional region where two species are dynamically balanced.