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

TL;DR

This paper investigates a three-component fermionic gas in a one-dimensional optical lattice, revealing a fully gapped system with multiple ordered phases and fractional excitations that condense into a Luttinger liquid upon doping.

Contribution

It introduces the concept of sesquions as fractional excitations in a three-component fermionic system and analyzes their behavior and phase diagram.

Findings

System is fully gapped with 8 possible ordered phases.

Trionic excitations decay into fractionalized pairs called sesquions.

Sesquions condense into a Luttinger liquid upon doping.

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 $\pi$ 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.