Signature of Mott-insulator transition with ultra-cold fermions in a one-dimensional optical lattice

TL;DR

This paper demonstrates how collective oscillations in ultra-cold fermions in a 1D optical lattice can serve as a signature of the Mott-insulator transition, supported by theoretical analysis and a proposed experimental setup.

Contribution

It introduces a method to identify the Mott-insulator transition through collective mode signatures in ultra-cold fermionic systems, combining Bethe ansatz and Luttinger liquid theory.

Findings

Collective oscillations change across the phase transition.

A phase diagram is established based on filling factor and interaction strength.

Experimental implementation for detecting the transition is proposed.

Abstract

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultra-cold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.