Time of flight observables and the formation of Mott domains of fermions and bosons on optical lattices

TL;DR

This paper uses quantum Monte Carlo simulations to identify energetic signatures of Mott domain formation in fermions and bosons on optical lattices, providing insights relevant for experimental detection of quantum phase transitions.

Contribution

It demonstrates that energy derivatives can signal Mott transitions in trapped fermions and bosons, linking theoretical predictions with experimental observables.

Findings

Minima in energy sums indicate Mott domain formation.

Energy derivatives show clear signatures of the Mott transition.

Results support detection of metal--Mott-insulator transition in experiments.

Abstract

We study, using quantum Monte Carlo simulations, the energetics of the formation of Mott domains of fermions and bosons trapped on one-dimensional lattices. We show that, in both cases, the sum of kinetic and interaction energies exhibits minima when Mott domains appear in the trap. In addition, we examine the derivatives of the kinetic and interaction energies, and of their sum, which display clear signatures of the Mott transition. We discuss the relevance of these findings to time-of-flight experiments that could allow the detection of the metal--Mott-insulator transition in confined fermions on optical lattices, and support established results on the superfluid--Mott-insulator transition in confined bosons on optical lattices.