Dynamic structure factor of ultracold Bose and Fermi gases in optical lattices

TL;DR

This paper studies the dynamic structure factor of ultracold Bose and Fermi gases in one-dimensional optical lattices at zero temperature, revealing signatures of quantum phase transitions and differences between bosonic and fermionic systems.

Contribution

It provides an exact numerical analysis of the dynamic structure factor across quantum phase transitions in lattice gases, highlighting experimental signatures and system differences.

Findings

Characteristic signatures of quantum phases in S(k,omega)

Centroid of strength distribution estimates excitation gaps

Differences in excitation gap origins between bosons and fermions

Abstract

We investigate the dynamic structure factor of atomic Bose and Fermi gases in one-dimensional optical lattices at zero temperature. The focus is on the generic behaviour of S(k,omega) as function of filling and interaction strength with the aim of identifying possible experimental signatures for the different quantum phase transitions. We employ the Hubbard or Bose-Hubbard model and solve the eigenvalue problem of the Hamiltonian exactly for moderate lattice sizes. This allows us to determine the dynamic structure factor and other observables directly in the phase transition regime, where approximation schemes are generally not applicable. We discuss the characteristic signatures of the various quantum phases appearing in the dynamic structure factor and illustrate that the centroid of the strength distribution can be used to estimate the relevant excitation gaps. Employing sum rules, these quantities can be evaluated using ground state expectation values only. Important differences between bosonic and fermionic systems are observed, e.g., regarding the origin of the excitation gap in the Mott-insulator phase.