Temperature-dependent excitation spectra of ultra-cold bosons in optical lattices

TL;DR

This study investigates how temperature affects the excitation spectra of ultra-cold bosons in optical lattices, revealing that sharp spectral peaks are not always reliable indicators of superfluidity, especially in 2D systems at finite temperatures.

Contribution

The paper introduces a combined Bogoliubov and quantum rotor approach to analyze the spectral function at various temperatures, highlighting differences between 2D and 3D systems.

Findings

Sharp peaks in spectral function persist in 2D at T>0 despite vanishing condensate.

No such sharp features are observed in 3D lattices at finite temperature.

Temperature influences the spectral signatures of superfluidity in optical lattice systems.

Abstract

Trapping ultra-cold atoms in optical lattices provides a unique environment for investigating quantum phase transitions between strongly correlated superfluid and Mott insulator phases. One of the major complications in the analysis of experiments is establishing of criteria for identifying the superfluid phase. Sharp features occurring while entering ordered state have been recognized as a signature of superfluidity. In the present work it is shown that sharp peaks are not necessarily a reliable diagnostic of phase coherence in these systems. Using the combined Bogoliubov method and the quantum rotor approach for phase variables, we calculate the momentum and energy-resolved single-particle spectral function $A(\mathbf{k}\omega)$ at arbitrary temperature $T$ and its shape in the presence of the superfluid phase. We find that in the two-dimensional system even at $T>0$, where condensate fraction vanishes, the remnants of the sharp coherence peak in $A(\mathbf{k}\omega)$ are present. In contrast, such a feature is not observed for the bosons loaded in the three-dimensional lattice.