Theoretical Analysis on Spectroscopy of Atomic Bose-Hubbard Systems

TL;DR

This paper introduces a numerical sum rule-based method to analyze microwave and laser spectra of ultracold bosonic atoms in optical lattices at finite temperatures, explaining spectral features and broadening mechanisms.

Contribution

It develops a two-mode approximation combined with the Gutzwiller method to accurately compute finite-temperature spectra, capturing multi-peak structures and thermal effects.

Findings

Spectral broadening relates to atom number fluctuations and quantum hopping.

The method reproduces experimental spectral features.

Spectra of superfluid and normal states can be analyzed separately.

Abstract

We provide a numerical method to calculate comprehensively the microwave and the laser spectra of ultracold bosonic atoms in optical lattices at finite temperatures. Our formulation is built up with the sum rules, up to the second order, derived from the general principle of spectroscopy. The sum rule approach allows us to discuss the physical origins of a spectral peak shift and also a peak broadening. We find that a spectral broadening of superfluid atoms can be determined from number fluctuations of atoms, while that of normal-state atoms is mainly attributed to quantum fluctuations resulting from hopping of atoms. To calculate spectra at finite temperatures, based on the sum rule approach, we provide a two-mode approximation assuming that spectra of the superfluid and normal state atoms can be calculated separately. Our method can properly deal with multi-peak structures of spectra resulting from thermal fluctuations and also coexisting of the superfluid and the normal states. By combining the two-mode approximation with a finite temperature Gutzwiller approximation, we calculate spectra at finite temperatures by considering realistic systems, and the calculated spectra show nice agreements with those in experiments.