Probing the Flat Band of Optically-Trapped Spin-Orbital Coupled Bose Gases Using Bragg Spectroscopy

TL;DR

This paper demonstrates how Bragg spectroscopy can be used to detect the transition from an ordinary band to a flat band in spin-orbital coupled Bose gases by observing changes in the excitation spectrum.

Contribution

It introduces a method to directly probe flat bands in ultracold atomic systems through Bragg spectroscopy by analyzing the excitation spectrum and dynamic structure factor.

Findings

Quadratic dispersion appears in flat bands with infinite effective mass.

Linear dispersion characterizes ordinary bands.

The transition from linear to quadratic dispersion indicates the emergence of a flat band.

Abstract

Motivated by the recent efforts in creating the flat band in ultracold atomic systems, we investigate how to probe the flat band in an optically-trapped spin-orbital coupled Bose-Einstein condensate using Bragg spectroscopy. We have found that the excitation spectrum and the dynamic structure factor of the condensate alter dramatically, when the band structure exhibits various level of flatness. In particular, when the band exhibits perfect flatness around the band minima corresponding to a near infinite effective mass, a quadratic dispersion emerges in the low-energy excitation spectrum; in sharp contrast, for the opposite case when an ordinary band is present, the familiar linear dispersion arises. Such linear-to-quadratic crossover in the energy spectrum presents a striking manifestation of the transition of an ordinary band into a flat band, thereby allows the direct probe of the flat band by using Bragg spectroscopy.