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

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.