  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.
