Fig. 3: High-order Bragg spectra.

a Second- and third-order Bragg diffractions correspond to the stimulated four- (I) and six-photon (II) processes with the momentum transfers ħq = 4ħk and 6ħk, respectively. Typical absorption images are taken after the 1 ms Bragg pulse and 22 ms time-of-flight, and about 10% atoms are coupled to the high-momentum states. b, c Diffracted faction of atoms as a function of frequency shift ∆ω normalized to the frequency difference ħq2/(2m) in the noninteracting limit. The resonance shift is determined by a Gaussian fit to the data (solid lines). Error bars denote the standard errors. In all panels, the scattering length is fixed at a = 3 a0