  We investigate the interaction between a single mode light field and an
elongated cigar shaped Bose-Einstein condensate (BEC), subject to a temporal
modulation of the trap frequency in the tight confinement direction. Under
appropriate conditions, the longitudinal sound like waves (Faraday waves) in
the direction of weak confinement acts as a dynamic diffraction grating for the
incident light field analogous to the acousto-optic effect in classical optics.
The change in the refractive index due to the periodic modulation of the BEC
density is responsible for the acousto-optic effect. The dynamics is
characterised by Bragg scattering of light fom the matter wave Faraday grating
and simultaneous Bragg scattering of the condensate atoms from the optical
grating formed due to the interference between the incident light and the
diffracted light fields. Varying the intensity of the incident laser beam we
observe the transition from the acousto-optic effect regime to the atomic Bragg
scattering regime, where Rabi oscillations between two momentum levels of the
atoms are observed. We show that the acousto-optic effect is reduced as the
atomic interaction is increased.
