  Numbers of tabletop experiments have made efforts to detect large extra
dimensions for the range from solar system to submillimeter system, but the
direct evidence is still lacking. Here we present a scheme to test the
gravitational law in 4+2 dimensions at microns by using cavity optomechanical
method. We have investigated the probe spectrum for coupled quantum levitated
oscillators in optical cavities. The results show that the spectral splitting
can be obtained once the large extra dimensions present. Compare to the
previous experiment, the sensitivity can be improved by the using of a specific
geometry and a shield mirror to control and suppress the effect of the Casimir
background. The weak frequency splitting can be optically read by the
pump-probe scheme. Thus we can detect the gravitational deviation in the bulk
based ADD model via spectroscopy without the isoelectronic technique.
