  We investigate the time-dependent nonlinear optical absorption of a clay
dispersion (Laponite) in organic dye (Rhodamine B) water solution displaying
liquid-arrested state transition. Specifically, we determine the characteristic
time $\tau_D$ of the nonlinear susceptibility build-up due as to the Soret
effect. By comparing $\tau_D$ with the relaxation time provided by standard
dynamic light scattering measurements we report on the decoupling of the two
collective diffusion times at the two very different length scales during the
aging of the out-of-equilibrium system. With this demonstration experiment we
also show the potentiality of nonlinear optics measurements in the study of the
late stage of arrest in soft materials.
