  Femtosecond pump-probe measurements find pronounced dimensionality dependence
of the optical nonlinearity in cuprates. Although the coherent two-photon
absorption (TPA) and linear absorption bands nearly overlap in both quasi-one
and two-dimensional (1D and 2D) cuprates, the TPA coefficient is one order of
magnitude smaller in 2D than in 1D. Furthermore, picosecond recovery of optical
transparency is observed in 1D cuprates, while the recovery in 2D involves
relaxation channels with a time scales of tens of picoseconds. The experimental
results are interpreted within the two-band extended Hubbard model.
