  We studied the ultrafast third-order optical nonlinearity in a single crystal
of multiferroic bismuth ferrite (BiFeO3) in the near-infrared range of 0.5-1.0
eV, where the material is fundamentally transparent,at room temperature. With
pump pulses at 1.55 eV, which is off-resonant to the strong inter-band charge
transfer (CT) transition, we observed instantaneous transient absorption with
pencil-like temporal profile originating from the two-photon CT transition from
the oxygen 2p to the iron 3p levels. In contrast, under pumping with 3.10-eV
photons, the pencil-like absorption change was not observed but decay profiles
showed longer time constants. Although the two-photon absorption coefficient is
estimated to be 1.5 cm/GW, which is ten (hundred) times smaller than that of
two(one)-dimensional cuprates, it is larger than those of common semiconductors
such as ZnSe and GaAs at the optical communication wavelength.
