  We report results from ultrafast two-color optical pump-probe spectroscopy on
bulk $\beta$-Ga$_2$O$_3$. A two-photon absorption scheme is used to photoexcite
carriers with the pump pulse and free-carrier absorption of the probe pulse is
used to record the subsequent dynamics of the photoexcited carriers. Our
results are consistent with carrier recombination via defect-assisted
processes. We also observe transient polarization-selective optical absorption
of the probe pulse by defect states under nonequilibrium conditions. A rate
equation model for electron and hole capture by defects is proposed and used to
explain the data. Whereas the rate constants for electron capture by defects
are found to be temperature-independent, they are measured to be strongly
temperature-dependent for hole capture and point to a lattice
deformation/relaxation process accompanying hole capture. Our results shed
light on the mechanisms and rates associated with carrier capture by defects in
$\beta$-Ga$_2$O$_3$.
