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$_3$.
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