  Point defects in crystalline materials often occur in multiple charge states.
Although many experimental methods to study and explore point defects are
available, techniques to explore the non-equilibrium dynamics of the charge
states of these defects at ultrafast (sub-nanosecond) time scales have not been
discussed before. We present results from ultrafast optical-pump
supercontinuum-probe spectroscopy measurements on $\beta$-Ga$_2$O$_3$. The
study of point defects in $\beta$-Ga$_2$O$_3$ is essential for its
establishment as a material platform for high-power electronics and deep-UV
optoelectronics. Use of a supercontinuum probe allows us to obtain the
time-resolved absorption spectra of material defects under non-equilibrium
conditions with picosecond time resolution. The probe absorption spectra shows
defect absorption peaks at two energies, $\sim$2.2 eV and $\sim$1.63 eV, within
the 1.3-2.5 eV probe energy bandwidth. The strength of the absorption
associated with each peak is time-dependent and the spectral weight shifts from
the lower energy peak to the higher energy peak with pump-probe delay. Further,
maximum defect absorption is seen for probe polarized along the crystal c-axis.
The time-dependent probe absorption spectra and the observed dynamics for all
probe wavelengths at all pump-probe delays can be fit with a set of rate
equations for a single multi-level defect. Based on first-principles
calculations within hybrid density functional theory we attribute the observed
absorption features to optical transitions from the valence band to different
charge states of Gallium vacancies. Our results demonstrate that broadband
ultrafast supercontinuum spectroscopy can be a useful tool to explore charge
states of defects and defect dynamics in semiconductors.
