  Efficient detection of single optical centers in solids is essential for
quantum information processing, sensing, and single-photon generation
applications. In this work, we use radio-frequency (RF) reflectometry to
electrically detect the photoionization induced by a single Er$^{3+}$ ion in
Si. The high bandwidth and sensitivity of the RF reflectometry provide
sub-100-ns time resolution for the photoionization detection. With this
technique, the optically excited state lifetime of a single Er$^{3+}$ ion in a
Si nano-transistor is measured for the first time to be 0.49 $\pm$ 0.04 $\mu$s.
Our results demonstrate an efficient approach for detecting a charge state
change induced by Er excitation and relaxation. This approach could be used for
fast readout of other single optical centers in solids and is attractive for
large-scale integrated optical quantum systems thanks to the multi-channel RF
reflectometry demonstrated with frequency multiplexing techniques.
