  We report on dual-gate reflectometry in a metal-oxide-semiconductor
double-gate silicon transistor operating at low temperature as a double quantum
dot device. The reflectometry setup consists of two radio-frequency resonators
respectively connected to the two gate electrodes. By simultaneously measuring
their dispersive response, we obtain the complete charge stability diagram of
the device. Charge transitions between the two quantum dots and between each
quantum dot and either the source or the drain contact are detected through
phase shifts in the reflected radio-frequency signals. At finite bias,
reflectometry allows probing charge transitions to excited quantum-dot states
thereby enabling direct access to the energy level spectra of the quantum dots.
Interestingly, we find that in the presence of charge transport across the two
dots the reflectometry signatures of interdot transitions display a dip-peak
structure containing quantitative information on the charge relaxation rates in
the double quantum dot.
