In recent years, hybrid circuit QED devices consisting of semiconductor double quantum dots coupled to microwave cavities have attracted a lot of attention. However, an important milestone that has not been reach with these systems is the strong coupling regime of cavity QED. Reaching this regime is challenging with quantum dots due to the lack of control over the decoherence mechanisms limiting charge relaxation and dephasing rates. We used a resonator-dot system to quantitatively extract charge fluctuations in the environment surrounding our single-electron GaAs double quantum dot, one source of decoherence in our experiment. We demonstrate a charge sensitivity of the microwave readout at the level of 8.5*10^-5 e/√Hz and use this sensitivity to quantitatively probe the low-frequency
charge noise of the heterostructure.

The presented analysis allows us to infer a lower bound for the dephasing rate originating from the low frequency charge noise in the vicinity of the double-dot. The inferred value is similar to that extracted from an analysis of frequency shifts and linewidth broadenings based on a master equation simulation. This emphasizes that charge noise is the main source of dephasing in our DQD-based charge qubit system.