Evaluating charge noise acting on semiconductor quantum dots in the circuit quantum electrodynamics architecture

We evaluate the charge noise acting on a GaAs/GaAlAs based semiconductor double quantum dot dipole-coupled to the voltage oscillations of a superconducting transmission line resonator. The in-phase (I) and the quadrature (Q) components of the microwave tone transmitted through the resonator are sensitive to charging events in the surrounding environment of the double dot with an optimum sensitivity of 8.5× ^{10 - 5} e / √ Hz . A low frequency 1/f type noise spectrum combined with a white noise level of 6.6 × ^{10 - 6 e 2} / Hz above 1 Hz is extracted, consistent with previous results obtained with quantum point contact charge detectors on similar heterostructures. The slope of the 1/f noise allows to extract a lower bound for the double-dot charge qubit dephasing rate which we compare to the one extracted from a Jaynes-Cummings Hamiltonian approach. The two rates are found to be similar emphasizing that charge noise is the main source of dephasing in our system.