Noise-specific beats in the higher-level Ramsey curves of a transmon qubit

In the higher levels of superconducting transmon devices, and more generally charge sensitive devices, $T_2^*$ measurements made in the presence of low-frequency time-correlated $1/f$ charge noise and quasiparticle-induced parity flips can give an underestimation of the total dephasing time. The charge variations manifest as beating patterns observed in the overlay of several Ramsey fringe curves, and are reproduced with a phenomenological Ramsey curve model which accounts for the charge variations. $T_2^*$ dephasing times which more accurately represent the total dephasing time are obtained. The phenomenological model is compared with a Lindblad master equation model. Both models are found to be in agreement with one another and the experimental data. Finally, the phenomenological formulation enables a simple method in which the power spectral density (PSD) for the low-frequency noise can be inferred from the overlay of several Ramsey curves.