Fig. 5: Dynamical decoupling and high frequency noise.
a Normalized echo amplitude as a function of total free evolution time using CPMG sequences at Bz,0= 405 mT. These sequences are composed of a series of nππy pulses, as depicted on the top of the figure for nπ = 4 and finished with a πx/2 probe at different timings τ + δτ, where δτ is swept to capture the whole echo. For each CPMG the echo is renormalized using the reference echo amplitude for τ = 1 μs. The different decay curves are fitted using the following expression \(A(t)=\exp[-{\left(t/{T}_{2}\right)}^{\beta }]\) with β = 1 + α. b Evolution of CPMG-enhanced T2 with number of refocusing pulses. T2 values are extracted from the decay curves in (a) and fitted using \({T}_{2}^{{n}_{\pi }}\propto {n}_{\pi }^{\frac{\alpha }{1+\alpha }}\). c Noise power spectral density of the qubit energy fluctuation for the evolution time corresponding to the CPMG \({T}_{2}^{{n}_{\pi }}\) times. Treating the CPMG sequence as a band pass filter allows to extract the noise PSD around the pulse repetition frequency. The 1/f trend, characteristic of charge noise, is plotted along the data points. d Noise power spectral density in terms of effective gate voltage. The low frequency data points are extracted from time ___domain current measurements on the flank of a SET Coulomb peak followed by Fourier transform. The high frequency points correspond to data points from (a), turned into voltage fluctuations knowing the longitudinal magnetic gradient and the charge displacement due to gate voltage.
