Scaling of Dynamical Decoupling for Spin Qubits

We investigate the scaling of coherence time T₂ with the number of π pulses n_π in a singlet-triplet spin qubit using Carr-Purcell-Meiboom-Gill (CPMG) and concatenated dynamical decoupling (CDD) pulse sequences. For an even numbers of CPMG pulses, we find a power law T₂∝(n_π)^γₑ, with γₑ=0.72±0.01, essentially independent of the envelope function used to extract T₂. From this surprisingly robust value, a power-law model of the noise spectrum of the environment, S(ω)~ω^-β, yields β=γₑ/(1-γₑ)=2.6±0.1. Model values for T₂(n_π) using β=2.6 for CPMG with both even and odd n_π up to 32 and CDD orders 3 through 6 compare very well with the experiment.