Scaling of Dynamical Decoupling for Spin Qubits

We investigate 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)^(γ_e), with γ_e = 0.72\pm0.01, 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 = γ_e/(1 - γ_e) = 2.6 \pm 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 experiment.

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