Scaling of Dynamical Decoupling for Spin Qubits

We investigate the scaling of coherence time T-2 with the number of pi pulses n(pi) 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 T-2 proportional to (n(pi))(gamma e), with gamma(e) = 0.72 +/- 0.01, essentially independent of the envelope function used to extract T-2. From this surprisingly robust value, a power-law model of the noise spectrum of the environment, S(omega) similar to omega(-beta), yields beta = gamma(e)/(1 - gamma(e)) = 2.6 +/- 0.1. Model values for T-2(n(pi)) using beta = 2.6 for CPMG with both even and odd n(pi) up to 32 and CDD orders 3 through 6 compare very well with the experiment.