We investigate scaling of coherence time, T2, 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, T2 = (n_{\pi})^({\gamma}_e), with {\gamma}_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({\omega}) ~ {\omega}^(-{\beta}), yields {\beta} = {\gamma}_e/(1 - {\gamma}_e) = 2.6 \pm 0.1. Model values for T2(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 experiment.
Cite
@article{arxiv.1108.3682,
title = {Scaling of Dynamical Decoupling for Spin Qubits},
author = {J. Medford and L. Cywinski and C. Barthel and C. M. Marcus and M. P. Hanson and A. C. Gossard},
journal= {arXiv preprint arXiv:1108.3682},
year = {2012}
}