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.
Categories: cond-mat.mes-hall quant-ph