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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. 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C. Gossard, C. Barthel, C. M. Marcus, J. Medford, L. Cywinski, M. P. Hanson","submitted_at":"2011-08-18T08:29:22Z","abstract_excerpt":"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. 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