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We study the performance of dynamical decoupling in suppressing decoherencecaused by soft-cutoff Gaussian noise, using short-time expansion of the noisecorrelations and numerical optimization. For the noise with soft cutoff at highfrequencies, there exists no dynamical decoupling scheme to eliminate thedecoherence to arbitrary orders of the short time, regardless of the timing orpulse shaping of the control under the population conserving condition. Weformulate the equations for optimizing pulse sequences that minimizesdecoherence up to the highest possible order of the short time for the noisecorrelations with odd power terms in the short-time expansion. In particular,we show that the Carr-Purcell-Meiboom-Gill sequence is optimal in short-timelimit for the noise correlations with a linear order term in the timeexpansion.

No-go theorem and optimization of dynamical decoupling against noise with soft cutoff