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We report on the anomalous behavior of control pulses for spins underspin-spin relaxation and subject to classical noise with a singularautocorrelation function. This behavior is not detected for noise with analyticautocorrelation functions. The effect is manifest in the different scalingbehavior of the deviation of a real pulse to the ideal, instantaneous one.While a standard pulse displays scaling $\propto \tau_\mathrm{p}^1$, afirst-order refocusing pulse normally shows scaling $\propto\tau_\mathrm{p}^2$. But in presence of cusps in the noise autocorrelation thescaling $\propto \tau_\mathrm{p}^{3/2}$ occurs. Cusps in the autocorrelationare characteristic for fast fluctuations in the noise with a spectral densityof Lorentzian shape. We prove that the anomalous exponent cannot be avoided; itrepresents a fundamental limit. On the one hand, this redefines the strategiesone has to adopt to design refocusing pulses. On the other hand, the anomalousexponent, if found in experiment, provides important information on the noiseproperties.

Anomalous behavior of control pulses in presence of noise with singular autocorrelation