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Anomalous behavior of control pulses in presence of noise with singular autocorrelation
We report on the anomalous behavior of control pulses for spins under
spin-spin relaxation and subject to classical noise with a singular
autocorrelation function. This behavior is not detected for noise with analytic
autocorrelation functions. The effect is manifest in the different scaling
behavior of the deviation of a real pulse to the ideal, instantaneous one.
While a standard pulse displays scaling , a
first-order refocusing pulse normally shows scaling . But in presence of cusps in the noise autocorrelation the
scaling occurs. Cusps in the autocorrelation
are characteristic for fast fluctuations in the noise with a spectral density
of Lorentzian shape. We prove that the anomalous exponent cannot be avoided; it
represents a fundamental limit. On the one hand, this redefines the strategies
one has to adopt to design refocusing pulses. On the other hand, the anomalous
exponent, if found in experiment, provides important information on the noise
properties.Comment: 11 pages, 8 figure
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