title: Anomalous behavior of control pulses in presence of noise with singular autocorrelation.
abstract: 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 ∝τp(1), a first-order refocusing pulse normally shows scaling ∝τp(2). But in presence of cusps in the noise autocorrelation the scaling ∝τp(3/2) 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.
authors.affiliation: Lehrstuhl für Theoretische Physik I, TU Dortmund, Otto-Hahn Straße 4, 44221 Dortmund, Germany.
authors.forename: Daniel
authors.initials: D
authors.lastname: Stanek
authors.affiliation: Lehrstuhl für Theoretische Physik I, TU Dortmund, Otto-Hahn Straße 4, 44221 Dortmund, Germany. Electronic address: benedikt.fauseweh@tu-dortmund.de.
authors.forename: Benedikt
authors.initials: B
authors.lastname: Fauseweh
authors.affiliation: Institut für Angewandte Materialien - IAM-AWP, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany.
authors.forename: Christopher
authors.initials: C
authors.lastname: Stihl
authors.affiliation: Jülich Centre for Neutron Science, JCNS, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany. Electronic address: s.pasini@fz-juelich.de.
authors.forename: Stefano
authors.initials: S
authors.lastname: Pasini
authors.affiliation: Lehrstuhl für Theoretische Physik I, TU Dortmund, Otto-Hahn Straße 4, 44221 Dortmund, Germany. Electronic address: goetz.uhrig@tu-dortmund.de.
authors.forename: Götz S
authors.initials: GS
authors.lastname: Uhrig
keywords: Decoherence; Decoupling pulses; Lorentzian spectral density; NMR; Spin echos