2014/04/30 by Daniel Stanek, Benedikt Fauseweh, Christopher Stihl +2
Physics and Astronomy · #NMR spectroscopy and applications #Quantum chaos and dynamical systems #cond-mat.mes-hall #cond-mat.str-el #quant-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1016/j.jmr.2014.06.009
published as J. Magn. Res. 245 (2014) 133-142 · 11 pages, 8 figures
openalex publication_date 2014/06/27 · arxiv created 2014/07/18 · arxiv updated 2014/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ∝ τp1, a first-order refocusing pulse normally shows scaling ∝ τp2. But in presence of cusps in the noise autocorrelation the scaling ∝ τp3/2 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.