Anomalous behavior of control pulses in presence of noise with singular autocorrelation
| Autor: | Benedikt Fauseweh, Stefano Pasini, Christopher Stihl, Daniel Stanek, Götz S. Uhrig |
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| Rok vydání: | 2014 |
| Předmět: |
Physics
Nuclear and High Energy Physics Quantum Physics Spins Condensed Matter - Mesoscale and Nanoscale Physics Strongly Correlated Electrons (cond-mat.str-el) Autocorrelation Relaxation (NMR) Biophysics Spectral density FOS: Physical sciences Condensed Matter Physics Biochemistry Pulse (physics) Condensed Matter - Strongly Correlated Electrons Quantum mechanics Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Exponent Quantum Physics (quant-ph) Scaling Noise (radio) |
| DOI: | 10.48550/arxiv.1404.3836 |
| Popis: | 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 $\propto \tau_\mathrm{p}^1$, a first-order refocusing pulse normally shows scaling $\propto \tau_\mathrm{p}^2$. But in presence of cusps in the noise autocorrelation the scaling $\propto \tau_\mathrm{p}^{3/2}$ 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. Comment: 11 pages, 8 figures |
| Databáze: | OpenAIRE |
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