On accuracy of dynamical decoupling based spectroscopy of Gaussian noise

Piotr Szańkowski, Łukasz Cywiński

Published 2017-08-18Version 1

The dynamical decoupling (DD) based noise spectroscopy relies on achieving the regime of evolution parameters, when the measured decay rate of qubit coherence is given by environmental noise spectrum spanned on frequency comb defined by the DD pulse sequences. Using properly chosen sequences allows for inverting this relation, and thus, the reconstruction of the spectrum. Here we investigate the conditions under which this regime is achieved, and the corrections to the aforementioned relation become negligible. To this end we focus on two representative examples of spectral densities: the long-tailed Lorentzian, and finite-ranged Gaussian --- both expected to be encountered when using the qubit for nanoscale nuclear resonance imaging. We have found that, in contrast to Lorentz spectrum, where the spectrosopic regime can be easily achieved, it is not the case for spectral densities with finite range. Consequently, it becomes difficult (especially with limited a priori knowledge) to avoid artifacts in the reconstructed spectrum. For Gaussian line-shape of environmental spectral density, direct application of the standard DD-based spectroscopy method leads to erroneous reconstruction of long-tail behavior of the spectrum. Fortunately, with the simple extension to standard reconstruction method that exploit the general properties of the corrections, their contribution can be completely circumvented.