Quantum noise spectroscopy of non-monotonous spectra

Understanding the physical origin of noise affecting quantum systems is important for nearly every quantum application. While quantum noise spectroscopy has been employed in various quantum systems, such as superconducting qubits and trapped ions, traditional spectroscopy methods are usually efficient in measuring noise spectra with mostly monotonically decaying contributions. However, there are important scenarios in which the noise spectrum is broadband and non-monotonous, thus posing a challenge to existing noise spectroscopy schemes.Here, we compared several methods for noise spectroscopy: spectral decomposition based on the CPMG sequence, the recently presented DYSCO sequence and a modified DYSCO sequence with a Gaussian envelope (gDYSCO).The performance of the sequences is quantified by analytic and numeric determination of the frequency resolution, bandwidth and sensitivity, revealing a supremacy of gDYSCO to reconstruct non-trivial features.Utilizing an ensemble of nitrogen-vacancy centres in diamond coupled to a high density 13C nuclear spin environment, we experimentally confirm our findings.The combination of the presented schemes offers potential to record high quality noise spectra as a prerequisite to generate quantum systems unlimited by their spin-bath environment.