Measuring Environmental Quantum Noise Exhibiting a Nonmonotonic Spectral Shape

Understanding the physical origin of noise affecting quantum systems is important for nearly every quantum application. Quantum-noise spectroscopy has been used in various quantum systems, such as superconducting qubits, nitrogen-vacancy centers, 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 nonmonotonous, thus posing a challenge to existing noise-spectroscopy schemes. Here we compare several methods for noise spectroscopy: spectral decomposition based on the Carr-Purcell-Meiboom-Gill sequence, the recently presented dynamic sensitivity control (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 nontrivial features. Using an ensemble of nitrogen-vacancy centers in diamond coupled to a high-density C13-nuclear-spin environment, we experimentally confirm our findings. The combination of the schemes presented offers potential to record high-quality noise spectra as a prerequisite to generate quantum systems unlimited by their spin-bath environment.