# Transition between continuous and discrete spectra in dynamical-decoupling noise spectroscopy

## TL;DR

This paper investigates how high-resolution dynamical decoupling pulse sequences enable the detection of discrete spectral lines in environmental noise, requiring a new approach to spectral density reconstruction.

## Contribution

It introduces a framework for transitioning from coarse-grained to discrete spectral density measurement in qubit noise spectroscopy.

## Key findings

- High-resolution filters reveal discrete spectral lines.
- Qubit decoherence behavior changes with spectral resolution.
- New methods are needed for spectral density reconstruction.

## Abstract

Here, we explore the prospects of carrying out the single qubit spectroscopy of environmental noise when the resolution of the frequency filters produced by the dynamical decoupling pulse sequences can be set high enough to reveal the discrete structure of the noise spectral density. The standard form of spectroscopy is applicable when the filter is unable to resolve the discrete spectral lines and only coarse grained approximation of the spectrum is recorded in the qubit's decoherence rate. When the discrete structure becomes accessible, the qubit probe evolves in a qualitatively different manner, and the procedure for recovering spectral density has to be redesigned.