Efficient continuous wave noise spectroscopy beyond weak coupling

TL;DR

This paper develops a more accurate noise spectroscopy protocol for quantum systems by extending the coherence decay analysis beyond weak coupling and Markovian assumptions, enabling better characterization of low-frequency noise.

Contribution

It introduces a generalized coherence decay model that accounts for higher-order noise effects and non-Markovian dynamics, improving spectral density estimation at low frequencies.

Findings

Numerical simulations confirm improved accuracy over traditional models.

The protocol extends reliable spectral density measurement to zero frequency.

It outperforms existing methods in regimes of strong coupling.

Abstract

The optimization of quantum control for physical qubits relies on accurate noise characterization. Probing the spectral density $S(\omega)$ of semi-classical phase noise using a spin interacting with a continuous-wave (CW) resonant excitation field has recently gained attention. CW noise spectroscopy protocols have been based on the generalized Bloch equations (GBE) or the filter function formalism, assuming weak coupling to a Markovian bath. However, this standard protocol can substantially underestimate $S(\omega)$ at low frequencies when the CW pulse amplitude becomes comparable to $S(\omega)$. Here, we derive the coherence decay function more generally by extending it to higher orders in the noise strength and discarding the Markov approximation. Numerical simulations show that this provides a more accurate description of the spin dynamics compared to a simple exponential decay, especially on short timescales. Exploiting these results, we devise a protocol that uses an experiment at a single CW pulse amplitude to extend the spectral range over which $S(\omega)$ can be reliably determined to $\omega=0$.