Environmental noise spectroscopy with qubits subjected to dynamical decoupling

Abstract

A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.

The dynamical-decoupling-based spatiotemporal noise spectroscopy

“…is the time-domain filter function that encapsulate the effects of the periodic pulse sequence described above [2,10,[61][62][63]. This filter function is depicted in figure 1: it has a form of a square wave, that switches between +1 and −1 at the moment that coincides with the timing of pulse application.…”

“…The idea is that, by scanning the wide range of settings of pulse sequence periods and measuring the corresponding qubit response, it is possible to reconstruct the frequency distribution of the noise, i.e. to perform the noise spectroscopy [2,[6][7][8].…”

“…The method of spatiotemporal spectroscopy presented in this work is most suited for characterizing stationary and spatially uniform Gaussian noise fields (or when the Gaussian approximation is adequate to describe qubit-noise coupling [2]). In such a case, all statistical properties of ξ are defined by the average value and the auto-correlation function (Gaussianity), that is respectively constant and depends only on the relative position and time (stationarity and uniformity)…”

“…Single qubits have been successfully used to characterize the frequency spectrum of environmental fluctuations affecting their coherence [1,2]. The basic principle is to subject the qubit to a periodic perturbation-a sequence of unitary operations or measurements-in order to make it sensitive only to certain frequencies of these fluctuations [3][4][5][6][7][8][9].…”

“…They can be identified with the Fourier series coefficients of the time-domain filter function[2,61,63], and of the spatial distribution of qubit block. Note how only the widths of passbands depend on the number of…”