Spectroscopy of cross-correlations of environmental noises with two qubits

TL;DR

This paper introduces a method to use two spatially separated qubits as a spectrometer for cross-correlations in environmental noise, revealing causal relations and signal propagation through the environment.

Contribution

It demonstrates how to reconstruct both real and imaginary parts of the cross-correlation spectrum using controlled qubit sequences, advancing noise spectroscopy techniques.

Findings

Reconstruction of real part of cross-correlation spectrum with identical pulse sequences.

Reconstruction of imaginary part of spectrum with distinct pulse sequences.

Entanglement enhances the signal for spectral reconstruction.

Abstract

A single qubit driven by an appropriate sequence of control pulses can serve as a spectrometer of local noise affecting its energy splitting. We show that by driving and observing two spatially separated qubits, it is possible to reconstruct the spectrum of cross-correlations of noises acting at various locations. When the qubits are driven by the same sequence of pulses, real part of cross-correlation spectrum can be reconstructed, while applying two distinct sequence to the two qubits allows for reconstruction of imaginary part of this spectrum. The latter quantity contains information on either causal correlations between environmental dynamics at distinct locations, or on the occurrence of propagation of noisy signals through the environment. We illustrate the former case by modeling the noise spectroscopy protocol for qubits coupled to correlated two-level systems. While entanglement between the qubits is not necessary, its presence enhances the signal from which the spectroscopic information is reconstructed.