Theory of Two-Qubit $T_2$ Spectroscopy of Quantum Many-Body Systems

TL;DR

This paper introduces a two-qubit $T_2$ spectroscopy method that uses pulse sequences to analyze environmental responses and noise, revealing correlation spreading, dispersion, and transport regimes in many-body quantum systems.

Contribution

It presents a novel pulse sequence approach for two-qubit sensors to separately extract response and noise, enabling detailed analysis of many-body dynamics.

Findings

Resolves spatio-temporal correlation spreading in many-body systems.

Identifies light-cone-like profiles and their modification under non-equilibrium conditions.

Distinguishes between ballistic, diffusive, and crossover transport regimes.

Abstract

Multi-qubit quantum sensors are rapidly emerging as platforms that extend the capabilities of conventional single-qubit sensing. In this work we show how suitable pulse sequences applied to a two-qubit sensor enable separate extraction of the response and noise of a probed environment within a $T_2$ spectroscopy framework. By resorting to representative examples, we demonstrate that this approach can resolve the spatio-temporal spreading of correlations in a many-body system. In particular, the resulting correlated dephasing signal captures features such as the dispersion of low-energy excitations, which manifest as light-cone-like profiles in the propagation of correlations. We further show that non-equilibrium conditions, for instance those induced by external driving, can modify this profile by producing additional fringes outside the light-cone. As a complementary application, we demonstrate that the method clearly distinguishes between different transport regimes in the system, including ballistic spreading, diffusive broadening, and the crossover between them.