Time correlations from steady-state expectation values

TL;DR

This paper introduces a method to estimate correlation times in quantum systems using steady-state expectation values, simplifying experimental and theoretical analysis of complex dynamics.

Contribution

The authors derive general bounds on correlation times based solely on steady-state measurements, applicable to a wide range of quantum systems and observables.

Findings

Bounds match analytical results in critical driven-dissipative resonators

Bounds provide insights into systems where only steady states are known

Method applicable to experimental and theoretical analysis of complex quantum dynamics

Abstract

Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a control parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to experimentally characterize ultrafast systems, and to theoretically analyze many-body models with dynamics that are analytically or numerically hard.