What do the two times in two-time correlation functions mean for interpreting tr-ARPES?

TL;DR

This paper clarifies how two-time correlation functions in time-resolved ARPES reflect contributions from a range of times, emphasizing the importance of Fourier uncertainty in interpreting measurements far from equilibrium.

Contribution

It introduces a framework for understanding two-time response functions in pump-probe spectroscopy, highlighting their non-local time contributions and implications for data interpretation.

Findings

Two-time response functions involve contributions from near times, not a single instant.

Fourier uncertainty relations reveal the temporal range involved in measurements.

This insight aids in correctly interpreting time-resolved photoemission data.

Abstract

Time-resolved angle-resolved photoemission spectroscopy is one of the most powerful pump-probe measurements of materials driven far from equilibrium. Unlike the linear-response regime, where the frequency-dependent response function is independent of time, in a far-from-equilibrium experiment, the response function depends on two times in the time domain. In this work, we describe how one can use time-dependent frequency response functions and how they involve contributions from times that are near to each other. This implies that they should not be thought of as a frequency-dependent response at a single definite time. Instead, the Fourier uncertainty relations show that they involve contributions from ranges of times and must be interpreted in this light. We use this insight to help understand what time-resolved photoemission measurements actually measure.