Holographic pump probe spectroscopy

TL;DR

This paper investigates the non-linear response of a holographic model to electric field pulses, revealing how different pulse frequencies influence thermalization and optical conductivity, with analytical and toy model insights.

Contribution

It provides a detailed analysis of holographic non-linear dynamics under electric pulses, linking thermalization behavior to quasinormal modes and offering analytical and toy model explanations.

Findings

High-frequency pulses lead to instant thermalization of the geometry.

Zero-frequency component pulses cause exponential relaxation with doubled quasinormal mode frequency.

Analytical and toy models effectively capture the observed holographic dynamics.

Abstract

We study the non-linear response of a 2+1 dimensional holographic model with weak momentum relaxation and finite charge density to an oscillatory electric field pump pulse. Following the time evolution of one point functions after the pumping has ended, we find that deviations from thermality are well captured within the linear response theory. For electric pulses with a negligible zero frequency component the response approaches the instantaneously thermalizing form typical of holographic Vaidya models. We link this to the suppression of the amplitude of the quasinormal mode that governs the approach to equilibrium. In the large frequency limit, we are also able to show analytically that the holographic geometry takes the Vaidya form. A simple toy model captures these features of our holographic setup. Computing the out-of-equilibrium probe optical conductivity after the pump pulse, we similarly find that for high-frequency pulses the optical conductivity reaches its final equilibrium value effectively instantaneously. Pulses with significant DC components show exponential relaxation governed by twice the frequency of the vector quasinormal mode that governs the approach to equilibrium for the background solution. We explain this numerical factor in terms of a simple symmetry argument.