Pump Built-in Hamiltonian Method for Pump-Probe Spectroscopy

TL;DR

This paper introduces a novel method called the pump built-in Hamiltonian for calculating nonlinear optical responses in interacting electronic systems, simplifying the process by transforming the Hamiltonian to avoid explicit pump-system interactions.

Contribution

The paper presents a new Hamiltonian transformation technique that enables linear response calculations for nonlinear optical phenomena in pumped systems.

Findings

Fermi edge singularity exponent varies with pump intensity

Method successfully applied to a one-dimensional two-band model

Pump built-in Hamiltonian simplifies nonlinear response calculations

Abstract

We propose a new method of calculating nonlinear optical responses of interacting electronic systems. In this method, the total Hamiltonian (system + system-pump interaction) is transformed into a different form that (apparently) does not have a system-pump interaction. The transformed Hamiltonian, which we call the pump built-in Hamiltonian, has parameters that depend on the strength of the pump beam. Using the pump built-in Hamiltonian, we can calculate nonlinear responses (responses to probe beams as a function of the pump beam) by applying the {\em linear} response theory. We demonstrate the basic idea of this new method by applying it to a one-dimensional, two-band model, in the case the pump excitation is virtual (coherent excitation). We find that the exponent of the Fermi edge singularity varies with the pump intensity.