Quantum theory of wave mixing on a two-level system

TL;DR

This paper develops a quantum scattering matrix approach to analyze wave mixing on a two-level system, explaining experimental observations of coherent side peaks through bosonic stimulated scattering.

Contribution

It introduces a fermionization technique and Green's function calculations to provide a quantum explanation of wave mixing phenomena in two-level systems.

Findings

Coherent side peaks are explained by bosonic stimulated scattering.

The approach aligns with experimental observations.

Provides a unified quantum framework for wave mixing analysis.

Abstract

We apply the scattering matrix formalism to wave mixing on a quantum two-level system. We carry out the fermionization of the two-level system degrees of freedom using the Popov-Fedotov semions, calculate n-particle Green's function, and apply the Lehmann-Symanzik-Zimmermannn reduction procedure. Using the developed approach, we provide a consistent quantum explanation of the appearance of coherent side peaks observed in an experiment on the scattering of bichromatic radiation on a two-level artificial atom \cite{dmitriev2019probing}. We show that the spectrum observed in the experiment is the result of bosonic stimulated scattering of photons from one mode of the bichromatic drive to another and vice versa.