Dressed state approach to matter wave mixing of bosons

TL;DR

This paper introduces a dressed state formalism to analyze matter wave mixing in bosonic systems, revealing oscillation and decay phenomena beyond mean-field approximations.

Contribution

It develops a novel dressed state approach to describe two- and three-wave mixing of bosonic matter waves, providing analytic spectra and population dynamics.

Findings

Oscillations induce mode population splitting analogous to Autler-Townes effect.

Derived analytic expressions for dressed spectrum and mode evolution.

Effects cannot be captured by mean-field theories.

Abstract

A dressed state approach to mixing of bosonic matter waves is presented. Two cases are studied using this formalism. In the first, two macroscopically populated modes of atoms (two-wave mixing) are coupled through the presence of light. In the second case, three modes of Bogoliubov quasiparticles (three-wave mixing) are coupled through s-wave interaction. In both cases wave mixing induces oscillations in the population of the different modes that decay due to interactions. Analytic expressions for the dressed basis spectrum and the evolution of the mode populations in time are derived both for resonant mixing and non-resonant mixing. Oscillations in the population of a given mode are shown to lead to a splitting in the decay spectrum of that mode, in analogy to the optical Autler-Townes splitting in the decay spectrum of a strongly driven atom. These effects cannot be described by a mean-field approximation.