Landau Damping in the Transverse Modulational Dynamics of Co-Propagating Light and Matter Beams

TL;DR

This paper analyzes the stability of co-propagating light and atomic beams in an optomechanical system, revealing conditions for instability and stabilization through Landau damping influenced by kinetic and nonlinear effects.

Contribution

It introduces a Landau stability analysis for coupled light-atom dynamics, incorporating electronic nonlinearity and saturation effects, extending previous models to include kinetic and optomechanical feedback.

Findings

Unstable for blue detuning below a critical wavenumber.

Unconditionally stable for red detuning below a saturation threshold.

Landau damping stabilizes high wavenumbers via atomic motion along Talbot carpet diagonals.

Abstract

The optomechanical coupling and transverse stability of a co-propagating monochromatic electromagnetic wave and mono-energetic beam of two-level atoms is investigated in the collisionless regime. The coupled dynamics are studied through a Landau stability analysis of the coupled gas- kinetic and paraxial wave equations, including the effect of the electronic nonlinearity. The resulting dispersion relation captures the interaction of kinetic and saturation effects and shows that for blue detuning the combined nonlinear interaction is unstable below a critical wavenumber which reduces to the result of Bespalov and Talanov in the limit of a negligible kinetic nonlinearity. For red detuning we find that under a saturation parameter threshold exists whereby the system stabilizes unconditionally. With negligible saturation, an optomechanical form of Landau damping stabilizes all wavenumbers above a critical wavenumber determined by the combined strength of the kinetic and refractive optomechanical feedback. The damping is mediated primarily by atoms traveling along the primary diagonals of the Talbot carpet.