Hidden symmetry and nonlinear paraxial atom optics

TL;DR

This paper reveals a hidden symmetry in the nonlinear wave equation to analyze the propagation of atom-laser beams, extending optical methods to atomic systems with mean-field interactions, and providing a unified framework for optical and atomic beam analysis.

Contribution

It introduces a generalized formalism for paraxial atom optics that accounts exactly for mean-field interactions using a hidden symmetry and moments-based approach.

Findings

Exact description of beam profile evolution including interactions

Generalized ABCD formalism for atomic beams

Application to guided atom laser experiments

Abstract

A hidden symmetry of the nonlinear wave equation is exploited to analyse the propagation of paraxial and uniform atom-laser beams in time-independent, quadratic and cylindrical potentials varying smoothly along the propagation axis. The quality factor and the paraxial ABCD formalism are generalized to account exactly for mean-field interaction effects in such beams. Using an approach based on moments, these theoretical tools provide a very simple and yet exact picture of the interacting beam profile evolution. Guided atom laser experiments are discussed. This treatment addresses simultaneously optical and atomic beams in a unified manner, exploiting the formal analogy between nonlinear optics and nonlinear paraxial atom optics.