Hidden symmetry and nonlinear paraxial atom optics

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.

Final Version. Changes in the abstract and minor changes in the text with respect to the version published in PRA

References in corpus (2)

• A quasi-monomode guided atom-laser from an all-optical Bose-Einstein condensate
• Quality factor of a matter-wave beam

Cited by in corpus (8)

• Atomic Interactions in Precision Interferometry Using Bose-Einstein Condensates
• Quantum control beyond the adiabatic regime in 2D curved matter-wave guides
• Non-local double-path Casimir phase in atom interferometers
• Dynamical local and non-local Casimir atomic phases
• Classical phase-space approach for coherent matter waves
• The theory of quantum levitators
• Modeling atom interferometry experiments with Bose-Einstein condensates in power-law potentials
• Focusing Atom Laser Beams