Generalized ABCD propagation for interacting atomic clouds

Abstract

We present a treatment of the nonlinear matter wave propagation inspired from optical methods, which includes interaction effects within the atom optics equivalent of the aberrationless approximation. The atom-optical ABCD matrix formalism, considered so far for non-interacting clouds, is extended perturbatively beyond the linear regime of propagation. This approach, applied to discuss the stability of a matter-wave resonator involving a free-falling sample, agrees very well with the predictions of the full nonlinear paraxial wave equation. An alternative optical treatment of interaction effects, based on the aberrationless approximation and suitable for cylindrical paraxial beams of uniform linear density, is also adapted for matter waves.

15 pages, 4 figures, Final version

References in corpus (6)

• Off-resonant Raman transitions impact in an atom interferometer
• Matter-wave Interferometry with Phase Fluctuating Bose-Einstein Condensates
• Theoretical tools for atom laser beam propagation
• Matter-wave cavity gravimeter
• Quality factor of a matter-wave beam
• Atom optics with rotating Bose-Einstein condensates

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• The theory of quantum levitators
• Classical phase-space approach for coherent matter waves
• Hidden symmetry and nonlinear paraxial atom optics
• Dynamical Casimir effects with atoms: from the emission of photon pairs to geometric phases
• Toward a test of angular momentum coherence in a twin-atom interferometer
• Focusing Atom Laser Beams