Caustic formation in expanding condensates of cold atoms

Abstract

We study the evolution of density in an expanding Bose-Einstein condensate that initially has a spatially varying phase, concentrating on behaviour when these phase variations are large. In this regime large density fluctuations develop during expansion. Maxima have a characteristic density that diverges with the amplitude of phase variations and their formation is analogous to that of caustics in geometrical optics. We analyse in detail caustic formation in a quasi-one dimensional condensate, which before expansion is subject to a periodic or random optical potential, and we discuss the equivalent problem for a quasi-two dimensional system. We also examine the influence of many-body correlations in the initial state on caustic formation for a Bose gas expanding from a strictly one-dimensional trap. In addition, we study a similar arrangement for non-interacting fermions, showing that Fermi surface discontinuities in the momentum distribution give rise in that case to sharp peaks in the spatial derivative of the density. We discuss recent experiments and argue that fringes reported in time of flight images by Chen and co-workers [Phys. Rev. A 77, 033632 (2008)] are an example of caustic formation.

arXiv comment10 pages, 5 figures. Published version

References in corpus (7)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Observation of Phase Fluctuations in Bose-Einstein Condensates
• Optical Generation of Vortices in trapped Bose-Einstein Condensates
• Coherent Matter Wave Transport in Speckle Potentials
• Phase Coherence and Superfluid-Insulator Transition in a Disordered Bose-Einstein Condensate
• Density modulations in an elongated Bose-Einstein condensate released from a disordered potential
• Correlation functions of a Lieb-Liniger Bose gas

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• Diffraction catastrophes threaded by quantized vortex skeletons caused by atom-optical aberrations induced in trapped Bose-Einstein condensates
• Gravitational Caustics in an Atom Laser
• Emergence of caustics in dynamics of the Kitaev model