Caustic formation in expanding condensates of cold atoms

TL;DR

This paper investigates caustic formation in expanding Bose-Einstein condensates with large initial phase variations, revealing how density fluctuations and caustics develop, influenced by interactions, initial states, and fermionic effects, with experimental relevance.

Contribution

It provides a detailed analysis of caustic formation in expanding condensates with large phase variations, including effects of interactions, disorder, and fermionic systems, which is a novel comprehensive study.

Findings

Large density fluctuations develop during expansion with large initial phase variations.

Caustic formation is analogous to optical caustics and characterized by diverging densities.

Fermionic systems show sharp density derivatives due to Fermi surface discontinuities.

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.