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Journal of the Physical Society of Japan

Bright Solitons in a Two-Dimensional Bose–Einstein Condensate

Hiroki Saito, Masahito Ueda

Published Jan 1, 2003• 0 citations
Publisher

Abstract

We present two novel phenomena concerning bright solitons in a gaseous Bose–Einstein condensate with attractive interatomic interactions. (1) For the strength of interaction larger than a critical one, a vortex splits into two clusters (solitons) via the quadrupole dynamical instability. (2) A soliton can be stabilized in 2D free space by making the strength of interactions oscillate rapidly.

DOI
10.1143/jpsjs.72sc.140

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We present two novel phenomena concerning bright solitons in a gaseous Bose–Einstein condensate with attractive interatomic interactions. (1) For the strength of interaction larger than a critical one, a vortex splits into two clusters (solitons) via the quadrupole dynamical instability. (2) A soliton can be stabilized in 2D free space by making the strength of interactions oscillate rapidly.
Experiments on attractive Bose-Einstein condensates (BECs) have unlocked many intriguing out-of-equilibrium dynamics through the interplay between matter-wave dispersion and nonlinear attractive interaction. Competition between these effects leads to fascinating phenomena such as wave collapse, modulational instability, and formation of multidimensional bright solitons. This chapter reviews experimental studies on attractive condensates, with a primary focus on alkali atoms featuring two-body contact interactions. We review recent experimental advances in optical trapping and interaction control techniques, which have enabled new studies on attractive condensates in three and also in lower dimensions. Specifically, we discuss pioneering and recent experimental observations on the dynamics and stability of attractive BECs, including the formation of bright solitons, their collisions, and excitations in quasi-one-dimensional traps. Recent observations of the elusive two-dimensional Townes solitons and vortex solitons are also discussed in this Chapter. We then highlight an experimental technique revealing the nonclassical signatures of modulational instability in an attractive condensate.
By numerical and variational analysis of the three-dimensional Gross–Pitaevskii equation, we study the formation and dynamics of bright and vortex-bright solitons in a cigar-shaped dipolar Bose–Einstein condensate for large repulsive atomic interactions. A phase diagram showing the region of stability of the solitons is obtained. We also study the dynamics of breathing oscillation of the solitons as well as the collision dynamics of two solitons. At large velocities the frontal collision is elastic and the two three-dimensional solitons pass through each other undeformed. Two solitons placed side by side at rest coalesce to form a stable bound soliton molecule due to dipolar attraction. Movie clips illustrating collision and molecule-formation dynamics of two bright and vortex-bright solitons are included.
We model the formation of bright atomic solitons due to collapse of Bose-Einstein condensates with attractive interactions reported by S. L. Cornish et al., [Phys. Rev. Lett. 96 170401 (2006)] in a realistic three dimensional situation. We show that mean-field theory does not adequately explain the experiment, while the inclusion of quantum fluctuations gives rise to bright soliton formation at the appropriate time scales. The solitons are produced either in-phase or out-of-phase and their number increases with the strength of the attractive interaction.