Nonlinear waves in effectively attractive Bose-Einstein condensates

Nonlinear systems with attractive interactions support a remarkably rich variety of nonlinear wave patterns. A prominent example is the Peregrine soliton, recently realized by our group. This feature is localized not only in space but also in time and has attracted significant interest as a potential model for oceanic rogue waves, with closely related phenomena appearing in nonlinear optics. Peregrine solitons, however, represent only one member of a broader family of nonlinear excitations, including Akhmediev breathers, Kuznetsov–Ma breathers, cnoidal waves, and other structures that exemplify the complex dynamics of attractive systems.

In our experiments, we engineer effectively attractive interactions in a two‑component ⁸⁷Rb BEC via an effective renormalization of the interaction strength. By directly comparing this system with single‑component condensates exhibiting repulsive interactions, we are able to contrast nonlinear wave phenomenology across the attractive and repulsive regimes under otherwise similar conditions. The experimental observations are complemented by both one‑dimensional and full three‑dimensional numerical simulations, as well as analytic considerations.

The experimental capability to investigate these features without being dominated by modulational instability opens a rich avenue for nonlinear science with BECs and enables interesting comparisons with nonlinear wave phenomena in ocean dynamics and nonlinear optics.