Theoretical and numerical evidence for the potential realization of the Peregrine soliton in repulsive two-component Bose-Einstein condensates

TL;DR

This paper provides theoretical and numerical evidence that Peregrine solitons, a type of rogue wave, can potentially be realized in repulsive two-component Bose-Einstein condensates, suggesting feasible experimental observation methods.

Contribution

The study demonstrates the possibility of generating Peregrine solitons in two-component BECs using specific initial conditions and interactions, expanding the understanding of rogue wave formation in quantum fluids.

Findings

Peregrine solitons can emerge from power-law decaying initial states.

Narrow wave packets lead to periodic Peregrine revivals.

Broader wave packets produce cascades of Peregrine solitons in a Christmas-tree pattern.

Abstract

The present work is motivated by the recent experimental realization of the Townes soliton in an effective two-component Bose-Einstein condensate by B. Bakkali-Hassan et al. [Phys. Rev. Lett. 127, 023603 (2021)]. Here, we use a similar multicomponent platform to exemplify theoretically and numerically, within the mean-field Gross-Pitaevskii framework, the potential toward the experimental realization of a different fundamental wave structure, namely the Peregrine soliton. Leveraging the effective attractive interaction produced within the mixture's minority species in the immiscible regime, we illustrate how initialization of the condensate with a suitable power-law decaying spatial density pattern yields the robust emergence of the Peregrine wave in the absence and in the presence of a parabolic trap. We then showcase the spontaneous emergence of the Peregrine soliton via a suitably crafted wide Gaussian initialization, again both in the homogeneous case and in the trap scenario. It is also found that narrower wave packets may result in periodic revivals of the Peregrine soliton, while broader ones give rise to a cascade of Peregrine solitons arranged in a so-called Christmas-tree structure. Strikingly, the persistence of these rogue-wave structures is demonstrated in certain temperature regimes as well as in the presence of transversal excitations through three-dimensional computations in a quasi-one-dimensional regime. This proof-of-principle illustration is expected to represent a practically feasible way to generate and observe this rogue wave in realistic current ultracold atom experimental settings.