NSF Award
2408988
Vortices are persistent circulating flow patterns that arise in diverse physical contexts, ranging from classical hydrodynamics and superfluids to condensed matter physics and nonlinear optics. They are ubiquitous physical phenomena in the world around us and can be observed at very different scales, from microscopic vortex lines in superfluid liquid helium, to dust devils and tornadoes, and even to Jupiter's Great Red Spot. Bose-Einstein condensates of ultracold atoms (BECs) provide a pristine and controllable environment where numerous aspects of the fascinating realm of nonlinear vortex dynamics can be explored not just in theory but also through direct experiments. In addition to their intrinsic fundamental interest, these systems also exhibit localized solutions with potential practical applications: for example, it has been suggested that solitary waves could be used for unprecedented, improved sensitivity in interferometric and force-sensing devices. On the other hand, vortical structures, which are the focus of this proposal, also hold promise for other intriguing applications. For instance, they can provide an instance of 'analogue gravity' as a proxy to study the behavior of spinning black holes. It has also been proposed that BEC vortices could collapse in a manner akin to supermassive black holes and that supersonic expansion in BECs can replicate properties of an expanding universe in laboratory settings.<br/><br/>Through a bijective collaboration with experiments, this proposal aims to advance the current understanding of topological structures in BECs. Being based on universal models of modulated waves in nonlinear media, the underlying physical setting represents a fundamental playground to study topologically charged excitations that are, in turn, at the heart of an extremely wide variety of physical contexts in atomic, optical, wave physics, and beyond. The project will address the existence, stability, manipulation, and dynamics of vortex configurations in 2D and 3D settings from a novel and broad perspective. The PIs' plan is to develop effective lower dimensional, reduced evolution equations to gain novel insights on the properties of these coherent structures in the original, high-dimensional, models and to compare the theoretical results therefrom with numerical computations and circling all the way back to direct observations from atomic and polariton BEC experiments. The main goals of this proposal are multi-fold and include the following themes: the creation, removal, and interactions of vortices and soliton filaments and experimentally tailored external potentials by leveraging effective lower-dimensional dynamical models for the evolution of soliton filaments coupled with point-vortex models including the relevant case of open quantum systems in the presence of driving and damping for polariton condensates. Also, in close synergy with experimental collaborators, the study of the timely theme of synthetic magnetic monopoles and the elusive so-called Alice ring in spinor (chiefly F=2) BECs. The project aims to shed light on this highly complex, topological pattern forming system and, in particular, on the recent collaborator experiments where they observed that monopole instabilities give rise to topological patterns reminiscent of Alice rings.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
