A topological realization of spin polarization through vortex formation in collisions of Bose–Einstein condensates

Abstract

The global spin polarization of hadrons in heavy ion collisions has been measured in the solenoidal tracker at relativistic heavy ion collider experiments, which opens up a new window in the study of the hottest, least viscous, and most vortical fluid that has ever been produced in the laboratory. We present a different approach to spin polarization from conventional ones: a topological realization of spin polarization through quantum vortex formation in collisions of Bose–Einstein condensates. This approach is based on the observation that the vortex is a topological excitation in a superfluid in the presence of local orbital angular momentum and is an analog of spin degrees of freedom. The formation processes of vortices and vortex–antivortex pairs are investigated by solving the Gross–Pitaevskii equation with a large-scale parallel algorithm on a graphics processing unit to very high precision. In a rotating environment, the primary vortex with winding number one is stable against perturbation, which has minimal energy and fixed orbital angular momentum (OAM), but the vortices with larger winding numbers are unstable and will decay into primary vortices through a redistribution of the energy and vorticity. The injection of OAM can also be realized in non-central collisions of self-interacting condensates, part of the OAM of the initial state will induce the formation of vortices through concentration of energy and vorticity density around topological defects. Different from a hydrodynamical description, the interference of the wave function plays an important role in the transport of energy and vorticity, reflecting the quantum nature of the vortex formation process. The study of the vortex formation may shed light on the nature of particle spin and spin–orbit couplings in strong interaction matter produced in heavy-ion collisions.

High precision solutions to quantized vortices within Gross–Pitaevskii equation

“…Vortices are strongly nonlinear excitations in superfluids, which are quantized as topologic defects from the long range quantum phase coherence [1][2][3]. The formation, stability and dynamical properties of vortices have been intensively studied experimentally [4][5][6][7][8] and theoretically [9,10]. Vortices play important roles not only in many-body quantum systems, but also in dark matter [11][12][13] and the phase transition of the early universe [14][15][16][17].…”