Dynamical Crossover of Quantum Vortex-Pair Annihilation in a Bose-Einstein Condensate*

Understanding the fundamental mechanism of the vortex energy dissipation is one central issue in quantum fluid dynamics. It was discovered that a pair of persistent like-signed vortex clusters may emerge without any energy injection in two-dimensional turbulence of a uniform disk-shaped Bose-Einstein condensate (BEC). The annihilation of vortex-antivortex pairs, which remove the lowest-energy vortices and thereby boost the mean energy per vortex, is a key phenomenon for the emergence of this order. A later study revealed that vortex-pair annihilation emits intense sound waves, dampening all vortices' motion and possibly suppressing OV cluster formation. Therefore, the sound wave effects toward the vortex dissipation mechanism have attracted much attention. Past studies have shown contradictory results about the number of vortices involved in the annihilation process at absolute zero temperature. Some studies suggested a four-body process, whereas others indicated a three-body nature. To solve this discrepancy, we have analyzed the decay of vortex numbers in a boundary-less quasi-2D BEC and have discovered a dynamical crossover from four-body to three-body vortex annihilation processes with time evolution in a boundary-less uniform quasi-2D BEC. This dynamical crossover depends on the initial density of vortex pairs and occurs when the sound waves generated during the vortex annihilation process exceed a certain sound wave energy threshold. As the confinement along the third direction is weakened, the threshold sound wave energy decreases due to the enhancement of the 3D vortex reconnection channel, shifting the dynamical crossover to an earlier time. Our work reveals a fundamental mechanism for the dissipation of vortex energy, which may enhance our understanding of exotic matter and dynamics in quantum gases and may lead to a deeper insight into the emergent vortex orders in 2D manifolds of superfluid far from equilibrium.