Topological interactions in vortex-wave collisions in Bose-Einstein condensates

TL;DR

The paper addresses how energy is redistributed during vortex–vortex and vortex–wave interactions in 2D Bose–Einstein condensates by simulating the damped Gross–Pitaevskii equation and tracking defects with the smooth $D$-field. It employs a three-component kinetic-energy decomposition into incompressible $E_i$, compressible $E_c$, and quantum energy $E_q$ to reveal distinct transfer pathways, including a quantum-energy–mediated channel $E_i\to E_q\to E_c$ during vortex annihilation and topology-driven exchanges in vortex–wave collisions. A key finding is that solitary waves can either dissipate into sound or persist depending on their energy, with vortex–vortex dipole collisions exhibiting a threshold separation $\Delta r_c \approx 2.4\xi$ that governs annihilation versus partner exchange and an observed radiative scaling $E_c\sim c^3\xi^3/\Delta r^4$ for large separations. The work shows that turbulence decay is governed by collective dynamics—repeated wave–vortex encounters and configurational reorganizations—not by isolated annihilation events, with implications for other topological quantum systems such as superconductors and neutron star interiors.

Abstract

We study vortex-vortex and vortex-wave collisions in two-dimensional weakly interacting Bose-Einstein condensates, processes that play a central role in decaying quantum turbulence. Using numerical simulations of the Gross-Pitaevskii equation, we show that during collisions of vortex-antivortex dipoles, the kinetic energy is transferred from incompressible to compressible modes by two distinct mechanisms. Below the critical vortex separation for annihilation, the transfer is mediated by quantum energy released during annihilation events, while above the threshold it arises from vortex acceleration. In wave-vortex collisions, an incoming solitary wave splits into transient phase slips that interact with the vortex, one of the phase slips contributes to vortex annihilation, and the other phase slip acquires a stable core and forms a new vortex. By analyzing vortex trajectories and energy spectra, we provide new insights into energy transfer mechanisms in quantum turbulence and offer broader implications for topological interactions mediated by vortices.

Figures (12)

• Figure 1: Approach of the solitary wave to a vortex. Left panel: condensate density $|\Psi|^2$ with the superfluid current $\mathbf J$. Middle panel: pseudo-vorticity ($D$-field). Right panel: condensate phase $\theta$. The solitary wave, generated by imprinting with a vortex-antivortex pair with initial separation of $\Delta r = 1.6\xi$, carries weak pseudo-vorticity and is rotated so that its lobe with negative pseudo-vorticity approaches the vortex.
• Figure 2: Topological exchange during the collision. Left panel: condensate density $|\Psi|^2$ with superfluid current $\mathbf J$ as vector field. Middle panel: pseudo-vorticity, $D$-field. Right panel: condensate phase $\theta$.
• Figure 3: After the exchange. Left panel: condensate density $|\Psi|^2$ with superfluid current $\mathbf J$. Middle panel: pseudo-vorticity, $D$-field. Right panel: condensate phase $\theta$.
• Figure 4: Evolution of the outgoing solitary wave after the exchange. Every $2\tau$ we plot the region with the largest area where $\rho < 0.9\rho_0$. The figure shows the motion of a single solitary wave over time. Colours indicate different initial dipole separations. The vividness of colour indicates the depth of the wave. Larger separations (left) produce compact solitary waves that persist, while smaller separations (right) yield low-energy waves that rapidly disperse into sound.
• Figure 5: Evolution of the condensate density during dipole collision. Top panel: dipole collision with initial separation $\Delta r = 2.5\xi$. Bottom panel: $\Delta r = 2.1\xi$. Pink lines trace the phase slip trajectories. For $\Delta r < \Delta r_c$ (bottom) the slips annihilate, while for $\Delta r > \Delta r_c$ (top) they survive the collision, and the outgoing dipoles stabilize at a new separation.