Mass-driven vortex collisions in flat superfluids

Quantum vortices are often endowed with an effective inertial mass, due, for example, to massive particles in their cores. Such “massive vortices” display new phenomena beyond the standard picture of superfluid vortex dynamics, where mass is neglected. In this work, we demonstrate that massive vortices are allowed to collide, as opposed to their massless counterparts. We propose a scheme to generate controllable, repeatable, deterministic collisional events in pairs of quantum vortices. We demonstrate two mass-driven fundamental processes: (i) the annihilation of two counter-rotating vortices and (ii) the merging of two corotating vortices, thus pointing out new mechanisms supporting incompressible-to-compressible kinetic-energy conversion, as well as doubly quantized vortex stabilization in flat superfluids.

Figure 1

Comparison between the massive point vortex model of Eq. (2) (solid lines) and GP simulations (dots). (left) Trajectories of two vortices with opposite sign, initially at a distance $d/R=0.60$, for $N_b=0$, 1000, 3300, and 5400, respectively in blue, green, yellow and red. (right) Trajectories for two same-signed vortices, initially at a distance $d/R=0.34$, for $N_b=0$ and 13 500. The line thickness corresponds to the typical size of the filling BEC, ${\ell }_v$. Other parameters used in the simulations for a mixture of ${}^{87}\mathrm{Rb}$ and ${}^{41}\mathrm{K}$ are $N_a=5\times {10}^5,R=25\mu \mathrm{m}, d_z=0.82\mu \mathrm{m}$. ${\omega }_b=85\mathrm{rad}/\mathrm{s}$ for the left panel, while ${\omega }_b=250\mathrm{rad}/\mathrm{s}$ for the right panel. See related videos of GP simulations in the Supplemental Material [43].

Figure 2

Mass-driven collision of a pair of counter-rotating massive vortices. Starting from a pair of singly quantized vortices, upon colliding, the two vortices mutually annihilate and their incompressible kinetic energy is fully transferred into a sound pulse. First (second) row corresponds to the density (phase) field of the majority component (${}^{87}\mathrm{Rb}$). Here $N_b=5400$ (the other microscopic parameters are listed in the caption of Fig. 1), the collision time $t_{*}$ is 125 ms. See the full video of GP simulation in the Supplemental Material [43].

Figure 3

Mass-driven collision of a pair of corotating massive vortices. Starting from a pair of singly quantized vortices, upon collision, a single doubly quantized vortex is stabilized. Same microscopic model parameters (except that $N_b=1.35\times {10}^4$ and ${\omega }_b=250\mathrm{rad}/\mathrm{s}$) and graphical conventions of Fig. 2. The collision time is $t_{*}=9$ ms. See the full video of GP simulation in the Supplemental Material [43].

Figure 4

Increasing the number of core atoms ($N_b\propto {\eta }^{-1}$), the vortices get heavier and the collisional time ($t_{*}$) decreases. Below a critical value of $N_b$ (vertical lines), cores are too light and vortices do not collide at all. The stronger the harmonic confinement acting on component-$b$ atoms, the smaller are the collision time and the critical value for $N_b$. The main panel illustrates the data upon a suitable nondimensionalization procedure mirroring the emergence of only one characteristic parameter $\eta$, while the inset shows the original data in dimensionful units. Same model parameters and initial conditions of Fig. 2 were used. The blue dashed, yellow solid, and green dotted lines correspond to 70, 85, and 100 rad/s, respectively. In the main panel (inset), from bottom to top (from top to bottom), data corresponding to 70, 85, and 100 rad/s are illustrated, respectively.

Figure 5

The proposed collisional protocol is robust with respect to variations of the initial intervortex separation. Red, ice blue, and purple lines correspond to an initial distance of $0.6R, R$, and $1.4R$, respectively (black dots represent the starting positions). The left (right) panel corresponds to counter- (co-) rotating vortices. The assumed microscopic parameters are listed in the caption of Fig. 1. (left panel) $N_b=5400, {\omega }_b=85\mathrm{rad}/\mathrm{s}$. (right panel) $N_b=5000, {\omega }_{b,x}=120\mathrm{rad}/\mathrm{s}, {\omega }_{b,y}=400\mathrm{rad}/\mathrm{s}$ for the red line, ${\omega }_{b,x}=120\mathrm{rad}/\mathrm{s}, {\omega }_{b,y}=700\mathrm{rad}/\mathrm{s}$ for the ice-blue line, and ${\omega }_{b,x}=80\mathrm{rad}/\mathrm{s}, {\omega }_{b,y}=700\mathrm{rad}/\mathrm{s}$ for the purple line. See related videos of GP simulations in the Supplemental Material [43].

Figure 6

The (magnitude of) the acceleration $|{\ddot{\mathit{r}}}_j|$ of the two massive vortices along their collisional trajectories is maximum at the start (green flags), just before the collision (orange star) and at the changes of direction. Model parameters coincide with those used for Figs. 1, 2, 3.

Figure 7

Maximum acceleration experienced by a massive vortex before colliding $\left[{max}_t\left|{\ddot{\mathit{r}}}_j\left(t\right)\right|\right]$ according to the collisional protocol illustrated in the left panel of Figs. 1 and 2. The same model parameters are assumed. The white region correspond to the absence of collisional events and its boundary represents the relation ${\tilde{N}}_b\left({\omega }_b\right)$ mentioned in the main text.