Vortex leapfrogging and superfluid dissipation mechanisms in a fluid of light

Abstract

We report the experimental observation of vortex leapfrogging in a two-dimensional fluid of light. By imprinting two vortex-antivortex pairs and tracking their real-time evolution through phase-resolved imaging, we observe a dynamics that is accurately described by a point-vortex model with an outward background flow. By precisely controlling the initial vortex separation, we identify configurations in which leapfrogging breaks down and determine the corresponding dissipation mechanisms. The first originates from phase-slip events occurring at large injected velocities. The second arises when the injection of multi-charged vortices leads to the formation of a dispersive shock wave which acts as a continuous source of phase slippage. These mechanisms advance our understanding of vortex dynamics and dissipation in superfluids.

Figures (5)

• Figure 1: Temporal evolution of vortex leapfrogging.(a) Simplified setup. A laser beam is sent on an SLM and imaged at the input of the 20 cm-long Rb vapor cell. The phase modulation leads to the creation of two counter-rotating pairs vortices in the transverse plane. The output plane of the nonlinear medium is imaged after an interferometer (not shown). (b) Experimental images of the field amplitude. The rows $l_0$ to $l_3$ display the temporal evolution within each single loop. The last panel of row $l_n$ is recorded and re-injected as first panel of loop $l_{n+1}$. (c) Upper vortices trajectory (top) and point vortex model prediction (bottom) for $\Delta {R} = 5\xi$ and $\Delta {r} = 1.5\xi$. The dashed line indicates the $x$-coordinate of the vortex pair barycenter at each loop transition.
• Figure 2: Nucleation of phase slips. Leapfrogging evolution in the first loop from left to right $\tau_{l_0}=89,120,125,144$ with vortex-antivortex pairs initially at positions $(0,\pm 1.75\xi)$ and $(0,\pm 3.25\xi)$. (a) - Top: experimental images of the field amplitude with the amplitude profile along the $x$-axis (white curve). Bottom: associated phase. The phase $\phi_0$ measured in the absence of any vortices is removed. The oriented white curves are streamlines. The topological charges are indicated by blue and red dots (vortices), orange diamonds (saddles) and green diamonds (nodes). (b) - Unwraped phase profile along the $x$-axis. The $2\pi$ phase slip is clearly observed between $\tau=120$ and $\tau=123$. (c) - Total velocity field along the $x$-axis. A large positive extremun at $\tau=120$ is immediately followed by a negative minimum at $\tau=123$.
• Figure 3: Dispersive shock waves and wavetrain. Two counter-rotating vortex of charge $\ell=\pm10$ are imprinted at the input of the medium with two separation distance of $\Delta\tilde{R}=43,30$. (a) - Input velocity profile along the x-axis between the vortices. The inset gives the associated amplitude profile. The blue and light blue curves shows the results for an injected velocity peak $u_0$ of respectively $0.9$ and $1.3$ in speed of sound unit. (b) - Output amplitude images at $\tau_{l_0}=140$ for the two configuration with their associated amplitude along the dark line. (c) - Total velocity along $x$. (d) - Density (top), velocity (bottom) profile obtained in a one-dimensional NLSE with the two initial states shown in (a).
• Figure 4: Critical points - From left to right, phase map of a positive vortex, an anti-vortex pair and two phase extrema, respectively. The associated streamlines are superimposed on the images. Vortex and anti-vortex are represented by blue and red dots, saddle and nodes by orange and green diamond.
• Figure 5: Background velocity - Measured outward flow versus $r/\xi$ from the beam center. Each color plot gives the background velocity at different value of $\tau$ in a single loop. The dashed line at $r/\xi\sim11$ indicate the vortex pair barycenter at the last loop of Fig. \ref{['fig:setup']}(c).