Swimming against a superfluid flow: Self-propulsion via vortex-antivortex shedding in a quantum fluid of light

Abstract

A superfluid flows without friction below a critical velocity, exhibiting zero drag force on impurities. Above this threshold, superfluidity breaks down, and the internal energy is redistributed into incoherent excitations such as vortices. We demonstrate that a finite-mass, mobile impurity immersed in a flowing two-dimensional paraxial superfluid of light can \textit{swim} against the superfluid current when this critical velocity is exceeded. This self-propulsion is achieved by the periodic emission of quantized vortex-antivortex pairs downstream, which impart an upstream recoil momentum that results in a net propulsive force. Analogous to biological systems that minimize effort by exploiting wake turbulence, the impurity harnesses this vortex backreaction as a passive mechanism of locomotion. Reducing the impurity dynamics to the motion of its center of mass and using a point-vortex model, we quantitatively describe how this mechanism depends on the impurity geometry and the surrounding flow velocity. Our findings establish a fundamental link between internal-energy dissipation in quantum fluids and concepts of self-propulsion in active-matter systems, and opens new possibilities for exploiting vortices for controlled quantum transport at the microscale.

Figures (3)

• Figure 1: Hydrodynamic flow of superfluid light past a mobile optical impurity.a -- Schematic of the experimental setup. The fluid beam is generated with a 780 nm laser beam, sent through a 20 cm-long hot rubidium-vapor cell maintained at 150 °C. The optical impurity is generated by injecting a narrower, 795 nm beam, which overlaps the fluid beam. The relative angle between the two beams controls the transverse flow velocity. b -- Intensity of the impurity beam, measured along the rubidium cell using the top camera and a frequency filter at 795 nm. Each segment is normalized relative to its maximum value. Here, the Mach number of the flow is $\beta = 0.7$. The observed shift of the beam relative to its smoothed white dashed reference position, corresponding to the fluid of light at rest, indicates that the impurity moves upstream in the transverse plane. c -- Transverse intensity of the fluid of light at the cell output for $\beta = 0$ and $\beta = 0.4$. Top: fluid amplitudes taken with a 780 nm filter. Middle: impurity amplitudes taken with a 795 nm filter. Bottom: associated phase of the fluid. Each amplitude image is normalized to its maximum amplitude value. The vortex-antivortex pair generated downstream at $\beta=0.4$ is highlighted with white circles centered on the $\pm2\pi$ phase-windings, respectively.
• Figure 2: Upstream motion of the impurity by vortex-antivortex shedding.a -- Output amplitude images of the fluid for increasing values of the incoming Mach number, from $\beta=0$ (top) to $\beta=1.1$ (bottom), with each image normalized by its maximum value. The typical radius of the impurity is $\simeq7.5\xi$. The dashed line indicates the initial position of the impurity, highlighting upstream motion from vortex shedding. b -- Associated vorticity and streamlines maps. A counterflow appears along the central axis of the vortex alley produced downstream. c -- Local flow velocity along the $x$ axis at the position of the impurity as a function of the incoming Mach number $\beta$. When the local flow velocity reaches the local sound velocity ($\simeq0.35c_{\mathrm{s}}$; thick purple line)---which occurs at $\beta\equiv\beta_{\mathrm{c}}\simeq0.35$---the flow transitions from superfluid to normal. This change is marked by the periodic emission of vortex-antivortex pairs (white circles) and the onset of a counterflow at the center of these pairs. The two vertical dashed lines correspond to images (i) and (ii) on panel (a), respectively. The inset shows the vortex-shedding frequency $1/\Delta z$ against $\beta$, obtained at each emission event. The solid line is obtained from a linear fit based on prediction \ref{['Eq:Deltaz']}. d -- Impurity trajectory of Fig. \ref{['fig:setup_swim']}(b) measured along the rubidium cell at $\beta=0.7$. The red lines show the fits obtained using Eqs. \ref{['Eq:Xz']} and \ref{['Eq:DensityImbaba']} at each vortex emission. e – Momentum distribution of the fluid's excitations in the upstream region in the reference frame of the fluid for $\beta=0,~0.4,~0.6,~1.1$. The inset of each image shows the associated polar plot.
• Figure 3: Density-weighted velocity and net momentum.a -- $x$ component of the incompressible density-weighted velocity for $\beta=0.2$ (top), 0.5 (middle), and 1.1 (bottom). The respective right panels show cuts along the white dashed lines at $y=0$. The dark solid lines indicate the impurity position and the dark dashed lines correspond to $u_{x}^{\mathrm{inc}}(x,0)=0$. b -- Downstream $x$ component of the net momentum of the fluid as a function of $\beta$, in the reference frame of the fluid. Purple squares, blue triangles and gray reversed triangles respectively show the total, incompressible (vortex), and compressible (sound) contributions.