Stokes drift and impurity transport in a quantum fluid

Stokes drift is a classical fluid effect in which traveling waves transfer momentum to tracers of the fluid, resulting in a nonzero drift velocity in the direction of the incoming wave; this effect is the driving mechanism allowing particles, i.e., impurities, to be transported by the flow. In a classical (viscous) fluid this happens usually due to the presence of viscous drag forces; because of the eventual absence of viscosity in quantum fluids, impurities are driven by inertial effects and pressure gradients only. We present theoretical predictions of a Stokes drift analogous in quantum fluids finding that, at the leading order, the drift direction and amplitude depend on the initial impurity position with respect to the wave phase, and at the second order, our theoretical model recovers the classical Stokes drift but with a coefficient that depends on the relative particle-fluid density ratio. Our theoretical predictions are obtained for classical impurities using multitime analytical asymptotic expansions. Numerical simulations of a two-dimensional Gross-Pitaevskii equation coupled with a classical impurity corroborate our findings. Our findings are experimentally testable, for instance, using fluids of light obtained in photorefractive crystals.