Turbulence Excitation in Counter-Streaming Paraxial Superfluids of Light

TL;DR

This paper develops a theoretical framework and numerical simulations to study turbulence and instabilities in superfluid-like light fluids, revealing vortex formation and turbulence onset in optical systems.

Contribution

It introduces a new theory describing kinetic instabilities in counter-streaming paraxial light superfluids and characterizes their nonlinear development and turbulence saturation.

Findings

Identification of a kinetic instability in interacting light superfluids.

Numerical evidence of vortex nucleation and turbulence saturation.

Discussion of experimental observation possibilities.

Abstract

Turbulence in the quantum (superfluid) regime, similarly to its classical counterpart, continues to attract a great deal of scientific inquiry, due to the yet high number of unresolved problems. While turbulent states can be routinely created in degenerate atomic gases, there is no generic scheme to produce turbulence in fluids of light. Under paraxial propagation, light in bulk nonlinear media behaves as a two-dimensional superfluid, described by a nonlinear Schr\"{o}dinger equation formally equivalent to the Gross-Pitaevskii model of a weakly interacting Bose gas, where photon-photon interactions are mediated by a third order (Kerr) nonlinearity. Here, we develop the theory describing the onset of a kinetic instability when two paraxial optical fluids with different streaming velocities interact via the optical nonlinearity. From numerical simulations of the nonlinear Schr\"{o}dinger equation, we further characterize the onset of the instability and describe its saturation in the form of vortex nucleation and excitation of turbulence. The experimental observation of such effects is also discussed. The class of instabilities described here thus provide a natural route towards the investigation of quantum (superfluid) turbulence, structure formation and out-of-equilibrium dynamics in superfluids of light.