Rayleigh-Taylor instability in nonlinear Schrödinger flow

Abstract

The Rayleigh-Taylor instability (RTI) is a fundamental fluid instability that occurs when a light fluid is accelerated into a heavier one. While techniques for observing the RTI in classical fluids continue to improve, the instability has not been demonstrated in quantum fluids. Here, we exploit the formal equivalence between condensed matter and coherent nonlinear optics to observe the superfluid-like instability directly in the optical system. For the RTI, an initial refractive index gradient sets the acceleration, while self-induced nonlinear interactions lead to velocity differences and shear. The experimental observations show that density fingering is always accompanied by vortex generation, with perturbation modes following a hybrid dynamics: horizontal modes (along the interface) propagate as an incompressible fluid, but the vertical length scale (mixing length) is set by compressible shock dynamics. The growth rate, obtained analytically, shows that inhibition due to diffraction has the same spectral form as viscosity and diffusion, despite the fact that the system is dispersive rather than dissipative. This gives rigorous support for the observation that turbulence in quantum fluids has the same scaling as turbulence in normal fluids. The results hold for any Schrödinger flow, e.g. superfluids and quantum plasma, and introduce a new class of fluid-inspired instabilities in nonlinear optics.