Two-dimensional acoustic horizon and ergosphere in a nonlocal photon superfluid

Abstract

Analogue gravity studies the physics of curved spacetime via an analogy with laboratory physics, opening a new window to test the concepts of general relativity experimentally. Sound waves in an inhomogeneous fluid flow behave as a scalar field in a curved spacetime metric. In this context, an acoustic horizon is understood as a surface or area in space where the orthogonal component of the flow speed across that surface equals the speed of sound resulting in a blocking of counter-propagating waves. Recently, quantum fluids of light have attracted particular interest in creating hydrodynamic analogues that are able to re-construct 2D spacetimes of black holes [1]. Photon fluids in a propagating geometry, where the fluid is established by the effective photon-photon interaction in a defocusing nonlinear medium, provide experimentally easy access to superfluidity that is vital for such studies [2]. Here we show that the superfluid character of the photon fluid allows us to build 2D spacetime geometries. By controlling the intensity and the topology of the spatial phase of the beam, we are able to identify a 2D black hole horizon and ergosphere in an analogue system for the first time. Our photon fluid is established in the transverse plane of a paraxially propagating CW laser beam, that is launched through a methanol/graphene solution with a thermal optical nonlinearity. The flow and speed of sound is a function of the spatial phase gradient and intensity of the laser, so controlling these parameters allows easy implementation of 2D flow geometries. With this, we realise the 2D spacetime of a rotating black hole and experimentally map the spatial structure of the local speed of sound of phonon-like excitations and the total flow in the photon fluid to identify an acoustic horizon and ergosphere (Fig. 1). We then add a weak probe beam to create small amplitude excitations in the black hole flow and experimentally observe scattering of these waves from a rotating spacetime, where the scattered part carries away angular momentum. Numerical simulations using the Nonlinear Schrodinger equation allow us to identify the scattering terms responsible and measure the probe's orbital angular momentum (OAM) spectrum. We see amplification of phonons that co propagate with the rotation (far right of Fig. 1), hence gaining energy from the rotating black hole, an effect that shares similarities to Penrose superradiance predicted for astrophysical black holes [3]. Summarising, we present experimental evidence of a two-dimensional horizon and ergosphere of an analogue, rotating black hole and study the scattering and instabilities of small amplitude waves in such a spacetime.