Optical simulations of gravitational effects in the Newton-Schrödinger system

Some predictions of Einstein's theory of general relativity (GR) still elude observation, hence analogous systems, such as optical set-ups, have been suggested as platforms for emulating GR phenomena. GR is inherently nonlinear: for example, the curvature of space is induced by masses whose dynamics is also affected by the curved space they themselves induce. But, thus far all GR emulation experiments with optical systems have reproduced only linear dynamics. Here, we study gravitational effects with optical wavepackets under a long-range nonlocal thermal nonlinearity. This system is mathematically equivalent to the Newton-Schrödinger model proposed to describe the gravitational self-interaction of quantum wavepackets. We emulate gravitational phenomena by creating interactions between a wavepacket and the gravitational potential of a massive star, observing gravitational lensing, tidal forces and gravitational redshift and blueshift. These wavepackets interact in the curved space they themselves induce, exhibiting complex nonlinear dynamics arising from the interplay between diffraction, interference and the emulated gravitational effects.