Nonlinear optical simulation of the post-Newton Schrödinger equation

One of the grand open problems of modern physics is the unification of Einstein’s general relativity and quantum mechanics. This challenge has been approached by the greatest physicists but there is still no complete theory and experimental evidence remains out of reach. The Newton–Schrödinger equation (NSE) offers insight into this puzzle, as it describes a quantum wavefunction under self-gravity dynamics. Having been studied theoretically for decades, optical experiment of this nonlinear model was demonstrated only in 2015. Although the NSE can be generalized to post-Newtonian gravity approximating general relativity, all experiments simulating nonlinear gravity so far have been limited to Newtonian gravity. Here we present experimental emulation of post-Newtonian dynamics by probing a new physical regime of nonlinearity that mimics larger masses in gravity. We find soliton solutions of the post-Newtonian–Schrödinger equations, distinct from their Newtonian counterparts and demonstrate them experimentally. We observe rich beam evolution requiring previously unconsidered nonlinear terms, thereby opening up new experimental capabilities for simulating wavefunction dynamics in the settings of general relativity.