We introduce and experimentally realize hyperbolic matter as a novel paradigm for topological states, made of particles moving in the hyperbolic plane with negative curvature. Curvature of space is emulated through a hyperbolic lattice using …

Curved spaces are usually associated with high-energy physics and cosmology. However, through the possibility of tabletop experiments emulating curved spaces and the interest in related synthetic matter, they have become relevant in condensed matter physics as well.

The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we …