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.
Spaces with negative curvature, however, are still difficult to realize experimentally. We show how to emulate a discretized version of negatively curved space, a so called hyperbolic lattice, using an electric circuit network. We present static and dynamical methods which allowed us to characterize and verify the negative curvature in the implemented model. The first method is based on comparing a "hyperbolic drum" to a drum in flat space, and the second on signal propagation along curved geodesics. Our experiments showcase a versatile platform for emulating hyperbolic lattices in tabletop experiments, which can be utilized to explore dynamics as well as to realize topological hyperbolic matter.
Future developments in this field have the potential to advance our understanding of physics in curved spaces and to provide new perspectives on problems in condensed matter theory, high-energy physics and cosmology.
