October 7, 2020
Thanks to Einstein, we know that our three-dimensional space is warped and curved. And in curved space, normal ideas of geometry and straight lines break down, creating a chance to explore an unfamiliar landscape governed by new rules. Spaces that have different geometric rules than those we usually take for granted are called non-Euclidean. Physicists are interested in new physics that curved space can reveal, and non-Euclidean geometries might even help improve designs of certain technologies. One type of non-Euclidean geometry that is of interest is hyperbolic space. Even a two-dimensional, physical version of a hyperbolic space is impossible to make in our normal, “flat” environment. But scientists can still mimic hyperbolic environments to explore how certain physics plays out in negatively curved space. In a recent paper in Physical Review A, a collaboration between Kollár’s research group and JQI Fellow Alexey Gorshkov’s group presented new mathematical tools to better understand simulations of hyperbolic spaces. The research builds on Kollár’s previous experiments to simulate orderly grids in hyperbolic space by using microwave light contained on chips. Their new toolbox includes what they call a “dictionary between discrete and continuous geometry” to help researchers translate experimental results into a more useful form. With these tools, researchers can better explore the topsy-turvy world of hyperbolic space.