Objects move through three dimensions in space. But a wide range of experiments that manipulate atoms, molecules, and light can engineer artificial matter in ways that break even that basic law of nature. Such matter can behave as if it were extended to four or more spatial dimensions or restricted to just one or two, as determined by experimental design.
The techniques used by those experiments can control not only dimensionality but also spatial geometries and potential-energy landscapes. Even in one dimension, these abilities have made synthetic dimensions an exciting method to explore topological physics, where precise control of the landscapes is necessary. Frequently, synthetic dimensions are created in ultrasmall and ultracold systems, where the experiments provide powerful access to the hard-to-understand world of interacting quantum matter, which underpins fields as diverse as quantum gravity and solid-state physics.
To understand synthetic dimensions, it helps to distill physical theories into two...
