Atomic interactions in everyday solids and liquids are so complex that some of these materials' properties continue to elude physicists' understanding.

Escher used hyperbolic geometry in many of his mind-bending pieces -- but is perfect for answering questions about particle interactions and other challenging mathematical questions.

When the researchers introduce photons into the lattice, they can answer a wide range of difficult questions by observing the photons' interactions in simulated hyperbolic space.

"You can throw particles together, turn on a very controlled amount of interaction between them, and see the complexity emerge," said Houck, who was the senior author of the paper published July 4 in the journal Nature.

Alicia Kollár, a postdoctoral research associate at the Princeton Center for Complex Materials and the study's lead author, said the goal is to allow researchers to address complex questions about quantum interactions, which govern the behavior of atomic and subatomic particles.

The centimeter-sized chip is etched with a circuit of superconducting resonators that provide paths for microwave photons to move and interact.

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