The research, published in Nature under the title “Hyperbolic lattices in circuit quantum electrodynamics” used superconducting circuits to create a lattice that functions as a hyperbolic space. 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.
"The problem is that if you want to study a very complicated quantum mechanical material, then computer modelling is very difficult," said Dr. Alicia Kollár, a postdoctoral research associate at the Princeton Center for Complex Materials. "We're trying to implement a model at the hardware level so that nature does the hard part of the computation for you."
The centimetre-sized chip is etched with a circuit of superconducting resonators that provide paths for microwave photons to move and interact. The resonators on the chip are arranged in a lattice pattern of heptagons, or seven-sided polygons. The structure exists on a flat plane, but simulates the unusual geometry of a hyperbolic plane.
"In normal 3-D space, a hyperbolic surface doesn't exist," explains Houck. "This material allows us to start to think about mixing quantum mechanics and curved space in a lab setting."
Trying to force a three-dimensional sphere onto a two-dimensional plane reveals that space on a spherical plane is smaller than on a flat plane. This is why the shapes of countries appear stretched out when drawn on a flat map of the spherical Earth. In contrast, a hyperbolic plane would need to be compressed in order to fit onto a flat plane.
To simulate the effect of compressing hyperbolic space onto a flat surface, the researchers used a special type of resonator called a coplanar waveguide resonator. When microwave photons pass through this resonator, they behave in the same way whether their path is straight or meandering. The meandering structure of the resonators offers flexibility to "squish and scrunch" the sides of the heptagons to create a flat tiling pattern, said Kollár, who is starting a faculty position at the University of Maryland and Joint Quantum Institute.