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Strange spiral geometry helps drive scientific boundaries

  Strange spiral geometry helps drive scientific boundaries
Princeton researchers have built an electronic matrix on a microchip that simulates particle interactions in a hyperbolic plane, a geometric surface where space curves from itself at each point. Credit: Kollár et al.

Atomic interactions in everyday solids and liquids are so complex that some of the properties of these materials continue to eliminate physicist's understanding. Solving the problems mathematically is beyond the capabilities of modern computers, so researchers at Princeton University have instead turned into an unusual branch of geometry.

Researchers led by Andrew Houck, professor of electrical engineering, have built an electronic matrix on a microchip that simulates particle shifts in a hyperbolic plane, a geometric surface where space curves from itself at each point. A hyperbolic plan is difficult to predict ̵

1; the artist M.C. Escher used hyperbolic geometry in many of his bowing pieces, but is perfect for answering questions about particle interactions and other challenging mathematical issues.

The research team used superconducting circuits to create a grid that acts as a hyperbolic space. When the researchers present photons in the grid, they can respond to a wide range of difficult issues by observing the photon's interactions in simulated hyperbolic space.

"You can throw particles together, activate a very controlled amount of interaction between them, and see the complexity emerge," says Houck, who was the highest author of the magazine published July 4 in the journal Nature . .

Alicia Kollár, a postdoctoral researcher at the Princeton Center for Complex Materials and the Study's lead author, said the goal is to allow researchers to address complex queries of quantum interactions that govern the construction of atomic and subatomic particles.

"The problem is that if you want to study a very complicated quantum mechanical material, then the computer modeling is very difficult. We try to implement a model at the hardware level so that nature makes the difficult part of the calculation for you," says Kollár. [19659005] The centimeter-shaped The chip is etched with a circuit of superconducting resonators that provide pathways for microwave photos to move and interact. The resonators on the chip are arranged in a grid pattern of heptagons or seven sided polygons. The structure exists on a flat plane but simulates the unusual geometry of a hyperbolic plane.

  A strange wave geometry helps drive scientific boundaries
A schematic view of the resonators on the microchip arranged in a lattice pattern of heptagons, or seven sides of polygons. The structure exists on a plane, but simulates the unusual geometry of the a hyperbolic plan Credit: Kollár et al.

"In normal 3-D space, there is no hyperbolic surface," Houck said. "This material allows us to start thinking about mixing quantum mechanics and curved space in a laboratory setting."

Trying to force a three-dimensional sphere on a two-dimensional plane reveals that space on a spherical plane is smaller than on a plane plane. Therefore, the shapes of the countries appear to be extended when drawn on a flat map of the spherical earth. In contrast, a hyperbolic plane must be compressed to fit on a plane.

"It is a space that you can mathematically write down but it is very difficult to visualize because it is too big to fit into our space," Kollár explained.

To simulate the effect of compressing hyperbolic space on a flat surface, the researchers used a special type of resonator called a coplanar waveguide resonator. When microwave photos pass through this resonator, they behave in the same way whether their path is straight or winding. The resonant winding structure gives flexibility to "squish and scrunch" the sides of the heptagons to create a flat tile pattern, Kollár says.

Look at the chip's central heptagon similar to looking through a fisheye camera lens, where objects at the edge of the field of view look smaller than in the middle – the heptagon looks smaller the longer they are from the center. This arrangement enables microwave photons moving through the resonator circuit to appear as particles in a hyperbolic space.

The chip's ability to simulate curved space could enable new investigations into quantum mechanics, including the properties of energy and matter in the distorted space-time around black holes. The material can also be useful for understanding complex webs of relationships in mathematical graph theory and communication networks. Kollár noted that this research could ultimately contribute to the design of new materials.

But first, Kollár and her colleagues must further develop the photonic material, both by continuing to investigate their mathematical foundation and by introducing elements that enable photons in the circuit to interact.

"In themselves, microwave photos do not affect each other – they pass immediately," Kollár said. Most of the applications of the material would require "do something to make it so that they can tell that there is another photo there."
[19659] Natural materials discovered to exhibit hyperbolicity in the plane

More information:
Alicia J. Kollár et al., Hyperbolic lattice in circuit quantum electrodynamics, Nature (2019). DOI: 10,1038 / s41586-019-1348-3

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Princeton University

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Strange spiral geometry helps drive scientific boundaries (2019, July 12)
July 12, 2019
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