Nanotechnology Now

Our NanoNews Digest Sponsors
Heifer International

Wikipedia Affiliate Button

Home > Press > Strange warping geometry helps to push scientific boundaries

A schematic of the resonators on the microchip, which 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.

CREDIT
Kollár et al.
A schematic of the resonators on the microchip, which 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. CREDIT Kollár et al.

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

Strange warping geometry helps to push scientific boundaries

Princeton, NJ | Posted on July 12th, 2019

Researchers led by Andrew Houck, a professor of electrical engineering, have built an electronic array on a microchip that simulates particle interactions in a hyperbolic plane, a geometric surface in which space curves away from itself at every point. A hyperbolic plane is difficult to envision -- the artist M.C. 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.

The research team 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.

"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 problem is that if you want to study a very complicated quantum mechanical material, then that computer modeling is very difficult. We're trying to implement a model at the hardware level so that nature does the hard part of the computation for you," said Kollár.

The centimeter-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," said 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.

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

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.

Looking at the chip's central heptagon is akin to looking through a fisheye camera lens, in which objects at the edge of the field of view appear smaller than in the center -- the heptagons look smaller the farther they are from the center. This arrangement allows microwave photons that move through the resonator circuit to behave like particles in a hyperbolic space.

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

But first, Kollár and her colleagues will need to further develop the photonic material, both by continuing to examine its mathematical basis and by introducing elements that enable photons in the circuit to interact.

"By themselves, microwave photons don't interact with each other -- they pass right through," said Kollár. Most applications of the material would require "doing something to make it so that they can tell there's another photon there."

###

Kollár plans to continue this line of research as she begins a faculty position at the University of Maryland this summer. Mattias Fitzpatrick, who graduated with a Ph.D. in electrical engineering on June 4, co-authored the study along with Kollár and Houck. Fitzpatrick will begin a postdoctoral fellowship with Assistant Professor of Electrical Engineering Nathalie de Leon.

This research was supported by the National Science Foundation, including the Division of Materials Research and the Multidisciplinary University Research Initiatives program.

####

For more information, please click here

Contacts:
Molly Sharlach

Copyright © Princeton University

If you have a comment, please Contact us.

Issuers of news releases, not 7th Wave, Inc. or Nanotechnology Now, are solely responsible for the accuracy of the content.

Bookmark:
Delicious Digg Newsvine Google Yahoo Reddit Magnoliacom Furl Facebook

Related Links

RELATED JOURNAL ARTICLE:

Related News Press

News and information

Self-driving microrobots December 10th, 2019

CEA-Leti Thin-Film Batteries Target Extended Applications and Improved Performance in Medical Implants: IEDM 2019 Paper Reports Millimeter-Scale TFBs Exhibit the Best Performance In Both Energy and Power Densities December 10th, 2019

Arrowhead Pharmaceuticals Closes Underwritten Public Offering with Gross Proceeds of $266.8 Million December 7th, 2019

'Buildings' in human bone may hold key to stronger 3D-printed lightweight structures December 6th, 2019

Physics

"Inverse Design for Self-Assembly: Patchy Particles, Machine Learning, and the Truth about Entropy" December 3rd, 2019

Theorem explains why quantities such as heat and power can fluctuate in microscopic system: Brazilian researchers participate in theoretical study that could have practical applications in nanoscale machine optimization November 26th, 2019

Cage molecules act as molecular sieves for hydrogen isotope separation November 1st, 2019

Super-strong magnetic supercrystals can assemble themselves October 25th, 2019

Govt.-Legislation/Regulation/Funding/Policy

Self-driving microrobots December 10th, 2019

'Buildings' in human bone may hold key to stronger 3D-printed lightweight structures December 6th, 2019

Artificial cells act more like the real thing December 6th, 2019

Scientists see defects in potential new semiconductor: Discovery could help in effort to make high-powered electronics more efficient December 5th, 2019

Possible Futures

Self-driving microrobots December 10th, 2019

CEA-Leti Thin-Film Batteries Target Extended Applications and Improved Performance in Medical Implants: IEDM 2019 Paper Reports Millimeter-Scale TFBs Exhibit the Best Performance In Both Energy and Power Densities December 10th, 2019

'Buildings' in human bone may hold key to stronger 3D-printed lightweight structures December 6th, 2019

Artificial cells act more like the real thing December 6th, 2019

Optical computing/Photonic computing

Armored with plastic 'hair' and silica, new perovskite nanocrystals show more durability November 29th, 2019

Tiny, biocompatible laser could function inside living tissues: Nanolaser has potential to treat neurological disorders or sense disease biomarkers September 23rd, 2019

Nano bulb lights novel path: Rice University engineers create tunable, nanoscale, incandescent light source September 20th, 2019

Breakthrough enables storage and release of mechanical waves without energy loss: The development may have broad implications for efficient harvesting, storing, and control of energy flow for mechanical and optical applications August 30th, 2019

Discoveries

Artificial cells act more like the real thing December 6th, 2019

Scientists see defects in potential new semiconductor: Discovery could help in effort to make high-powered electronics more efficient December 5th, 2019

Electro-optical device provides solution to faster computing memories and processors: First-of-a-kind electro-optical device provides solution to faster and more energy efficient computing memories and processors December 2nd, 2019

Growing nano-tailored surfaces using micellar brushes November 29th, 2019

Materials/Metamaterials

Toward more efficient computing, with magnetic waves: Circuit design offers a path to 'spintronic' devices that use little electricity and generate practically no heat November 29th, 2019

NAUM’19 reviewed the increasing contribution of graphene nanotubes to sustainable development November 21st, 2019

Scientists probe the limits of ice: Transition between ice and liquid water gets fuzzy at the nanoscale November 9th, 2019

Disordered proteins become stable, 'super-sticky' materials: Improved protein control could lead to wound-healing gels and other applications November 3rd, 2019

Announcements

Self-driving microrobots December 10th, 2019

CEA-Leti Thin-Film Batteries Target Extended Applications and Improved Performance in Medical Implants: IEDM 2019 Paper Reports Millimeter-Scale TFBs Exhibit the Best Performance In Both Energy and Power Densities December 10th, 2019

Arrowhead Pharmaceuticals Closes Underwritten Public Offering with Gross Proceeds of $266.8 Million December 7th, 2019

'Buildings' in human bone may hold key to stronger 3D-printed lightweight structures December 6th, 2019

Interviews/Book Reviews/Essays/Reports/Podcasts/Journals/White papers/Posters

Self-driving microrobots December 10th, 2019

'Buildings' in human bone may hold key to stronger 3D-printed lightweight structures December 6th, 2019

Artificial cells act more like the real thing December 6th, 2019

Scientists see defects in potential new semiconductor: Discovery could help in effort to make high-powered electronics more efficient December 5th, 2019

Photonics/Optics/Lasers

Armored with plastic 'hair' and silica, new perovskite nanocrystals show more durability November 29th, 2019

Researchers synthesize 'impossible' superconductor October 3rd, 2019

Trapping and moving tiny particles using light September 24th, 2019

Tiny, biocompatible laser could function inside living tissues: Nanolaser has potential to treat neurological disorders or sense disease biomarkers September 23rd, 2019

NanoNews-Digest
The latest news from around the world, FREE



  Premium Products
NanoNews-Custom
Only the news you want to read!
 Learn More
NanoStrategies
Full-service, expert consulting
 Learn More











ASP
Nanotechnology Now Featured Books




NNN

The Hunger Project