UMD-NIST Self-Directing AI System Discovers New Material

When the words “artificial intelligence” (AI) come to mind, your first thoughts may be supercomputers, or robots that perform tasks without assistance from humans. Now, a multi-institutional team led by researchers from the University of Maryland (UMD) and National Institute of Standards and Technology (NIST) working with collaborators at Stanford University, University of Washington, University of Pennsylvania, and Duke University have accomplished something not too far off. They developed an AI algorithm called CAMEO that discovered a useful new material without requiring additional training from scientists. The AI system could help reduce the amount of trial-and-error time scientists spend in the lab, while maximizing productivity and efficiency in their research.

The research team published their work on CAMEO in Nature Communications on November 24, 2020.

In the field of materials science, scientists seek to discover new materials that can be used in specific applications. “For example, we are always looking are new quantum materials which can be used for quantum computers and sensors,” said physics affiliate Ichiro Takeuchi, a professor of materials science and engineering and member of the Quantum Materials Center (QMC) at UMD.

But finding such new materials usually takes a large number of coordinated experiments and time-consuming theoretical searches. If a researcher is interested in how a material’s properties vary with different temperatures, then that may mean 10 experiments at 10 different temperatures. Temperature, however, is just one parameter. If there are five parameters, each with 10 values, then that researcher must run the experiment 10 x 10 x 10 x 10 x 10 times, a total of 100,000 experiments. It’s nearly impossible for a researcher to run that many experiments via brute force due to the years or decades it may take.

That’s where CAMEO comes in. Short for Closed-Loop Autonomous System for Materials Exploration and Optimization, CAMEO can ensure that each experiment maximizes the scientist’s knowledge and understanding, skipping over experiments that would give redundant information. Helping scientists reach their goals faster with fewer experiments also enables  labs to use their limited resources more efficiently. But how is CAMEO able to do this?

Method Behind the Process

Active learning is a machine learning technique in which computer programs can access data and process it themselves, automatically updating the knowledge and deciding the optimum sequence of information acquisition. This is the basis for CAMEO, a self-learning AI that uses prediction and uncertainty to determine which experiment to try next.

As implied by its name, CAMEO looks for a useful new material by operating in a closed loop: it determines which experiment to run on a material, does the experiment, and collects the data. It can also ask for more information, such as the crystal structure of the desired material, from the scientist before running the next experiment, which is informed by all past experiments achieved in the loop.  

“The key to our experiment was that we were able to unleash CAMEO on a combinatorial library where we had made a large array of materials with all different compositions,” said Takeuchi. “In a usual combinatorial study, every material in the array would have been measured one by one to look for the compound with the best properties. Depending on the property of interest, even with a fast measurement setup, that can take a long, long time. With CAMEO, it only took a small fraction of total number of measurements to home in on the best material.”

The AI is also designed to contain knowledge of key principles, some of which includes knowledge of past simulations and lab experiments, how the equipment works, and physical concepts. For example, the researchers armed CAMEO with the knowledge of phase diagrams, which describes how the arrangement of atoms in a material changes with chemical composition and temperature.

Understanding how atoms are arranged in a material is important in determining its properties such as how hard, or how electrically-insulating it is, and how well it is suited for a specific application.

“The AI is unsupervised,” said NIST researcher, Aaron Gilad Kusne. “Many types of AI need to be trained or supervised. Instead of asking it to learn physical laws, we encode them into the AI. You don’t need a human to train the AI.”

One of the best ways to figure out the structure of a material is by bombarding it with x-rays, in a technique called x-ray diffraction. By identifying the angles at which the x-rays bounce off, scientists determine how atoms are arranged in a material, enabling them to figure out its crystal structure. However, a single in-house x-ray diffraction experiment can take an hour or more. At a synchrotron facility, a large machine the size of a football field that accelerates electrically charged particles at close to the speed of light, this process can take 10 seconds, because the fast-moving particles emit large numbers of x-rays. This is the method used in the study at the Stanford Synchrotron Radiation Lightsource.

CAMEO then decides which material composition to study next and focuses the x-rays on the appropriate part of the sample where that composition exists, to investigate its atomic structure. With each new iteration, CAMEO learns from past measurements and identifies the next material to study.  This allows the AI to explore how a material’s composition impacts its structure and use this information to find the best material for the task.

“Think of this process as trying to make the perfect cake,” Kusne said. “You’re mixing different types of ingredients, flour, eggs, or butter, using a variety of recipes to make the best cake. With the AI, it’s searching through the ‘recipes’ or experiments to determine the best composition for the material.”

That is how CAMEO discovered the material  which the group shortened to GST467. CAMEO was provided with 177 potential materials to investigate, covering a large range of compositional recipes. To arrive at this material, CAMEO performed 19 different experimental cycles, which took 10 hours, compared to the estimated 90 hours it would have taken a scientist with the full set of 177 materials.

The New Material

The material is composed of three different elements (germanium, antimony and tellurium, Ge-Sb-Te) and is a phase-change memory material, that is, it changes its atomic structure from crystalline (solid material with atoms in designated, regular positions) to amorphous (solid material with atoms in random positions) when quickly melted by applying heat. This type of material is used in memory applications such as data storage. Although there are infinite composition variations possible in the Ge-Sb-Te alloy system, the new material GST467 discovered by CAMEO is optimal for phase-change applications.

The research team wanted CAMEO to find the best Ge-Sb-Te alloy, one that had the largest difference in optical contrast between the crystalline and amorphous states. Optical contrast, for example on a DVD disc, allows a scanning laser to read the disc by distinguishing between regions that have high or low reflectivity. They found that GST467 has twice the contrast for a phase change material compared to GST225 or , a well-known material that’s commonly used for DVDs. The larger contrast enables the new material to outperform the old material by a significant margin.

The key part of the experiments was conducted at the Stanford National Accelerator Laboratory (SLAC) at Stanford University, for the U.S. Department of Energy Office of Science. SLAC researchers helped oversee the experiments run by CAMEO.

UMD researchers provided the materials used in the experiments and researchers at the University of Washington – led by Electrical and Computer Engineering Professor, Mo Li – demonstrated the new material in a patterned phase-change memory device. 

The new material GST467 has applications for photonic switching devices, which control the direction of light in a circuit. They can also be applied in neuromorphic computing, a field of study focused on developing devices that emulate the structure and function of neurons in the brain, opening possibilities for new kinds of computers as well as other applications such as extracting useful data from complex images.

The work also involved collaboration with electron microscopists at NIST who performed high-resolution microscopy to understand the microstructure of the newly found compound.

Applications to other Materials

The researchers believe CAMEO can be used for other types of materials, such as high-temperature alloys and quantum materials. The code for CAMEO is open source and will be freely available for use by scientists and researchers.

There had been other reports of closed-loop materials and chemistry optimization work. The critical distinguishing feature of the present work with CAMEO is that it was used to discover a novel solid state material whose functionality is encoded in the composition-structure-property relationship of crystalline materials, and as such, the algorithm was able to navigate the course of discovery path by tracking the structural origins of materials functionalities.

One application of CAMEO is minimizing experimental costs since using synchrotron facilities requires time, researchers need a written proposal to use the equipment, and money. But with AI running the experiments, they can be carried out quicker. Researchers estimate a 10-fold reduction in time for experiments using CAMEO since the number of experiments performed can be cut by one tenth. Because the AI is running the measurements, collecting data and performing the  analysis, this also reduces the amount of knowledge a researcher needs to run the experiment. All the researcher must focus on is running the AI.

Another potential benefit is providing the ability to work remotely for scientists. “This opens up a wave of scientists to still work and be productive without actually being in the lab,” said SLAC researcher Apurva Mehta. This could mean if scientists wanted to work on research involving contagious diseases or viruses, such as COVID-19, they could do so safely and remotely while relying on the AI to conduct the experiments in the lab.

Researchers are continuing to improve the AI and try to make the algorithms capable of solving ever more complex problems. “The ultimate goal is to incorporate synthesis of crystalline materials in the closed loop – this is particularly hard since standard synthesis tools of crystalline functional materials are not equipped with measurement capabilities,” said Takeuchi. “That calls for some novel hardware integration as well as advances in AI. The future is robot materials science.”  

Original story:

Going Beyond the Anti-Laser May Enable Long-Range Wireless Power Transfer

Ever since Nikola Tesla spewed electricity out in all directions with his coil back in 1891, scientists have been thinking up ways to send electrical power through the air. The dream is to charge your phone or laptop, or maybe even a healthcare device such as a pacemaker, without the need for wires and plugs. The tricky bit is getting the electricity to find its intended target, and getting that target to absorb the electricity instead of just reflect it back into the air—all preferably without endangering anyone along the way.

These days, you can wirelessly charge a smartphone by putting it within an inch of a charging station. But usable long-range wireless power transfer, from one side of a room to another or even across a building, is still a work in progress. Most of the methods currently in development involve focusing narrow beams of energy and aiming them at their intended target. These methods have had some success, but are so far not very efficient. And having focused electromagnetic beams flying around through the air is unsettling.Arcs of electricity generated by a Tesla coil. (Credit: Airarcs/CC BY-SA 3.0)Arcs of electricity generated by a Tesla coil. (Credit: Airarcs/CC BY-SA 3.0)

Now, a team of researchers at the University of Maryland (UMD), in collaboration with a colleague at Wesleyan University in Connecticut, have developed an improved technique for wireless power transfer technology that may promise long-range power transmission without narrowly focused and directed energy beams. Their results, which widen the applicability of previous techniques, were published Nov. 17, 2020 in the journal Nature Communications.

The team generalized a concept known as an “anti-laser.” In a laser, one photon triggers a cascade of many photons of the same color shooting out in a coherent beam. In an anti-laser, the reverse happens. Instead of boosting the number of photons, an anti-laser coherently and perfectly absorbs a beam of many precisely tuned photons. It’s kind of like a laser running backwards in time.

The new work, led by UMD Professor of Physics Steven Anlage of the Quantum Materials Center (QMC), demonstrates that it’s possible to design a coherent perfect absorber outside of the original time-reversed laser framework—a relaxation of some of the key constraints in earlier work. Instead of assuming directed beams traveling along straight lines into an absorption target, they picked a geometry that was disorderly and not amenable to being run backwards in time.

“We wanted to see this effect in a completely general environment where there's no constraints,” says Anlage. “We wanted a sort of random, arbitrary, complex environment, and we wanted to make perfect absorption happen under those really demanding circumstances. That was the motivation for this, and we did it.”

Anlage and his colleagues wanted to create a device that could receive energy from a more diffuse source, something that was less beam and more bath. Before tackling the wireless challenge, they set up their generalized anti-laser as a labyrinth of wires for electromagnetic waves to travel through. Specifically, they used microwaves, a common candidate for power transfer applications. The labyrinth consisted of a bunch of wires and boxes connected in a purposefully disordered way. Microwaves going through this labyrinth would get so tangled up that, even if it were possible to reverse time, this still wouldn’t untangle them.

Buried in the midst of this labyrinth was an absorber, the target to deliver power to. The team sent microwaves of different frequencies, amplitudes and phases into the labyrinth and measured how they were transformed. Based on these measurements, they were able to calculate the exact properties of input microwaves that would result in perfect power transfer to the absorber. They found that for correctly chosen input microwaves, the labyrinth absorbed an unprecedented 99.999% of the power they sent into it. This showed explicitly that coherent perfect absorption can be achieved even without a laser run backwards in time.

The team then took a step towards wireless power transfer. They repeated the experiment in a cavity, a plate of brass several feet in each direction with an oddly shaped hole in the middle. The shape of the hole was designed so that the microwaves would bounce around it in an unpredictable, chaotic way. They placed a power absorber inside the cavity, and sent microwaves in to bounce around the open space inside. They were able to find the right input microwave conditions for coherent perfect absorption with 99.996% efficiency.

Recent work by a collaboration of teams in France and Austria also demonstrated coherent perfect absorption in their own disordered microwave labyrinth. However, their experiment was not quite as general as the new work from Anlage and colleagues. In the previous work, the microwaves entering the labyrinth would still be untangled by a hypothetical reversal of time. This might seem like a subtle distinction, but the authors say showing that coherent perfect absorption doesn’t require any kind of order in the environment promises applicability virtually anywhere.

Generalizing previous techniques in this way invites ideas that sound like science fiction, like being able to wirelessly and remotely charge any object in a complex environment, such as an office building, with near perfect efficiency. Such schemes would require that the frequency, amplitude, and phase of the electric power is custom tuned to specific targets. But there would be no need to focus a high-powered beam and aim it at the laptop or phone—the electrical waves themselves would be designed to find their chosen target.

“If we have an object which we want to deliver power to, we will first use our equipment to measure some properties of the system,” says Lei Chen, a graduate student in electrical and computer engineering at UMD and the lead author of the paper. “Based on those properties we can get the unique microwave signals for this kind of system. And it will be perfectly absorbed by the object. For every unique object, the signals will be different and specially designed.”

Although this technique shows great promise, much remains to be done before the advent of wireless and plug-less offices. The perfect absorber depends crucially on the power being tuned just right for the absorber. A slight change in the environment—such as moving the target laptop or raising the blinds in the room—would require an immediate retuning of all the parameters. So, there would need to be a way to quickly and efficiently find the right conditions for perfect absorption on the fly, without using too much power or bandwidth. Additionally, more work needs to be done to determine the efficacy and safety of this technique in realistic environments.

Even though it’s not yet time to throw away all your power cords, coherent perfect absorption may come in handy in many ways. Not only is it general to any kind of target, it is also not limited to optics or microwaves.  “It's not wedded to one specific technology,” says Anlage, “This is a very general wave phenomenon. And the fact that it's done in microwaves is just because that's where the strengths are in my lab. But you could do all of this with acoustics, you could do this with matter waves, you could do this with cold atoms. You could do this in many, many different contexts.”

In addition to Chen and Anlage, Tsampikos Kottos, a professor at Wesleyan University, was a co-author on the paper.

Written by Dina Genkina (This email address is being protected from spambots. You need JavaScript enabled to view it.)


UMD Physicists Contribute to New B Meson Finding

Scientists have known for decades of a massive imbalance between the amount of matter and antimatter in the universe. To resolve the discrepancy, they attempt to recreate the first instant after the Big Bang through fierce collisions of subatomic particles, followed by intense scrutiny of the resulting forces and pieces.  A premiere effort is CERN’s LHCb experiment, in which B mesons’ disintegration provides clues that may someday explain why matter has predominated over antimatter. Although the Standard Model is shown to contain a mechanism that violates the charge-parity (CP) symmetry – the symmetry that ensures equal treatment of reactions involving matter or antimatter particles – it can only account for a small part of the observed matter-antimatter imbalance in the universe. A major goal of the LHCb experiment is to discover possible sources of CP violation beyond the Standard Model.

Now, the LHCb collaboration has announced a major new development, based on data collected during LHC Run 2, confirming and significantly strengthening an anomalous observation in decays of B mesons. At an October 28 CERN workshop, a result of a measurement of the CP violation in a B meson B+→K+π0 was announced.  This is the most precise measurement of CP asymmetry yet found in this decay, and an important data point in studies of B meson decays, following results gained by the BaBar, Belle and Tevatron experiments, as well as LHCb.  This result significantly strengthens the anomalous difference with the measured CP asymmetry in the counterpart decay channel of the neutral B meson (B0→K+π-), an effect yet to be satisfactorily explained in the Standard Model.The images above show the reconstructed invariant mass distribution of K+π0 and K-π0 mass distributions. Clear enhancements at the B+ (left) and B- (right) masses are visible.The images above show the reconstructed invariant mass distribution of K+π0 and K-π0 mass distributions. Clear enhancements at the B+ (left) and B- (right) masses are visible.

UMD postdoc Will Parker made the recent presentation, which can be seen here.

The UMD flavor physics group has been working on B meson decays since 1995 with the design and development of the BaBar experiment at SLAC and since 2014 with the LHCb experiment at CERN. “We are happy that we now have the most precise measurement of this anomaly, which is of huge interest in the particle physics community,” said Distinguished University Professor Hassan Jawahery.

Along with Jawahery, Parker, Phoebe Hamilton and Jason Andrews (PhD 2018),  who carried out this measurement, the UMD LHCb group includes Assistant Professor Manuel Franco Sevilla, researcher Svende Braun, and graduate students Alex Fernez, Yipeng Sun, and Zishuo Yang. In 2019, the LHCb experiment observed CP violation in decays of D mesons. That finding was rated a Physics World Breakthrough of the Year finalist for 2019

To learn more about the new B+→K+π0 result, see the LHCb announcement:  The full paper will be submitted to Physical Review Letters.

A Billion Tiny Pendulums Could Detect the Universe’s Missing Mass

Researchers at the National Institute of Standards and Technology (NIST), the University of Maryland's Joint Quantum Institute (JQI), and their colleagues have proposed a novel method for finding dark matter, the cosmos’s mystery material that has eluded detection for decades. Dark matter makes up about 27% of the universe; ordinary matter, such as the stuff that builds stars and planets, accounts for just 5% of the cosmos. (A mysterious entity called dark energy, accounts for the other 68%.)

According to cosmologists, all the visible material in the universe is merely floating in a vast sea of dark matter—particles that are invisible but nonetheless have mass and exert a gravitational force. Dark matter’s gravity would provide the missing glue that keeps galaxies from falling apart and account for how matter clumped together to form the universe’s rich galactic tapestry. 

The proposed experiment, in which a billion millimeter-sized pendulums would act as dark matter sensors, would be the first to hunt for dark matter solely through its gravitational interaction with visible matter. The experiment would be one of the few to search for dark matter particles with a mass as great as that of a grain of salt, a scale rarely explored and never studied by sensors capable of recording tiny gravitational forces.

Previous experiments have sought dark matter by looking for nongravitational signs of interactions between the invisible particles and certain kinds of ordinary matter. That’s been the case for searches for a hypothetical type of dark matter called the WIMP (weakly interacting massive particles), which was a leading candidate for the unseen material for more than two decades. Physicists looked for evidence that when WIMPs occasionally collide with chemical substances in a detector, they emit light or kick out electric charge. 

Dark matter, the hidden stuff of our universe, is notoriously difficult to detect. In search of direct evidence, NIST researchers have proposed using a 3D array of pendulums as force detectors, which could detect the gravitational influence of passing dark matter particles. When a dark matter particle is near a suspended pendulum, the pendulum should deflect slightly due to the attraction of both masses. However, this force is very small, and difficult to isolate from environmental noise that causes the pendulum to move. To better isolate the deflections from passing particles, NIST researchers propose using a pendulum array. Environmental noise affects each pendulum individually, causing them to move independently. However, particles passing through the array will produce correlated deflections of the pendulums. Because these movements are correlated, they can be isolated from the background noise, revealing how much force a particle delivers to each pendulum and the particle’s speed and direction, or velocity.

Researchers hunting for WIMPs in this way have either come up empty-handed or garnered inconclusive results; the particles are too light (theorized to range in mass between that of an electron and a proton) to detect through their gravitational tug. 

With the search for WIMPs seemingly on its last legs, researchers at NIST and their colleagues are now considering a more direct method to look for dark matter particles that have a heftier mass and therefore wield a gravitational force large enough to be detected.

“Our proposal relies purely on the gravitational coupling, the only coupling we know for sure that exists between dark matter and ordinary luminous matter,” said study co-author Daniel Carney, a theoretical physicist jointly affiliated with JQI, the National Institute of Standards and Technology (NIST), the Joint Center for Quantum Information and Computer Science (QuICS), and the Fermi National Accelerator Laboratory. 

The researchers—who also include Adjunct Professor Jacob Taylor, Sohitri Ghosh of JQI and QuICS, and Gordan Krnjaic of the Fermi National Accelerator Laboratory—calculate that their method can search for dark matter particles with a minimum mass about half that of a grain of salt, or about a billion billion times the mass of a proton. The scientists reported their findings recently in Physical Review D(link is external).

Because the only unknown in the experiment is the mass of the dark matter particle, not how it couples to ordinary matter, “if someone builds the experiment we suggest, they either find dark matter or rule out all dark matter candidates over a wide range of possible masses,” said Carney. The experiment would be sensitive to particles ranging from about 1/5,000 of a milligram to a few milligrams. 

That mass scale is particularly interesting because it covers the so-called Planck mass, a quantity of mass determined solely by three fundamental constants of nature and equivalent to about 1/5,000 of a gram. 

Carney, Taylor and their colleagues propose two schemes for their gravitational dark matter experiment. Both involve tiny, millimeter-size mechanical devices acting as exquisitely sensitive gravitational detectors. The sensors would be cooled to temperatures just above absolute zero to minimize heat-related electrical noise and shielded from cosmic rays and other sources of radioactivity. In one scenario, a myriad of highly sensitive pendulums would each deflect slightly in response to the tug of a passing dark matter particle.

Similar devices (with much larger dimensions) have already been employed in the recent Nobel-prize-winning detection of gravitational waves, ripples in the fabric of space-time predicted by Einstein’s theory of gravity. Carefully suspended mirrors, which act like pendulums, move less than the length of an atom in response to a passing gravitational wave. 

In another strategy, the researchers propose using spheres levitated by a magnetic field or beads levitated by laser light. In this scheme, the levitation is switched off as the experiment begins, so that the spheres or beads are in free fall. The gravity of a passing dark matter particle would ever so slightly disturb the path of the free-falling objects. 

“We are using the motion of objects as our signal,” said Taylor. “This is different from essentially every particle physics detector out there.” 

The researchers calculate that an array of about a billion tiny mechanical sensors distributed over a cubic meter is required to differentiate a true dark matter particle from an ordinary particle or spurious random electrical signals or “noise” triggering a false alarm in the sensors. Ordinary subatomic particles such as neutrons (interacting through a nongravitational force) would stop dead in a single detector. In contrast, scientists expect a dark matter particle, whizzing past the array like a miniature asteroid, would gravitationally jiggle every detector in its path, one after the other. 

Noise would cause individual detectors to move randomly and independently rather than sequentially, as a dark matter particle would. As a bonus, the coordinated motion of the billion detectors would reveal the direction the dark matter particle was headed as it zoomed through the array.

To fabricate so many tiny sensors, the team suggests that researchers may want to borrow techniques that the smartphone and automotive industries already use to produce large numbers of mechanical detectors.

Thanks to the sensitivity of the individual detectors, researchers employing the technology needn’t confine themselves to the dark side. A smaller-scale version of the same experiment could detect the weak forces from distant seismic waves as well as that from the passage of ordinary subatomic particles, such as neutrinos and single, low-energy photons (particles of light). 

The smaller-scale experiment could even hunt for dark matter particles—if they impart a large enough kick to the detectors through a nongravitational force, as some models predict, Carney said. 

“We are setting the ambitious target of building a gravitational dark matter detector, but the R&D needed to achieve that would open the door for many other detection and metrology measurements,” said Carney. 

Researchers at other institutions have already begun conducting(link is external) preliminary experiments using the NIST team’s blueprint.

This story was originally published by NIST News(link is external). It has been adapted with minor changes here. JQI is a research partnership between UMD and NIST, with the support and participation of the Laboratory for Physical Sciences

Reference Publication: 
"Proposal for gravitational direct detection of dark matter,"Daniel Carney, Sohitri Ghosh, Gordan Krnjaic, Jacob M. Taylor., Phys. Rev. D, 102, 072003 (2020)


Mind and Space Bending Physics on a Convenient Chip

Thanks to Einstein, we know that our three-dimensional space is warped and curved. And in curved space, normal ideas of geometry and straight lines break down, creating a chance to explore an unfamiliar landscape governed by new rules. But studying how physics plays out in a curved space is challenging: Just like in real estate, location is everything.

“We know from general relativity that the universe itself is curved in various places,” says Assistant Professor JQI Fellow Alicia Kollár, who is also a Fellow of the Joint Quantum Institute and the Quantum Technology Center. “But, any place where there's actually a laboratory is very weakly curved because if you were to go to one of these places where gravity is strong, it would just tear the lab apart.”

Spaces that have different geometric rules than those we usually take for granted are called non-Euclidean(link is external). If you could explore non-Euclidean environments, you would find perplexing landscapes. Space might contract so that straight, parallel lines draw together instead of rigidly maintaining a fixed spacing. Or it could expand so that they forever grow further apart. In such a world, four equal-length roads that are all connected by right turns at right angles might fail to form a square block that returns you to your initial intersection.On the left is a representation of a grid of heptagons in a hyperbolic space. To fit the uniform hyperbolic grid into “flat” space, the size and shape of the heptagons are distorted. In the appropriate hyperbolic space, each heptagon would have an identical shape and size, instead of getting smaller and more distorted toward the edges. On the right is a circuit that simulates a similar hyperbolic grid by directing microwaves through a maze of zig-zagging superconducting resonators. (Credit: Springer Nature; Produced by Princeton, Houck Lab)On the left is a representation of a grid of heptagons in a hyperbolic space. To fit the uniform hyperbolic grid into “flat” space, the size and shape of the heptagons are distorted. In the appropriate hyperbolic space, each heptagon would have an identical shape and size, instead of getting smaller and more distorted toward the edges. On the right is a circuit that simulates a similar hyperbolic grid by directing microwaves through a maze of zig-zagging superconducting resonators. (Credit: Springer Nature; Produced by Princeton, Houck Lab)

These environments overturn core assumptions of normal navigation and can be impossible to accurately visualize. Non-Euclidean geometries are so alien that they have been used in videogames and horror stories(link is external) as unnatural landscapes that challenge or unsettle the audience.

But these unfamiliar geometries are much more than just distant, otherworldly abstractions. Physicists are interested in new physics that curved space can reveal, and non-Euclidean geometries might even help improve designs of certain technologies. One type of non-Euclidean geometry that is of interest is hyperbolic space—also called negatively-curved space. Even a two-dimensional, physical version of a hyperbolic space is impossible to make in our normal, “flat” environment. But scientists can still mimic hyperbolic environments to explore how certain physics plays out in negatively curved space.

In a recent paper in Physical Review A, a collaboration between the groups of Kollár and JQI Fellow Alexey Gorshkov, who is also a physicist at the National Institute of Standards and Technology, presented new mathematical tools to better understand simulations of hyperbolic spaces. The research builds on Kollár’s previous experiments(link is external) to simulate orderly grids in hyperbolic space by using microwave light contained on chips. Their new toolbox includes what they call a “dictionary between discrete and continuous geometry” to help researchers translate experimental results into a more useful form. With these tools, researchers can better explore the topsy-turvy world of hyperbolic space.

The situation isn’t precisely like Alice falling down the rabbit hole, but these experiments are an opportunity to explore a new world where surprising discoveries might be hiding behind any corner and the very meaning of turning a corner must be reconsidered.

“There are really many applications of these experiments,” says JQI postdoctoral researcher Igor Boettcher, who is the first author of the new paper. “At this point, it's unforeseeable what all can be done, but I expect that it will have a lot of rich applications and a lot of cool physics.”

A Curved New World

In flat space, the shortest distance between two points is a straight line, and parallel lines will never intersect—no matter how long they are. In a curved space, these basics of geometry no longer hold true. The mathematical definitions of flat and curved are similar to the day to day meaning when applied to two dimensions. You can get a feel for the basics of curved spaces by imagining—or actually playing around with—pieces of paper or maps.

For instance, the surface of a globe (or any ball) is an example of a two-dimensional positively curved space. And if you try to make a flat map into a globe, you end up with excess paper wrinkling up as you curve it into a sphere. To have a smooth sphere you must lose the excess space, resulting in parallel lines eventually meeting, like the lines of longitude that start parallel at the equator meeting at the two poles. Due to this loss, you can think of a positively curved space as being a less-spacy space than flat space.

Hyperbolic space is the opposite of a positively curved space—a more-spacy space. A hyperbolic space curves away from itself at every point. Unfortunately, there isn’t a hyperbolic equivalent of a ball that you can force a two-dimensional sheet into; it literally won’t fit into the sort of space that we live in.

The best you can do is make a saddle (or a Pringle) shape where the surrounding sheet hyperbolically curves away from the center point. Making every point on a sheet similarly hyperbolic is impossible; there isn’t a way to keep curving and adding paper to create a second perfect saddle point without it bunching up and distorting the first hyperbolic saddle point.

The extra space of a hyperbolic geometry makes it particularly interesting since it means that there is more room for forming connections. The differences in the possible paths between points impacts how particles interact and what sort of uniform grid—like the heptagon grid shown above—can be made. Taking advantage of the extra connections that are possible in a hyperbolic space can make it harder to completely cut sections of a grid off from each other, which might impact designs of networks like the internet(link is external).

Navigating Labyrinthine Circuits

Since it is impossible to physically make a hyperbolic space on Earth, researchers must settle for creating lab experiments that reproduce some of the features of curved space. Kollár and colleagues previously showed that they can simulate a uniform, two-dimensional curved space. The simulations are performed using circuits (like the one shown above) that serve as a very organized maze for microwaves to travel through.

A feature of the circuits is that microwaves are indifferent to the shapes of the resonators that contain them and are just influenced by the total length. It also doesn’t matter at what angle the different paths connect. Kollár realized that these facts mean the physical space of the circuit can effectively be stretched or squeezed to create a non-Euclidean space—at least as far as the microwaves are concerned.

In their prior work, Kollár and colleagues were able to create mazes with various zigs-zagging path shapes and to demonstrate that the circuits simulated hyperbolic space. Despite the convenience and orderliness of the circuits they used, the physics playing out in them still represents a strange new world that requires new mathematical tools to efficiently navigate.

Hyperbolic spaces offer different mathematical challenges to physicists than the Euclidean spaces in which they normally work. For instance, researchers can’t use the standard physicist trick of imagining a lattice getting smaller and smaller to figure out what happens for an infinitely small grid, which should act like a smooth, continuous space. This is because in a hyperbolic space the shape of the lattice changes with its size due to the curving of the space. The new paper establishes mathematical tools, such as a dictionary between discrete and continuous geometry, to circumvent these issues and make sense of the results of simulations.

With the new tools, researchers can get exact mathematical descriptions and predictions instead of just making qualitative observations. The dictionary allows them to study continuous hyperbolic spaces even though the simulation is only of a grid. With the dictionary, researchers can take a description of microwaves traveling between the distinct points of the grid and translate them into an equation describing smooth diffusion, or convert mathematical sums over all the sites on the grid to integrals, which is more convenient in certain situations.

“If you give me an experiment with a certain number of sites, this dictionary tells you how to translate it to a setting in continuous hyperbolic space,” Boettcher says. “With the dictionary, we can infer all the relevant parameters you need to know in the laboratory setup, especially for finite or small systems, which is always experimentally important.”

With the new tools to help understand simulation results, researchers are better equipped to answer questions and make discoveries with the simulations. Boettcher says he’s optimistic about the simulations being useful for investigating the AdS/CFT correspondence(link is external), a physics conjecture for combining theories of quantum gravity and quantum field theories using a non-Euclidean description of the universe. And Kollár plans to explore if these experiments can reveal even more physics by incorporating interactions into the simulations.

“The hardware opened up a new door,” Kollár says. “And now we want to see what physics this will let us go to.”

Research Contact: Igor Boettcher, This email address is being protected from spambots. You need JavaScript enabled to view it.
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Media Contact:  Bailey Bedford, This email address is being protected from spambots. You need JavaScript enabled to view it.
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