Alicia Kollár Bridges Abstract Math with Realities of the Lab

Eugene Wigner, a Nobel Prize-winning mathematical physicist, once said, “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.”

Indeed, mathematics may seem abstract or even irrelevant until it’s used to describe the natural world around us. The reverse is occasionally also true: Physical realities, when brought to a mathematician’s attention, can inspire new questions and new discoveries. 

The research of Alicia Kollár, a Chesapeake Assistant Professor of Physics at the University of Maryland and a Fellow of the Joint Quantum Institute, embodies the give and take of this relationship between physics and mathematics. In her lab, she brings abstract theories to life and in turn collaborates on new theorems. She has forged a research program of manipulating light on a chip, coaxing the light into behaving as though it lives on the surface of a sphere, or a mathematical abstraction known as a hyperbolic surface. She also collaborates with mathematicians, furthering both the understanding of what these chips can do and their underlying mathematics. 

Alicia KollárAlicia KollárA direct collaboration with pure mathematicians is uncommon for a physicist, particularly an experimentalist. But Kollár is no stranger to mathematics. Raised by two mathematicians in Princeton, New Jersey, she was exposed to the discipline early on. However, Kollár said her parents didn’t pressure her to pursue mathematics growing up. 

“It never crossed my dad’s mind to try to force me to do what he loved,” Kollár said. “He considered that pointless, like ‘You should go into research for you, not for somebody else’s expectations.’” 

Her father, János Kollár, a professor of mathematics at Princeton, had a slightly different take. 

“She was always interested in science, so I didn’t need to apply any influence,” he said. “If she was only interested in rock music it might have been different.”

Free to pursue whatever she pleased (short of rock music), Kollár studied advanced math, but without much enthusiasm. 

“I was fortunate to be able to take quite a bit of college-level pure math as a high schooler,” she said. “And I would say that I think I was good at it, but I didn’t love it. I just kind of didn’t care.” 

What really caught Kollár’s attention was physics. Her high school physics teacher’s style really resonated with her. 

“He was a crusty old dude that loved Far Side cartoons,” she recalled. “And he wouldn’t put up with anybody that was too cool for school. He taught non-calculus physics, but he taught that you have to think about it—not ‘Here’s a method learn how to do it.’ We became really good friends, and I really liked thinking about how it works, you know, the physical intuition part of physics.”

She attended college at Princeton University, remaining in her hometown and further developing her fascination with physics. 

“I was sort of divided between math and physics as a freshman,” Kollár said. “But the more physics I took, I never looked back.”

During her first summer research experience, she was charged with taking apart a telescope mount for a cosmology group. That’s when she found her calling as an experimentalist.  

“I had a lot of fun that summer,” she said, smiling. “I ended up building a 1500-pound steel support structure. I was up to my eyeballs in machine oil and loving every minute of it.”

When applying to graduate schools, Kollár’s soon-to-be Ph.D. adviser Benjamin Lev, now an associate professor of physics and applied physics at Standford University, called her and convinced her to join his lab. He enticed her with the promise that, as an atomic and optical physicist, she could do both theory and experiment side by side. She joined his group at the University of Illinois at Urbana-Champaign, and, in her first year, moved with the whole team to Stanford.

Kollár’s Ph.D. work consisted of building a novel experimental apparatus from scratch, designed to trap atoms and photons together and allow them to influence each other in significant, controllable ways. The resulting experimental setup launched a new direction in its field, according to Lev. 

“From beginning to end, it was just an amazing graduate school experience, where you see something from the inception of the idea to actually showing that this new experimental technique can work,” Lev said. “And she was always a thought partner. We were thinking through the ideas, writing the equations on the board, working with theorists, and she was an equal thought partner on all of that.”

After graduate school, Kollár found herself returning to Princeton. “Princeton is a black hole,” she said. “You can never quite leave. Maybe it’s the Hotel California, you know?”

She became a postdoctoral researcher in the lab of Andrew Houck, a professor of electrical and computer engineering and a Fellow in the Princeton Center for Theoretical Science. Houck worked with coplanar waveguides—little paths printed on a circuit board that confine light in a tube the thickness of a human hair. These paths have become the setting of many of Kollár’s mathematical explorations. 

Kollár was in her office one day, playing around with one of these coplanar waveguide chips. This one contained a waveguide lattice—a repeating grid, one waveguide after the other. Lattices are a familiar concept to physicists from the study of metals, where atomic nuclei form repeating patterns, extending in all three directions.

Kollar’s mathematical training bubbled up, flooding her brain with ideas. She envisioned a similar lattice, but instead of one dimension it would extend in two. And, she realized, thanks to the properties of coplanar waveguides, there was a lot of flexibility in the ways she could shape these grids.  

Instead of being points, as in a conventional lattice of nuclei in a metal, the sites of this lattice were paths—lines that guide light around. And, Kollár could bend and stretch these lines however she wanted without changing the underlying physics, as long as the total length stayed the same. 

Kollár realized that by scrunching and stretching these waveguides, she could connect them to each other in ways that aren’t possible for normal lattices of points, at least not in the world we are used to. Instead, the waveguides would act as though they are on the surface of a sphere, or a mathematical construction known as a hyperbolic surface, where traditional ideas of parallel lines, triangles and navigation break down.  

A hyperbolic surface is, in a sense, the opposite of a sphere. So much so that a two-dimensional hyperbolic surface can’t exist within our three-dimensional world—basically, it doesn’t fit. Kollár said the best way to imagine hyperbolic space is with some of M. C. Escher’s pictures. 

Kollár and her collaborators successfully showed that coplanar waveguides can indeed form lattices that act as though they live on a hyperbolic surface. 

Kollár found that these hyperbolic lattices had some cool physics properties. In particular, she found that they gave rise to something called flat bands—paradoxical places where, regardless of how fast a particle is moving, its energy stays the same. These flat bands are thought to be behind some of the most intriguing unexplained physical effects, like the fractional quantum Hall effect, spin-​liquids, and even some cases of high-temperature superconductivity. 

“When I discovered these flat bands, I actually thought I made a mistake in my code,” Kollár said, “I turned around to my lab partner, and I was like, ‘I think I messed up but if I didn’t, this is really cool.’ And so at the time, we didn't understand where that was coming from. What we've since come to understand is that was really just the tip of the iceberg.”

To understand the full potential of this new technique, Kollár joined forces with Peter Sarnak, professor of mathematics at the Institute for Advanced Study at Princeton. This collaboration has proved extremely fruitful. Together, they showed that the flat bands were far from a mistake. In fact, they proved that the flat bands must exist in any hyperbolic lattice of the kind Kollár creates.

“There's been this constant feedback between very general math theorems leading to good examples and then good examples leading to new math theorems,” Kollár said.

Now, she is leading her own group at UMD and is working on coupling bits of quantum information—called qubits—to these exotic lattices. She has assembled a group of like-minded students, interested in addressing novel physics. Although there’s no way to know exactly what the future holds for Kollár, it’s fair to anticipate that she will continue to follow her nose to interesting and unexpected places. 

“I think what was special about Alicia is that she always had her own mind and she did not want to follow what others were doing,” her father, János, said. “It can be frustrating when you're a two-year-old, but I think in the long run if you can follow your own mind very seriously it can work out very well.”

Written by Dina Genkina

Thomas Ferbel, 1937- 2022

Thomas Ferbel, a UMD visiting professor since 2013, died at his home on Saturday, March 12. He was 84.

Ferbel was born in 1937 in Radom, Poland. During the tumult of World War II, he and his family endured exile in a Russian gulag and later, a camp for displaced persons in Stuttgart. Eventually, Ferbel arrived in New York and received a B.A. in Chemistry from Queens College, CUNY, and his and Ph.D. in Physics from Yale University (where his favorite professor was Bob Gluckstern, later the chancellor of this campus and a professor of physics).Thomas FerbelThomas Ferbel

After a postdoctoral appointment at Yale, Ferbel accepted a faculty position at the University of Rochester in 1965.  While there, he received an Alfred P. Sloan Fellowship, a John S. Guggenheim Fellowship and an Alexander von Humboldt Prize.

He was elected a Fellow of the American Physical Society in 1984, and served as the U.S. program manager for the Large Hadron Collider from 2004-08.

In 2020, Ferbel described both his early years and his life as a physicist as part of the American Institute of Physics Oral History project. The transcript is available here: https://www.aip.org/history-programs/niels-bohr-library/oral-histories/46304

Bennewitz Named Finalist for Hertz Fellowship

Elizabeth Bennewitz, a first-year physics graduate student at JQI and QuICS, has been named a finalist for a 2022 Hertz Fellowship. Out of more than 650 applicants, Bennewitz is one of 45 finalists with a chance of receiving up to $250,000 in support from the Fannie and John Hertz Foundation.

The fellowships provide up to five years of funding for recipients pursuing a Ph.D. The foundation seeks(link is external) individuals who intend to tackle “major, near-term problems facing society.”Elizabeth Bennewitz (credit:  Dan Spencer)Elizabeth Bennewitz (credit: Dan Spencer)

“This whole group of finalists have accomplished so much, and I’m very humbled to be among other people starting their Ph.D.s who are also pursuing big problems in science,” says Bennewitz. “I'm very honored to be part of this finalist group.”

Bennewitz is working with JQI and QuICS Fellow Alexey Gorshkov and is interested in researching large collections of interacting quantum particles—what scientists call many-body quantum systems. These systems are important to understanding cutting-edge physics and quantum computer technologies and can also be the basis of simulations that could provide insights into complex problems in physics, material science and chemistry.

“During my PhD, I want to develop tools and techniques that help harness the computational power of quantum devices in order to simulate these large quantum many-body systems,” Bennewitz says. “I’m excited to be pursuing this research at Maryland because of its commitment to quantum information and quantum computing research as well as its rich collaboration between theorists and experimentalists.”

Bennewitz is just at the beginning of her graduate student career, but she has already started investigating how quantum simulators might be used to understand the interactions of the particles that are responsible for holding the nuclei of atoms together.

“I'm very happy for Elizabeth, and I'm honored and excited that she chose to work with my group,” Gorshkov says.

An announcement of the winning fellows is expected to be made in May.

“I'm very thankful for all the opportunities I had before I got here,” Bennewitz says. “I would not be where I am today without the support and guidance I received from my professors and peers at Bowdoin College and Perimeter.”

Original story by Bailey Bedford: https://jqi.umd.edu/news/jqi-graduate-student-finalist-hertz-fellowship

Kollár Awarded Sloan Research Fellowship

Assistant Professor Alicia Kollár has been awarded a prestigious 2022 Sloan Research Fellowship. This award is given to early career researchers by the Alfred P. Sloan Foundation to recognize distinguished performance and the potential to make substantial contributions to their field. Each fellowship provides $75,000 to support the fellow’s research over two years.

Kollár will use the fellowship to support her research into creating new synthetic materials that are designed using quantum physics and applied mathematics. These synthetic materials can reveal physics that is difficult or impossible to observe in traditional materials.

“What really excites me about this award is to see support for the more interdisciplinary side of my research,” Kollár says. “My original background is in quantum physics and that's been where my grant support has come from so far, but this Sloan award is focused on looking at questions at the intersection of math and physics.”Alicia Kollár Alicia Kollár

This line of Kollár’s research uses mathematical tools based on the field of graph theory—the study of relationships between objects (in terms of a “graph” made of “vertices” that are connected by “edges”). Researchers use the tools to produce stripped down descriptions of materials in terms of just nodes and their connections—like if there is a connection where electrons can hop between specific points in a material. These descriptions don’t care about the exact distance between atoms or molecules or their precise orientation relative to each other but only about what connections exist between points. This approach is useful for identifying overarching features of different types of materials and is especially helpful in sorting out which material properties are derived from the basic connections being investigated, as opposed to those related to the quirks of a material’s particular components.

This mathematical perspective allows researchers, like Kollár, to design abstract connections that should produce unique properties, but it isn’t easy to then translate the idea on a page into a material that has the exact desired connections. Going from pure math to a real material is much harder than the reverse process of stripping details away from a well-studied material; to do so requires the exhaustive work of recognizing and juggling all the idiosyncrasies of real chemistry. The details of all the possible choices of atoms and how they interact and arrange themselves makes matching the elegant mathematical design to a physical material prohibitively challenging.

So instead Kollár has focused on synthetic materials made of circuits of resonators and superconducting qubits that house traveling microwaves. These circuits easily recreate the flexible connections of graph-theoretic descriptions and can let the complex physics play out, revealing features that current simulations can’t calculate. Essentially, Kollár can custom design the desired connections in a synthetic material and see if the results are interesting instead of going through the hassle of searching for a chemical structure that naturally has the connections every time she wants to do a new experiment. She has even been able to create connections that simulate a negatively curved space—a space impossible to create in the lab because they have “more space” than our normal space.

The insights from these synthetic materials have the potential to reveal new material behaviors and to give researchers a better understanding of how to best use graph-theoretic techniques.

Besides making these synthetic materials she is also working to push the mathematical side of this approach, including identifying new mathematical rules that govern one dimensional graphs that might provide insights into codes used in quantum computing.

 “This Sloan Fellowship will give my group the opportunity to really dig in to optimizing how synthetic materials are made in order to make them as versatile a tool as possible,” Kollár says.

The Sloan fellowships are awarded to untenured teaching faculty who work in the fields of chemistry, computer science, Earth system science, economics, mathematics, neuroscience, physics, or a related field. Candidates are nominated by their colleagues, and then fellows are selected by an independent committee of researchers in the relevant field based on the candidates’ “independent research accomplishments, creativity, and potential to become leaders in the scientific community through their contributions to their field,” according to the Sloan website. Other UMD winners this year are Lei Chen of mathematics and Pratyush Tiwary of chemistry/biochemisty and IPST. 

“Today’s Sloan Research Fellows represent the scientific leaders of tomorrow,” says Adam F. Falk, president of the Alfred P. Sloan Foundation. “As formidable young scholars, they are already shaping the research agenda within their respective fields—and their trailblazing won’t end here.”

 

Original story by Bailey Bedford: https://jqi.umd.edu/news/jqi-fellow-kollar-awarded-sloan-research-fellowship