Kollár Research Group

One of the mind-bending ideas that physicists and mathematicians have come up with is that space itself—not just objects in space—can be curved. When space curves (as happens dramatically near a black hole), sizes and directions defy normal intuition. Understanding curved spaces is important to expanding our knowledge of the universe, but it is fiendishly difficult to study curved spaces in a lab setting (even using simulations). A previous collaboration between researchers at JQI explored using labyrinthine circuits made of superconducting resonators to simulate the physics of certain curved spaces. In particular, the team looked at hyperbolic lattices that represent spaces—called negatively curved spaces—that have more space than can fit in our everyday “flat” space. Our three-dimensional world doesn’t even have enough space for a two-dimensional negatively curved space. Now, in a paper published in the journal Physical Review Letters on Jan. 3, 2022, the same collaboration between the groups of JQI Fellows Alicia Kollár and Alexey Gorshkov, who is also Fellow of the Joint Center for Quantum Information and Computer Science, expands the potential applications of the technique to include simulating more intricate physics. They’ve laid a theoretical framework for adding qubits—the basic building blocks of quantum computers—to serve as matter in a curved space made of a circuit full of flowing microwaves. Specifically, they considered the addition of qubits that change between two quantum states when they absorb or release a microwave photon—an individual quantum particle of the microwaves that course through the circuit. 

JQI Fellow Alicia Kollár has received a prestigious Faculty Early Career Development (CAREER) award from the National Science Foundation (NSF) for a proposal aimed at developing a new window into the physics of particles interacting inside of materials and performing educational outreach. The award will provide $675,000 of funding over five years for her proposal titled “Engineering Interacting Photons in Superconducting-Circuit Lattices.” Kollár will use the funds to investigate new physics that might be revealed by making particles of light (called photons) behave more like particles of matter (like electrons). Her plan is to tailor environments for photons by combining superconducting components into specialized circuits. 

Our recent paper "Gap Sets for the Spectra of Cubic Graphs" which harnesses condensed-matter-physics methods for computing tight-binding band structures to tackle questions about the possible spectra of adjacency operators on 3-regular graphs was accepted for publication in a new journal of the American Mathematical Society: "Communications of the AMS." The article will feature in the inaugural volume of CAMS.

JQI Fellow Alicia Kollár has been awarded a grant by the Air Force’s Young Investigator Research Program (YIP). She is one of 36 early-career researchers around the US to receive the three-year, $450,000 award.

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. Spaces that have different geometric rules than those we usually take for granted are called non-Euclidean. 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. 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 Kollár’s research group and JQI Fellow Alexey Gorshkov’s group presented new mathematical tools to better understand simulations of hyperbolic spaces. The research builds on Kollár’s previous experiments 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.

New mathematical physics result is on the arXiv (2005.05379), including unique quasi-one-dimensional lattices with the largest possible bang gaps.

Our mathematical-physics paper on the connection between circuit QED lattices and combinatorial graph theory (Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands and Implementations in Circuit QED) was accepted fro Publication in a mathematical journal: "Communications in Mathematical Physics". 

JQI has named four new Fellows in 2019, bringing the total number to 35. All four of the new arrivals have appointments in the Department of Physics at the University of Maryland. One Fellow is also a professor in the Department of Electrical and Computer Engineering at UMD and another is a physicist at the National Institute of Standards and Technology (NIST).

Alicia Kollár arrived in August as a JQI Fellow and the Chesapeake Assistant Professor of Physics. She is also a founding member of the QTC.

JQI has named four new Fellows in 2019, bringing the total number to 35. All four of the new arrivals have appointments in the Department of Physics at the University of Maryland. One Fellow is also a professor in the Department of Electrical and Computer Engineering at UMD and another is a physicist at the National Institute of Standards and Technology (NIST).