Embracing Uncertainty Helps Bring Order to Quantum Chaos

In physics, chaos is something unpredictable. A butterfly flapping its wings somewhere in Guatemala might seem insignificant, but those flits and flutters might be the ultimate cause of a hurricane over the Indian Ocean. The butterfly effect captures what it means for something to behave chaotically: Two very similar starting points—a butterfly that either flaps its wings or doesn’t—could lead to two drastically different results, like a hurricane or calm winds.

But there's also a tamer, more subtle form of chaos in which similar starting points don’t cause drastically different results—at least not right away. This tamer chaos, known as ergodicity, is what allows a coffee cup to slowly cool down to room temperature or a piece of steak to heat up on a frying pan. It forms the basis of the field of statistical mechanics, which describes large collections of particles and how they exchange energy to arrive at a shared temperature. Chaos almost always grows out of ergodicity, forming its most eccentric variant.A system is ergodic if a particle traveling through it will eventually visit every possible point. In quantum mechanics, you never know exactly what point a particle is at, making ergodicity hard to track. In this schematic, the available space is divided into quantum-friendly cells, and an ergodic particle (left) winds through each of the cells, while a non-ergodic one (right) only visits a few. (Credit: Amit Vikram/JQI)A system is ergodic if a particle traveling through it will eventually visit every possible point. In quantum mechanics, you never know exactly what point a particle is at, making ergodicity hard to track. In this schematic, the available space is divided into quantum-friendly cells, and an ergodic particle (left) winds through each of the cells, while a non-ergodic one (right) only visits a few. (Credit: Amit Vikram/JQI)

Where classical, 19th-century physics is concerned, ergodicity is pretty well understood. But we know that the world is fundamentally quantum at the smallest scales, and the quantum origins of ergodicity have remained murky to this day—the uncertainty inherent in the quantum world makes classical notions of ergodicity fail. Now, Victor Galitski and colleagues in the Joint Quantum Institute (JQI) have found a way to translate the concept of ergodicity into the quantum realm. They recently published their results in the journal Physical Review Research. This work was supported by the DOE Office of Science (Office of Basic Energy Sciences).

“Statistical mechanics is based on the assumption that systems are ergodic,” Galitski says. “It’s an assumption, a conjecture, and nobody knows why. And our work sheds light on this conjecture.”

In the classical world, ergodicity is all about trajectories. Imagine an air hockey puck bouncing around a table. If you set it in motion, it will start bouncing off the walls, changing direction with each collision. If you wait long enough, that puck will eventually visit every point on the table's surface. This is what it means to be ergodic—to visit every nook and cranny available, given enough time. If you paint the puck’s path as you go, you will eventually color in the whole table. If lots of pucks are unleashed onto the table, they will bump into each other and eventually spread out evenly over the table.

To translate this idea of ergodicity into the quantum world of individual particles is tough. For one, the very notion of a trajectory doesn't quite make sense. The uncertainty principle dictates that you cannot know the precise position and momentum of a particle at the same time, so the exact path it follows ends up being a little bit fuzzy, making the normal definitions of chaos and ergodicity challenging to apply. 

Physicists have thought up several alternate ways to look for ergodicity or chaos in quantum mechanics. One is to study the particle’s quantum energy levels, especially how they space out and bunch up. If the way they bunch up has a particular kind of randomness, the theory goes, this is a type of quantum chaos. This might be a nice theoretical tool, but it’s difficult to connect to the actual motion of a quantum particle. Without such a connection to dynamics, the authors say there’s no fundamental reason to use this energy level signature as the ultimate definition of quantum chaos. “We don't really know what quantum chaos [or ergodicity] is in the first place,” says Amit Vikram, a graduate student in physics at JQI and lead author of the paper. “Chaos is a classical notion. And so what people really have are different diagnostics, essentially different things that they intuitively associate with chaos.”

Galitski and Vikram have found a way to define quantum ergodicity that closely mimics the classical definition. Just as an air hockey puck traverses the surface of the table, quantum particles traverse a space of quantum states—a surface like the air hockey table that lives in a more abstract world. But to capture the uncertainty inherent to the quantum world, the researchers break the space up into small cells rather than treating it as individual points. It's as if they divided the abstract air hockey table into cleverly chosen chunks and then checked to see if the uncertainty-widened particle has a decent probability of visiting each of the chunks.

“Quantum mechanically you have this uncertainty principle that says that your resolution in trajectories is a little bit fuzzy. These cells kind of capture that fuzziness,” Vikram says. “It's not the most intuitive thing to expect that some classical notion would just carry over to quantum mechanics. But here it does, which is rather strange, actually.”

Picking the correct cells to partition the space into is no easy task—a random guess will almost always fail. Even if there is only one special choice of cells where the particle visits each one, the system is quantum ergodic according to the new definition. The team found that the key to finding that magic cell choice, or ruling that no such choice exists, lies in the particle’s quantum energy levels, the basis of previous definitions of quantum chaos. This connection enabled them to calculate that special cell choice for particular cases, as well as connect to and expand the previous definition.

One advantage of this approach is that it's closer to something an experimentalist can see in the dynamics—it connects to the actual motion of the particle. This not only sheds light on quantum ergodicity, quantum chaos and the possible origins of thermalization, but it may also prove important for understanding why some quantum computing algorithms work while others do not.

As Galitski puts it, every quantum algorithm is just a quantum system trying to fight thermalization. The algorithm will only work if the thermalization is avoided, which would only happen if the particles are not ergodic. “This work not only relates to many body systems, such as materials and quantum devices, but that also relates to this effort on quantum algorithms and quantum computing,” Galitski says.

Original story by Dina Genkina: https://jqi.umd.edu/news/embracing-uncertainty-helps-bring-order-quantum-chaos

Reference Publications Dynamical quantum ergodicity from energy level statistics, A. Vikram Anand, and V. Galitski, Physical Review Research, 5, (2023)

Thomas Antonsen Honored by the American Physical Society

Distinguished University Professor Thomas M. Antonsen will receive the American Physical Society’s (APS) 2023 James Clerk Maxwell Prize for Plasma Physics for “pioneering contributions in the theory of magnetized plasma stability, RF, current drive, laser-plasma interactions, and charged particle beam dynamics”.  He will be honored at the 65th Annual Meeting of the APS Division of Plasma Physics in October.Thomas AntonsenThomas Antonsen

The James Clerk Maxwell Prize annually recognizes outstanding contributions to the field of plasma physics.  The prize is named after a nineteenth century Scottish physicist known for his work with electricity, magnetism and light.

Antonsen joined the department, then known as the Department of Electrical Engineering and Physics, in 1984.  He is highly recognized in his esearch fields of plasma theory, nonlinear dynamics and chaos, and currently holds appointments in Electrical and Computer Engineering (ECE), the Institute for Research in Electronics and Applied Physics (IREAP), Physics, and the Maryland Energy Innovation Institute.

In 2017, he was appointed University of Maryland Distinguished University Professor, the highest recognition for faculty members.  Other awards include the Clark School of Engineering Outstanding Research Award, the IEEE Plasma Science and Applications Award, the John R. Pierce Award for Excellence in Vacuum Electronics, and the IEEE Marie Sklodowska-Curie Award for contributions to plasma science. He is a fellow of IEEE and APS.

Antonsen will receive $10,000 and recognition at the 65th Annual Meeting of the APS Division of Plasma Physics this fall in Denver, Colorado. 

Previous UMD physicists who have won the Maxwell Prize include Hans R. Griem, Roald Sagdeev, James Drake, Phillip A. Sprangle and Ronald C. Davidson.


Jean-Paul Richard, 1936 - 2023

Professor Emeritus Jean-Paul Richard, an experimentalist with numerous contributions to the understanding of gravity, died on September 6, 2023. He was 87.

A native of Québec City, Québec, Richard studied at the Université Laval before moving to France for his graduate work. Following doctoral studies in theoretical physics and physical sciences at the Université de Paris, Richard accepted a postdoctoral position at the University of Maryland in 1965. At that time, Joseph Weber was working to detect gravitational waves, which had been predicted by Albert Einstein but never confirmed.  

Following his postdoctoral appointment, Richard accepted a position as an Assistant Professor at UMD, where he would spend his entire career. Over the next three decades, he contributed to several developments, including Apollo 17’s  Lunar Surface Gravimeter.  

In addition, Richard worked to increase the sensitivity of Weber’s aluminum bars by developing a resonant capacitor transducer using field-effect transistors. He also developed a multimode detector achieving higher sensitivity over a wide band of frequencies, and then calculated improvements in the multimode detector by using an optical sensor.

Richard enjoyed visiting appointments at Rome’s La Sapienza and the Université Laval. After his retirement in 1995, he continued his work for three years as a UMD research scientist.

Though early UMD efforts never captured gravitational waves, scientists adapted and persisted. In late 2015, the LIGO experiment succeeded in detecting gravitational waves generated by the merger of two unimaginably distant black holes.

Reflecting on his work after the announcement, Richard said, “When I heard the LIGO news, I was shocked and stunned for a couple of days. It gave new value to my work and justified my efforts. That’s a very big thing."

Funeral arrangements are shown here: https://www.collinsfuneralhome.com/obituaries/Dr-Jean-Paul-Richard?obId=29100466#/obituaryInfo

Ph.D. Student’s Initiative Led to Numerous Research Collaborations and Accolades

A big part of research is working with other scientists. As an undergraduate and graduate student at the University of Maryland, Jacob Bringewatt (B.S. ’18, physics) put in the work knocking on doors and connecting with professors, which allowed him to explore a broad range of research projects and earned him accolades along the way.Jacob Bringewatt  Jacob Bringewatt

Bringewatt was torn deciding between a small liberal arts college and a bigger state university for college. He came to UMD to interview for a Banner/Key Scholarship and during the visit he spoke with Physics Professor Tom Cohen. Cohen emphasized that a strong research program—like the one UMD has—is an important component of a high-quality physics education. That conversation—and receiving the scholarship—pushed UMD to the top of Bringewatt’s list, and he enrolled in 2014.

As an incoming freshman, Bringewatt was eager to dive into theoretical physics research. During the first couple weeks of classes, he sought out Cohen to ask about joining a theoretical research project.

“He told me that I shouldn't do theory, even though he's a theorist,” Bringewatt said. “One should only do theory if they're like really bad at experiments or can't imagine doing anything else. I’ve learned since this is his standard line for eager undergrads.”


Bringewatt took Cohen’s advice and sought out an experimentalist: Physics Professor Carter Hall. Bringewatt joined Hall’s team and initially crunched numbers—analyzing experimental data instead of getting his hands dirty with experimental equipment. He eventually handled equipment in the lab and quickly realized it wasn’t for him. He still felt drawn to the math and theory side of physics. So he returned to Cohen, who directed him to Physics Professor William Dorland who was on sabbatical at the time. 

The summer before his junior year, Bringewatt wrote some computer code for Dorland to use in an ongoing project investigating how plasmas move. Dorland, who is a computational physicist, was interested in quantum computing and decided to spend some of his time during his sabbatical exploring the basics of quantum computation with Bringewatt. Their discussions developed into a collaboration with Stephen Jordan, who was then an adjunct associate professor of physics at UMD. The group investigated adiabatic quantum computation—a version of quantum computing that involves gradually evolving one quantum state into another. Bringewatt was the first author of a paper the collaboration wrote comparing the adiabatic quantum computing approach to a classical alternative. The experience focused Bringewatt on theoretical physics.

“I haven't really looked back since then,” Bringewatt said. “Maryland is a really good place to be for quantum computing. And, as a highly interdisciplinary field, it really does bring out the things I like most about research.”

Having settled on studying quantum theory, Bringewatt still had to decide where to attend grad school. UMD’s many experts and diverse research opportunities once again moved it to the top of his list. But he wanted to experience working in another group. So, before he graduated in 2018, he started visiting with professors. He found a match that felt right with Alexey Gorshkov, an adjunct associate professor of physics at UMD, and his group, which works on a broad range of theoretical physics topics.

During graduate school, Bringewatt has continued investigating adiabatic quantum computation, including collaborating with Michael Jarret (Ph.D. ’16, physics), who is now an assistant professor in the Mathematical Sciences Department at George Mason University. Together, they wrote a paper comparing classical and quantum adiabatic techniques for simulating quantum physics

Bringewatt also took on other challenges. A significant portion of his graduate research focuses on using quantum physics to push the limits of measurement technologies. This research involves improving sensor precision by optimizing the use of quantum entanglement—a fundamental quantum phenomenon that connects quantum particles and allows them to ignore some constraints of classical physics. The work looks at the smallest parts that contribute to a sensor, how the pieces interact, and how they come together during a measurement. By understanding sensors at this fundamental level, future technologies might be able to operate at the limits of what is allowed by physics.

Bringewatt shared this part of his research during the 2022 Three-Minute Thesis (3MT) competition hosted by UMD. 3MT competitions are hosted by many universities around the world to encourage graduate students to practice communicating technical research clearly and succinctly. In these events, the competitors distill a research project into a three-minute presentation that is accessible to someone unfamiliar with their field. Bringewatt was one of the eight winners in the campuswide competition, earning him a $1,000 prize. 

Jacob Bringewatt  delivers his 3-minute thesis.Jacob Bringewatt delivers his 3-minute thesis.“It was a fun challenge to explain in three minutes the big ideas behind a line of research I've been pursuing for several years with a number of excellent collaborators in Alexey Gorshkov's group,” Bringewatt said. 

As part of one of his projects on quantum sensor networks, Bringewatt, Gorshkov and UMD physics graduate student Adam Ehrenberg investigated the peak performance that networks of quantum sensors can achieve. His project built on previous work that had already established the best performance that is physically possible. Crucially, those results had assumed the maximum amount of entanglement—all the sensors are always connected to all the other sensors. But practically achieving maximum entanglement is difficult work, so Bringewatt and colleagues flipped the problem on its head. They identified the minimum amount of entanglement needed to achieve an optimal measurement, which for some cases didn't require maximum entanglement. They then developed protocols that achieve the theoretical target they had set. The team’s efforts earned them a place among the 12 groups of finalists for the 2022 UMD Invention of the Year Award.

"I'm honored to have gotten a chance to collaborate with Jake on many projects,” Gorshkov said. “I learned a lot from him and am very proud of his numerous achievements and well-deserved awards."

Even while juggling classes and research into both quantum sensors and adiabatic quantum computing, Bringewatt sought out new challenges. For his first four years as a graduate student, he was a Department of Energy (DOE) Computational Science Graduate Fellow. The program requires fellows to spend a summer working at a DOE laboratory, and it encourages them to explore new topics. 

Bringewatt was eager to try something completely new. He knew Zohreh Davoudi, associate professor of physics at UMD, from his undergraduate math methods course. And he was aware she studied nuclear theory and was interested in branching into quantum simulations. He thought a summer of nuclear theory might be interesting and have the additional benefit of providing a foundation to work with Davoudi. So, the first summer after starting graduate school, he requested to spend his summer at Jefferson Lab, which is home to a particle accelerator used for nuclear physics experiments. 

He spent his summer there as part of a team investigating the internal structure of protons. This small sample of nuclear physics research left Bringewatt eager for more, so he reached out to Davoudi. The timing worked out: She was looking for colleagues to collaborate with on developing quantum simulations of nuclear physics

He began attending Davoudi’s group meetings, and they eventually began pooling their skills on a project. Earlier this year, they published a paper on finding the best way to represent fermions—particles like electrons that can’t share their quantum state—and their interactions within quantum computer simulations. 

The topics of nuclear theory, quantum sensor research and adiabatic quantum computing have given Bringewatt diverse challenges and experiences throughout graduate school. As a result of his prodigious work ethic, he has been first author on ten research papers—an unusually high count for a graduate student.

“Being able to pursue these three distinct topics has been a real advantage of being here where there's a lot of experts on a wide array of things,” Bringewatt said. “I've gotten the chance to work with a lot of talented people with different areas of expertise, which has been really nice.”

Earlier this year, the College of Computer, Mathematical and Natural Sciences acknowledged his hard work and gave him the 2023 Board of Visitors Outstanding Graduate Student Award and a $5,000 prize. 

“I feel very honored to have received this recognition,” Bringewatt said. “Scientific research is never an individual effort, and having pursued both my undergraduate and graduate degree at the University of Maryland, I am extremely grateful to the university and all my mentors here who have enabled me to grow and excel as a young scientist.”

Bringewatt is wrapping up his research at UMD and looking for new collaborations and challenges as a postdoctoral researcher. He plans to graduate in the spring of 2024.

“I've been very happy to be at UMD,” Bringewatt said. “It's a great community, and, I think, the best of both worlds: It has a bunch of resources and world-class research, but people are also very approachable, friendly, and helpful. I feel extremely lucky for the years I’ve gotten to spend here.”

Written by Bailey Bedford


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