Attacking Quantum Models with AI: When Can Truncated Neural Networks Deliver Results?

Currently, computing technologies are rapidly evolving and reshaping how we imagine the future. Quantum computing is taking its first toddling steps toward delivering practical results that promise unprecedented abilities. Meanwhile, artificial intelligence remains in public conversation as it’s used for everything from writing business emails to generating bespoke images or songs from text prompts to producing deep fakes.

Some physicists are exploring the opportunities that arise when the power of machine learning—a widely used approach in AI research—is brought to bear on quantum physics. Machine learning may accelerate quantum research and provide insights into quantum technologies, and quantum phenomena present formidable challenges that researchers can use to test the bounds of machine learning.

When studying quantum physics or its applications (including the development of quantum computers), researchers often rely on a detailed description of many interacting quantum particles. But the very features that make quantum computing potentially powerful also make quantum systems difficult to describe using current computers. In some instances, machine learning has produced descriptions that capture the most significant features of quantum systems while ignoring less relevant details—efficiently providing useful approximations.An artistic rendering of a neural network consisting of two layers. The top layer represents a real collection of quantum particles, like atoms in an optical lattice. The connections with the hidden neurons below account for the particles’ interactions. (Credit: Modified from original artwork created by E. Edwards/JQI)An artistic rendering of a neural network consisting of two layers. The top layer represents a real collection of quantum particles, like atoms in an optical lattice. The connections with the hidden neurons below account for the particles’ interactions. (Credit: Modified from original artwork created by E. Edwards/JQI)

In a paper published May 20, 2024, in the journal Physical Review Research, two researchers at JQI presented new mathematical tools that will help researchers use machine learning to study quantum physics. And using these tools, they have identified new opportunities in quantum research where machine learning can be applied.

“I want to understand the limit of using traditional classical machine learning tools to understand quantum systems,” says JQI graduate student Ruizhi Pan, who was the first author of the paper.

The standard tool for describing collections of quantum particles is the wavefunction, which provides a complete description of the quantum state of the particles. But obtaining the wavefunction for more than a handful of particles tends to require impractical amounts of time and resources.

Researchers have previously shown that AI can approximate some families of quantum wavefunctions using fewer resources. In particular, physicists, including CMTC Director and JQI Fellow Sankar Das Sarma, have studied how to represent quantum states using neural networks—a common machine learning approach in which webs of connections handle information in ways reminiscent of the neurons firing in a living brain. Artificial neural networks are made of nodes—sometimes called artificial neurons—and connections of various strengths between them.

Today, neural networks take many forms and are applied to diverse applications. Some neural networks analyze data, like inspecting the individual pixels of a picture to tell if it contains a person, while others model a process, like generating a natural-sounding sequence of words given a prompt or selecting moves in a game of chess. The webs of connections formed in neural networks have proven useful at capturing hard-to-identify relationships, patterns and interactions in data and models, including the unique interactions of quantum particles described by wavefunctions.

But neural networks aren’t a magic solution to every situation or even to approximating every wavefunction. Sometimes, to deliver useful results, the network would have to be too big and complex to practically implement. Researchers need a strong theoretical foundation to understand when they are useful and under what circumstances they fall prey to errors.

In the new paper, Pan and JQI Fellow Charles Clark investigated a type of neural network called a restricted Boltzmann machine (RBM), in which the nodes are split into two layers and connections are only allowed between nodes in different layers. One layer is called the visible, or input, layer, and the second is called the hidden layer, since researchers generally don’t directly manipulate or interpret it as much as they do the visible layer.

“The restricted Boltzmann machine is a concept that is derived from theoretical studies of classical ‘spin glass’ systems that are models of disordered magnets,” Clark says. “In the 1980s, Geoffrey Hinton and others applied them to the training of artificial neutral networks, which are now widely used in artificial intelligence. Ruizhi had the idea of using RBMs to study quantum spin systems, and it turned out to be remarkably fruitful.”

For RBM models of quantum systems, physicists frequently use each node of the visible layer to represent a quantum particle, like an individual atom, and use the connections made through the hidden layer to capture the interactions between those particles. As the size and complexity of quantum states grow, a neural net increasingly needs more and more hidden nodes to keep up, eventually becoming unwieldy.

However, the exact relationships between the complexity of a quantum state, the number of hidden nodes used in a neural network, and the resulting accuracy of the approximation are difficult to pin down. This lack of clarity is an example of the black box problem that permeates the field of machine learning. It exists because researchers don’t meticulously engineer the intricate web of a neural network but instead rely on repeated steps of trial and error to find connections that work. This approach often delivers more accurate or efficient results than researchers know how to achieve by working from first principles, but it doesn’t explain why the connections that make up the neural network deliver the desired result—so the results might as well have come from a black box. This built-in inscrutability makes it difficult for physicists to know which quantum models are practical to tackle with neural networks.

Pan and Clark decided to peek behind the veil of the hidden layer and investigate how neural networks boil down the essence of quantum wavefunctions. To do this, they focused on neural network models of a one-dimensional line of quantum spins. A spin is like a little magnetic arrow that wants to point along a magnetic field and is key to understanding how magnets, superconductors and most quantum computers function.

Spins naturally interact by pushing and pulling on each other. Through chains of interactions, even two distant spins can become correlated—meaning that observing one spin also provides information about the other spin. All the correlations between particles tend to drive quantum states into unmanageable complexity. 

Pan and Clark did something that at first glance might not seem relevant to the real world: They imagined and analyzed a neural network that uses infinitely many hidden nodes to model a fixed number of spins.

“In reality of course we don't hope to use a neural network with an infinitely large system size,” Pan says. “We often want to use finite size neural networks to do the numerical computations, so we need to analyze the effects of doing truncations.”

Pan and Clark already knew that using more hidden nodes generally produced more accurate results, but the research community only had a fuzzy understanding of how the accuracy suffers when fewer hidden nodes are used. By backing up and getting a view of the infinite case, Pan and Clark were able to describe the hypothetical, perfectly accurate representation and observe the contributions made by the infinite addition of hidden nodes. The nodes don’t all contribute equally. Some capture the basics of significant features, while many contribute small corrections.

The pair developed a method that sorts the hidden nodes into groups based on how much correlation they capture between spins. Based on this approach, Pan and Clark developed mathematical tools for researchers to use when developing, comparing and interpreting neural networks. With their new perspective and tools, Pan and Clark identified and analyzed the forms of errors they expect to arise from truncating a neural network, and they identified theoretical limits on how big the errors can get in various circumstances. 

In previous work, physicists generally relied on restricting the number of connections allowed for each hidden node to keep the complexity of the neural network in check. This in turn generally limited the reach of interactions between particles that could be modeled—earning the resulting collection of states the name short-range RBM states.

Pan and Clark’s work revealed a chance to apply RBMs outside of those restrictions. They defined a new group of states, called long-range-fast-decay RBM states, that have less strict conditions on hidden node connections but that still often remain accurate and practical to implement. The looser restrictions on the hidden node connections allow a neural network to represent a greater variety of spin states, including ones with interactions stretching farther between particles.

“There are only a few exactly solvable models of quantum spin systems, and their computational complexity grows exponentially with the number of spins,” says Clark. “It is essential to find ways to reduce that complexity. Remarkably, Ruizhi discovered a new class of such systems that are efficiently attacked by RBMs. It’s the old hero-returns-home story: from classical spin glass came the RBM, which grew up among neural networks, and returned home with a gift of order to quantum spin systems.”

The pair’s analysis also suggests that their new tools can be adapted to work for more than just one-dimensional chains of spins, including particles arranged in two or three dimensions. The authors say these insights can help physicists explore the divide between states that are easy to model using RBMs and those that are impractical. The new tools may also guide researchers to be more efficient at pruning a network’s size to save time and resources. Pan says he hopes to further explore the implications of their theoretical framework.

“I'm very happy that I realized my goal of building our research results on a solid mathematical basis,” Pan says. “I'm very excited that I found such a research field which is of great prospect and in which there are also many unknown problems to be solved in the near future.”

Original story by Bailey Bedford:

IceCube Observes Seven Astrophysical Tau Neutrino Candidates

Neutrinos are tiny, weakly interacting subatomic particles that can travel astronomical distances undisturbed. As such, they can be traced back to their sources, revealing the mysteries surrounding the cosmos. High-energy neutrinos that originate from the farthest reaches beyond our galaxy are called astrophysical neutrinos and are the main subject of study for the IceCube Neutrino Observatory, a cubic-kilometer-sized neutrino telescope at the South Pole. In 2013, IceCube presented its first evidence of high-energy astrophysical neutrinos originating from cosmic accelerators, beginning a new era in astronomy. 

These cosmic messengers come in three different flavors: electron, muon, and tau, with astrophysical tau neutrinos being exceptionally difficult to pin down. Now, in a new study recently accepted as an “Editors’ Suggestion” by Physical Review Letters, the IceCube Collaboration presents the discovery of the once-elusive astrophysical tau neutrinos, a new kind of astrophysical messenger. 

IceCube detects neutrinos using cables (strings) of digital optical modules (DOMs), with a total of 5,160 DOMs embedded deep within the Antarctic ice. When neutrinos interact with molecules in the ice, charged particles are produced that then emit blue light while traveling through the ice, which is then registered and digitized by the individual DOMs. The light produces distinctive patterns, one of which is double cascade events from high-energy tau neutrino interactions within the detector.

The production of a double pulse waveform. The photons from a neutrino interaction (blue) arrive at the top middle DOM at time tI, producing the first peak in the waveform, while photons from the tau lepton decay (purple) arrive at the same DOM at time tD, producing the second peak. Credit: Jack Pairin/IceCube CollaborationThe production of a double pulse waveform. The photons from a neutrino interaction (blue) arrive at the top middle DOM at time tI, producing the first peak in the waveform, while photons from the tau lepton decay (purple) arrive at the same DOM at time tD, producing the second peak. Credit: Jack Pairin/IceCube Collaboration

Since prior IceCube analyses saw hints from searches for subtle signatures produced by astrophysical tau neutrinos, the researchers remained motivated to pinpoint tau neutrinos. After rendering each event into three images (see figure below), they trained convolutional neural networks (CNNs) optimized for image classification to distinguish images produced by tau neutrinos from images produced by various backgrounds. After having simulations run that confirmed its sensitivity to tau neutrinos, the technique was then applied to 10 years of IceCube data acquired between 2011 and 2020. The result was seven strong candidate tau neutrino events. 

“The detection of seven candidate tau neutrino events in the data, combined with the very low amount of expected background, allows us to claim that it is highly unlikely that backgrounds are conspiring to produce seven tau neutrino imposters,” said Doug Cowen, a professor of physics at Penn State University and one of the study leads. “The discovery of astrophysical tau neutrinos also provides a strong confirmation of IceCube’s earlier discovery of the diffuse astrophysical neutrino flux.”

Candidate astrophysical tau neutrino detected on November 13, 2019. Each column corresponds to one of the three neighboring strings of the selected event. Each figure in the top row shows the DOM number, proportional to the depth, versus the time of the digitized PMT signal in 3-ns bins, with the bin color corresponding to the size of the signal in each time bin, for each of the three strings. The total number of photons detected by each string is provided at the upper left in each figure. In the most-illuminated string (left column), the arrival of light from two cascades is visible as two distinct hyperbolas. The bottom row of figures shows the “saliency” for one of the CNNs for each of the three strings. The saliency shows where changes in light level have the greatest impact on the value of the CNN score. The black line superimposed on the saliency plots shows where the light level goes to zero and is effectively an outline of the figures in the top row. The saliency is largest at the leading and trailing edges of the light emitted by the two tau neutrino cascades, showing that the CNN is mainly sensitive to the overall structure of the event. Credit: IceCube CollaborationCandidate astrophysical tau neutrino detected on November 13, 2019. Each column corresponds to one of the three neighboring strings of the selected event. Each figure in the top row shows the DOM number, proportional to the depth, versus the time of the digitized PMT signal in 3-ns bins, with the bin color corresponding to the size of the signal in each time bin, for each of the three strings. The total number of photons detected by each string is provided at the upper left in each figure. In the most-illuminated string (left column), the arrival of light from two cascades is visible as two distinct hyperbolas. The bottom row of figures shows the “saliency” for one of the CNNs for each of the three strings. The saliency shows where changes in light level have the greatest impact on the value of the CNN score. The black line superimposed on the saliency plots shows where the light level goes to zero and is effectively an outline of the figures in the top row. The saliency is largest at the leading and trailing edges of the light emitted by the two tau neutrino cascades, showing that the CNN is mainly sensitive to the overall structure of the event. Credit: IceCube CollaborationCowen added that the probability of the background mimicking the signal was estimated to be less than one in 3.5 million. 

UMD Research Scientist Erik Blaufuss served as an internal reviewer for the analysis, carefully studying the methods and techniques used to make the discovery. Assistant Professor Brian Clark leads the scientific working group in IceCube that produced the result. The IceCube collaboration includes several UMD faculty, including  Kara Hoffman, Greg Sullivan, and Michael Larson, in addition to several graduate students and postdocs. The UMD group plays a leading role in the maintenance and operations of the detector, as well as the simulation and analysis of the data. 

Future analyses will incorporate more of IceCube’s strings, since this study used just three of them. The new analysis would increase the sample of tau neutrinos that can then be used to perform the first three-flavor study of neutrino oscillations—the phenomenon where neutrinos change flavors—over cosmological distances. This type of study could address questions such as the mechanism of neutrino production from astrophysical sources and the properties of space through which neutrinos travel. 

Currently, there is no tool specifically designed to determine the energy and direction of tau neutrinos that produce the signatures seen in this analysis. Such an algorithm could be used to better differentiate a potential tau neutrino signal from background and to help identify candidate tau neutrinos in real time at the South Pole. Similar to current IceCube real-time alerts issued for other neutrino types, alerts for tau neutrinos could be issued to the astronomical community for follow-up studies.

All in all, this exciting discovery comes with the “intriguing possibility of leveraging tau neutrinos to uncover new physics,” said Cowen. 

+ info “Observation of Seven Astrophysical Tau Neutrino Candidates with IceCube,” The IceCube Collaboration: R. Abbasi et al. Accepted by Physical Review Letters.

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A Focused Approach Can Help Untangle Messy Quantum Scrambling Problems

The world is a cluttered, noisy place, and the ability to effectively focus is a valuable skill. For example, at a bustling party, the clatter of cutlery, the conversations, the music, the scratching of your shirt tag and almost everything else must fade into the background for you to focus on finding familiar faces or giving the person next to you your undivided attention. 

Similarly, nature and experiments are full of distractions and negligible interactions, so scientists need to deliberately focus their attention on sources of useful information. For instance, the temperature of the crowded party is the result of the energy carried by every molecule in the air, the air currents, the molecules in the air picking up heat as they bounce off the guests and numerous other interactions. But if you just want to measure how warm the room is, you are better off using a thermometer that will give you the average temperature of nearby particles rather than trying to detect and track everything happening from the atomic level on up. A few well-chosen features—like temperature and pressure—are often the key to making sense of a complex phenomenon.

It is especially valuable for researchers to focus their attention when working on quantum physics. Scientists have shown that quantum mechanics accurately describes small particles and their interactions, but the details often become overwhelming when researchers consider many interacting quantum particles. Applying the rules of quantum physics to just a few dozen particles is often more than any physicist—even using a supercomputer—can keep track of. So, in quantum research, scientists frequently need to identify essential features and determine how to use them to extract practical insights without being buried in an avalanche of details.A collection of quantum particles can store information in various collective quantum states. The above model represents the states as blue nodes and illustrates how interactions can scramble the organized information of initial states into a messy combination by mixing the options along the illustrated links. (Credit: Amit Vikram, UMD)A collection of quantum particles can store information in various collective quantum states. The above model represents the states as blue nodes and illustrates how interactions can scramble the organized information of initial states into a messy combination by mixing the options along the illustrated links. (Credit: Amit Vikram, UMD)

In a paper published in the journal Physical Review Letters in January 2024, Professor Victor Galitski and JQI graduate student Amit Vikram identified a new way that researchers can obtain useful insights into the way information associated with a configuration of particles gets dispersed and effectively lost over time. Their technique focuses on a single feature that describes how various amounts of energy can be held by different configurations a quantum system. The approach provides insight into how a collection of quantum particles can evolve without the researchers having to grapple with the intricacies of the interactions that make the system change over time.

This result grew out of a previous project where the pair proposed a definition of chaos for the quantum world. In that project, the pair worked with an equation describing the energy-time uncertainty relationship—the less popular cousin of the Heisenberg uncertainty principle for position and momentum. The Heisenberg uncertainty principle means there’s always a tradeoff between how accurately you can simultaneously know a quantum particle’s position and momentum. The tradeoff described by the energy-time uncertainty relationship is not as neatly defined as its cousin, so researchers must tailor its application to different contexts and be careful how they interpret it. But in general, the relationship means that knowing the energy of a quantum state more precisely increases how long it tends to take the state to shift to a new state.

When Galitski and Vikram were contemplating the energy-time uncertainty relationship they realized it naturally lent itself to studying changes in quantum systems—even those with many particles—without getting bogged down in too many details. Using the relationship, the pair developed an approach that uses just a single feature of a system to calculate how quickly the information contained in an initial collection of quantum particles can mix and diffuse.

The feature they built their method around is called the spectral form factor. It describes the energies that quantum physics allows a system to hold and how common they are—like a map that shows which energies are common and which are rare for a particular quantum system.

The contours of the map are the result of a defining feature of quantum physics—the fact that quantum particles can only be found in certain states with distinct—quantized—energies. And when quantum particles interact, the energy of the whole combination is also limited to certain discrete options. For most quantum systems, some of the allowed energies are only possible for a single combination of the particles, while other energies can result from many different combinations. The availability of the various energy configurations in a system profoundly shapes the resulting physics, making the spectral form factor a valuable tool for researchers.

Galitski and Vikram tailored a formulation of the energy time uncertainty relationship around the spectral form factor to develop their method. The approach naturally applies to the spread of information since information and energy are closely related in quantum physics. 

While studying this diffusion, Galitski and Vikram focused their attention on an open question in physics called the fast-scrambling conjecture, which aims to pin down how long it takes for the organization of an initial collection of particles to be scrambled—to have its information mixed and spread out among all interacting particles until it becomes effectively unrecoverable. The conjecture is not concerned just with the fastest scrambling that is possible for a single case, but instead, it is about how the time that the scrambling takes changes based on the size or complexity of the system. 

Information loss during quantum scrambling is similar to an ice sculpture melting. Suppose a sculptor spelled out the word “swan” in ice and then absentmindedly left it sitting in a tub of water on a sunny day. Initially, you can read the word at a glance. Later, the “s” has dropped onto its side and the top of the “a” has fallen off, making it look like a “u,” but you can still accurately guess what it once spelled. But, at some point, there’s just a puddle of water. It might still be cold, suggesting there was ice recently, but there’s no practical hope of figuring out if the ice was a lifelike swan sculpture, carved into the word “swan” or just a boring block of ice. 

How long the process takes depends on both the ice and the surroundings: Perhaps minutes for a small ice cube in a lake or an entire afternoon for a two-foot-tall centerpiece in a small puddle.

The ice sculpture is like the initial information contained in a portion of the quantum particles, and the surrounding water is all the other quantum particles they can interact with. But, unlike ice, each particle in the quantum world can simultaneously inhabit multiple states, called a quantum superposition, and can become inextricably linked together through quantum entanglement, which makes deducing the original state extra difficult after it has had the chance to change. 

For practical reasons, Galitski and Vikram designed their technique so that it applies to situations where researchers never know the exact states of all the interacting quantum particles. Their approach works for a range of cases spanning those where information is stored in a small chunk of all the interacting quantum particles to ones where the information is on a majority of particles—anything from an ice cube in a lake to a sculpture in a puddle. This gives the technique an advantage over previous approaches that only work for information stored on a few of the original particles.

Using the new technique, the pair can get insight into how long it takes a quantum message to effectively melt away for a wide variety of quantum situations. As long as they know the spectral form factor, they don’t need to know anything else. 

“It's always nice to be able to formulate statements that assume as little as possible, which means they're as general as possible within your basic assumptions,” says Vikram, who is the first author of the paper. “The neat little bonus right now is that the spectral form factor is a quantity that we can in principle measure.”

The ability of researchers to measure the spectral form factor will allow them to use the technique even when many details of the system are a mystery. If scientists don’t have enough details to mathematically derive the spectral form factor or to tailor a custom description of the particles and their interactions, a measured spectral form factor can still provide valuable insights. 

As an example of applying the technique, Galitski and Vikram looked at a quantum model of scrambling called the Sachdev-Ye-Kitaev (SYK) model. Some researchers believe there might be similarities between the SYK model and the way information is scrambled and lost when it falls into a black hole. 

Galitski and Vikram’s results revealed that the scrambling time became increasingly long as they looked at larger and larger numbers of particles instead of settling into conditions that scrambled as rapidly as possible. 

“Large collections of particles take a really long time to lose information into the rest of the system,” Vikram says. “That is something we can get in a very simple way without knowing anything about the structure of the SYK model, other than its energy spectrum. And it's related to things people have been thinking about simplified models for black holes. But the real inside of a black hole may turn out to be something completely different that no one's imagined.”

Galitski and Vikram are hoping future experiments will confirm their results, and they plan to continue looking for more ways to relate a general quantum feature to the resulting dynamics without relying on many specific details. They and their colleagues are also investigating properties of the spectral form factor that every system should satisfy and are working to identify constraints on scrambling that are universal for all quantum systems.

Original story by Bailey Bedford:

This research was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0001911. 

New Laser Experiment Spins Light Like a Merry-go-round

In day-to-day life, light seems intangible. We walk through it and create and extinguish it with the flip of a switch. But, like matter, light actually carries a little punch—it has momentum. Light constantly nudges things and can even be used to push spacecraft. Light can also spin objects if it carries orbital angular momentum (OAM)—the property associated with a rotating object’s tendency to keep spinning.

Scientists have known that light can have OAM since the early 90s, and they’ve discovered that the OAM of light is associated with swirls or vortices in the light’s phase—the position of the peaks or troughs of the electromagnetic waves that make up the light. Initially, research on OAM focused on vortices that exist in the cross section of a light beam—the phase turning like the propeller of a plane flying along the light’s path. But in recent years, physicists at UMD, led by UMD Physics Professor Howard Milchberg, have discovered that light can carry its OAM in a vortex turned to the side—the phase spins like a wheel on a car, rolling along with the light. The researchers called these light structures spatio-temporal optical vortices (STOVs) and described the momentum they carry as transverse OAM.

“Before our experiments, it wasn’t appreciated that particles of light—photons—could have sideways-pointing OAM,” Milchberg says. “Colleagues initially thought it was weird or wrong. Now research on STOVs is rapidly growing worldwide, with possible applications in areas such as optical communications, nonlinear optics, and exotic forms of microscopy.”

In an article published on Feb. 28, 2024, in the journal Physical Review X, the team describes a novel technique they used to change the transverse OAM of a light pulse as it travels. Their method requires some laboratory tools, like specialized lasers, but in many ways, it resembles spinning a playground merry-go-round or twisting a wrench.Similarities exist between spinning everyday items, like a playground merry-go-round, and spinning vortices of light. Image credit: Martin VorelSimilarities exist between spinning everyday items, like a playground merry-go-round, and spinning vortices of light. Image credit: Martin Vorel

“Because STOVs are a new field, our main goal is gaining a fundamental understanding of how they work. And one of the best ways to do that is to mess with them,” says Scott Hancock, a UMD physics postdoctoral researcher and first author of the paper. “Basically, what are the physics rules for changing the transverse OAM of a light pulse?”

In previous work, Milchberg, Hancock and colleagues described how they created and observed pulses of light that carry transverse OAM, and in a paper published in Physical Review Letters in 2021, they presented a theory that describes how to calculate this OAM and provides a roadmap for changing a STOV’s transverse OAM.

The consequences described in the team’s theory aren’t so different from the physics at play when kids are on a playground. When you spin a merry-go-round you change the angular momentum by pushing it, and the effectiveness of a push depends on where you apply the force—you get nothing from pushing inwards on the axle and the greatest change from pushing sideways on the outer edge. The mass of the merry-go-round and everything on it also impact the angular momentum. For instance, kids jumping off a moving merry-go-round carry away some of the angular momentum, making the merry-go-round easier to stop.

The team’s theory of the transverse OAM of light looks very similar to the physics governing the spin of a merry-go-round. However, their merry-go-round is a disk made of light energy laid out in one dimension of space and another of time instead of two spatial dimensions, and its axis is moving at the speed of light. Their theory predicts that pushing on different parts of a merry-go-round light pulse can change its transverse OAM by different amounts and that if a bit of light is scattered off a speck of dust and leaves the pulse then the pulse loses some transverse OAM with it.

The team focused on testing what happened when they gave the transverse OAM vortices a shove. But changing the transverse OAM of a light pulse isn’t as easy as giving a merry-go-round a solid push; there isn’t any matter to grab onto and apply a force. To change the transverse OAM of a light pulse, you need to flick its phase.

As light journeys through space, its phase naturally shifts, and how fast the phase changes depends on the index of refraction of the material that the light travels through. So Milchberg and the team predicted that if they could create a rapid change in the refractive index at selected locations in the pulse as it flew by, it would flick that portion of the pulse. However, if the entire pulse passes through the area with a new index of refraction, they predicted that there would be no change in OAM—like having someone on the opposite side of a merry-go-round trying to slow it down while you are trying to speed it up.

To test their theory, the team needed to develop the ability to flick a small section of a pulse moving at the speed of light. Luckily, Milchberg’s lab already had invented the appropriate tools. In multiple previous experiments, the group has manipulated light by using lasers for the rapid generation of plasmas—a phase of matter in which electrons have been torn free from their atoms. The process is useful because the plasma brings with it a new index of refraction.

In the new experiment, the team used a laser to make narrow columns of plasma, which they called transient wires, that are small enough and flash into existence quickly enough to target specific regions of the pulse mid-flight. The index of refraction of a transient wire plays the role of a child pushing the merry-go-round.

The researchers generated the transient wire and meticulously aligned all their beams so that the wire precisely intercepted the desired section of the OAM-carrying pulse. After part of the pulse passed through the wire and received a flick, the pulse reached a special optical pulse analyzer the team invented. As predicted, when the researchers analyzed the collected data, they found that the refractive index flick changed the pulse’s transverse OAM.

They then made slight adjustments in the orientation and timing of the transient wire to target different parts of the light pulse. The team performed multiple measurements with the transient wire crossing through the top and bottom of two types of pulses: STOVs that already carried transverse OAM and a second type called a Gaussian pulse without any OAM at all. For the two cases, corresponding to pushing an already spinning or a stationary merry-go-round, they found that the biggest push was achieved by applying the transient wire flick near the top and bottom edges of the light pulse. For each position, they also adjusted the timing of the transient wire laser on various runs so that different amounts of the pulse traveled through the plasma and the vortex received a different amount of kick.Researchers who previously generated vortices of light that they describe as “edge-first flying donuts” have now performed experiments where they disturb the path of the vortices mid-flight to study changes to their momentum.  Image credit: Intense Laser-Matter Interactions Lab, UMDResearchers who previously generated vortices of light that they describe as “edge-first flying donuts” have now performed experiments where they disturb the path of the vortices mid-flight to study changes to their momentum. Image credit: Intense Laser-Matter Interactions Lab, UMD

The team also showed that, like a merry-go-round, pushing with the spin adds OAM and pushing against it removes OAM. Since opposite edges of the optical merry-go-round are traveling in opposite directions, the plasma wire could fulfill both roles by changing its position even though it always pushed in the same direction. The group says the calculations they performed using their theory are in excellent agreement with the results from their experiment.

“It turns out that ultrafast plasma provides a precision test of our transverse OAM theory,” says Milchberg. “It registers a measurable perturbation to the pulse, but not so strong a perturbation that the pulse is completely messed up.”

The team plans to continue exploring the physics associated with transverse OAM. The techniques they have developed could provide new insights into how OAM changes over time during the interaction of an intense laser beam with matter (which is where Milchberg’s lab first discovered transverse OAM). The group plans to investigate applications of transverse OAM, such as encoding information into the swirling pulses of light. Their results from this experiment demonstrate that the naturally occurring fluctuations in the index of refraction of air are too slow to change a pulse’s transverse OAM and distort any information it is carrying.

“It's at an early stage in this research,” Hancock says. “It's hard to say where it will go. But it appears to have a lot of promise for basic physics and applications. Calling it exciting is an understatement.”

Story by Bailey Bedford

In addition to Milchberg, and Hancock, graduate student Andrew Goffin and UMD physics postdoctoral associate Sina Zahedpour were co-authors.

The Many Wonders of Uranium Ditelluride

In the menagerie of exotic materials, superconductors boast their own vibrant ecosystem.

All superconductors allow electricity to flow without any resistance. It’s their hallmark feature. But in many cases, that’s where the similarities end.

Some superconductors, like aluminum, are conventional—run-of-the-mill, bread-and-butter materials that are well understood and hold no surprises. Others are deemed unconventional: They are not yet fully understood, but that seem to follow a known pattern. But one material—uranium ditelluride (UTe2)—defies classification, continuously baffling scientists with a plethora of unexpected behaviors. 

“At first, we thought this was going to be another interesting superconductor like some other uranium compounds that have been studied in the past,” says Johnpierre Paglione, a professor of physics at the University of Maryland (UMD) and the director of the Quantum Materials Center (QMC). “But at this point, it's gone beyond that. And it's become a much richer example of how crazy a superconductor can get.”

Most superconductors start doing their resistance-less thing when they get super cold. But temperature is only one of the knobs available to researchers studying a material in the lab. Some materials slip into superconductivity when you dial in other aspects of their environment, like the pressure they’re subjected to or the strength of a magnetic field they’re bathed in. UTe2 isn’t fussy about these properties, and it happily hosts superconductivity in all kinds of different situations. And as researchers continue studying the material, they are finding more questions than answers. 

“This one material seems to do 100 different things,” says Nicholas Butch, who is a physicist at the National Institute of Standards and Technology (NIST) and a member of QMC. “Somebody asked me after one of my talks ‘What right does one material have to do all these things?’ and I said ‘Right?’”

Butch and Paglione, together with colleagues at UMD, NIST, QMC and elsewhere, have been at the forefront of exploring the many wonders of UTe2. Postdocs Shang Ran and Corey Frank, working at both NIST and QMC have spearheaded many of the efforts, from discovering superconductivity in the material to testing samples at National High Magnetic Field Laboratory facilities around the country and experimenting with different preparation techniques. And the buzz around UTe2 is catching on: QMC has been sharing the samples they synthesize with researchers at other universities, including the University of Illinois at Urbana-Champaign and Cornell University, and further study by these groups resulted in the discovery of yet more unexpected behaviors. Uranium ditelluride (UTe2)Uranium ditelluride (UTe2)

A serendipitous discovery

Back in 2018, UMD and NIST postdoc Shang Ran was trying to synthesize U7Te12—a mixture of uranium and tellurium that’s predicted to have intriguing magnetic properties. Instead, Ran kept accidentally making UTe2. He found some literature from the 1960s suggesting UTe2 might have some interesting magnetic properties as well, and after consulting Butch, the two decided to cool it down anyway to see what would happen. Ran stuck the sample into a special helium-powered refrigerator. To his surprise, superconducting currents started to flow.

“We accidentally synthesized this uranium ditelluride, and it turned out it’s a superconductor. So, miracle!” Ran says. “That certainly brought excitement to the community and to our research.”

Ran became captivated with UTe2, and the team went on to poke and prod at it to try to understand its superconducting properties. To start, they set out to explore one of the key behaviors for any superconductor—its response to a magnetic field.  

In superconductors, electrons floating around in the material couple up, forming what’s known as Cooper pairs. These pairs act in concert with each other, and with the other pairs around them, allowing the electrons to flow without resistance. However, a strong magnetic field can break up the pairs, destroying the superconducting magic. One of the main signatures of a superconductor is how much magnetic juice it can withstand, and Ran and his collaborators set out to find this landmark for uranium ditelluride. 

To their surprise, uranium ditelluride remained a superconductor as they turned the field all the way up to the maximum power they has access to in the lab—20 tesla. That’s the combined magnetic strength of about two thousand fridge magnets, or ten times the magnetic field in an MRI machine. “I was shocked when [graduate student Chris Eckgerg] showed me the data,” says Ran. “I asked him ‘Did you measure correctly?’ We measured again and it was all correct. So, we realized, okay, there's some very strange thing going on.”

It wasn’t until they brought the material to the National High Magnetic Field Laboratory in Tallahassee, Florida that they finally found a magnet strong enough to tear apart UTe2’s Cooper pairs: It took an astounding 35 tesla to break the bond. For comparison, the first superconductor ever discovered—mercury—loses its superconductivity at a mere 0.1 tesla. This tipped off Ran, Butch, and the others that UTe2 was no conventional superconductor. They guessed that the electrons inside UTe2 form Cooper pairs in an unusually resilient way.

A special kind of dance

The electrons in a superconductor are kind of like a group of couples on a dance floor. In conventional superconductors, the electron pairs dance together in a straight line, a simple dance where partners mirror each other known as spin-singlet pairing. This synchronized movement allows them to glide effortlessly across the dance floor without any hindrance. However, in some unconventional superconductors, the electron pairs dance in swirly circles, spinning around each other as they glide across the dance floor. This unique dance style, known as spin-triplet pairing, gives them a different kind of coordination.

One consequence of this swirly dance pattern is that breaking up the partners with a magnetic field is much harder, which would explain the high magnetic field UTe2 could withstand. To check if that was going on inside UTe2, the QMC team collaborated with the group of Yuji Furukawa at Iowa State University. The Iowa team used their best techniques for distinguishing between the electron dance patterns, nuclear magnetic resonance spectroscopy. These studies confirmed Ran’s suspicions that UTe2 is a rare spin-triplet superconductor

Fewer than a dozen materials are suspected of spin-triplet pairing, and the other candidates are difficult to study—they are either hard to synthesize reliably or they only become superconducting under intense pressures or extremely low temperatures. Uranium ditelluride appears to be the most user-friendly spin-triplet superconductor to date, presenting a rare opportunity for researchers. 

“This is the only triplet superconductor I know that can be studied by so many different probes,” says Vidya Madhavan, a condensed matter physicist and professor at the University of Illinois at Urbana-Champaign (UIUC) who is a longtime collaborator of the QMC team. 

In addition to satisfying a physicist’s basic curiosity, spin-triplet superconductors might be useful as platforms for quantum computing. Spin-triplet pairing is a necessary ingredient for a yet rarer property that hasn’t been confirmed in any superconductor to date—a non-trivial topology. If spin-triplet pairing imbues electron couples with killer dance moves, a non-trivial topology warps the whole dance floor with curves and twists, radically changing the dance patterns of all the couples en masse. 

In the months following the discovery of UTe2’s swirly dance patterns, some evidence suggested that UTe2 might not only be a spin-triplet superconductor but also possess that topological special sauce. The evidence is not yet conclusive, but researchers are hard at work trying to sort this out, as well as understand more about what makes UTe2 tick. And their sleuthing keeps turning up more surprises. 

Superconductivity raised from the dead (and the never-born)

Ran and his labmates were wondering why 35 tesla seemed to be the magic number that broke superconductivity in UTe2. In search of clues, they went back to the National High Magnetic Field Lab.  They kept turning up the magnetic field even higher, looking at how the non-superconducting chunk responded. They also tilted the sample, putting the magnetic field off-kilter from UTe2’s natural crystal structure. 

Shockingly, as they kept rotating the sample, superconductivity reappeared at a field of 40 tesla. This was strange. Turning the field up really high killed the superconductivity, but if you kept going it came back to life. This phenomenon was termed Lazarus superconductivity after the biblical figure raised from the dead. Lazarus superconductivity is extremely rare, though not entirely unprecedented. It’s cropped up in a handful of materials before, and scientists think they have plausible mechanisms for explaining the effect. But none of those mechanisms seemed applicable to UTe2. 

In 2020, Ran joined the physics department at Washington University in St Louis, passing the torch of Butch’s QMC lab to a new postdoctoral researcher, Corey Frank. Frank had just completed her PhD in solid-state chemistry—the perfect background for mastering different ways of concocting the UTe2 crystal. She played with the initial concentrations of the starting materials as well as precise techniques and temperatures of preparation. Among other things, Frank developed a protocol for making UTe2 samples that are just shy of superconducting by making them intentionally just a bit dirty, peppering the crystals with purposefully introduced defects. These defects gum up the pathways by which electrons pair up and find their dance partners, preventing the development of superconductivity. “You can learn a lot about a phase by studying what kills it,” Frank says. 

Frank and her colleagues made a purposefully dirty sample and took it with them on another trip to the National High Magnetic Field Laboratory, this time in Los Alamos, New Mexico. They stuck the sample into the huge magnets and cranked up the field. Once the field was high enough and the sample had the right orientation, the resistance through the material dropped to zero—superconductivity was revived. 

“I was so excited,” Frank recalls. “You're not allowed to jump when you're on the platform of a high-field magnet, but I had to get down from the magnet so I could jump. It was amazing.”

This was completely unprecedented. In all the previous Lazarus superconducting materials, the mechanism behind the rebirth was presumed to involve recreating the conditions at a low magnetic field. Here, recreating conditions at a low magnetic field would not result in superconductivity because the samples had intentional defects, and yet there it was—superconductivity raised not from the dead, but from the never-born, a high-field superconducting phase all its own. The team reported this phenomenon last year in a preprint.

“We know how high field superconductivity works, the rules that govern that, and this one breaks those rules,” Frank says. “So the fact that we have this much more robust high-field phase is wild. I cannot overemphasize how unexpected it is.” 

The authors have some ideas of what could be causing this behavior, and they say further experiments are needed to figure out if those ideas are correct. For now, the experiments are on hold as they require even stronger magnetic fields than the National High Magnetic Field Laboratory currently offers. In the meantime, the QMC team is still studying how this superconductivity dies, comparing their revived samples to others in search of a pattern. 

Making waves 

Over many years Ran, Frank, and other members of the Butch lab have mastered the dual feats of growing pure uranium ditelluride crystals and studying their overall behavior—superconductivity, response to magnetic fields, and more. But they lacked the tools and expertise to zoom in on the microscopic, atom-by-atom behavior of UTe2. So they’ve enlisted the help of Vidya Madhavan’s team at UIUC.

In her lab, Madhavan has a scanning tunneling microscope (STM). An STM works by bringing a bit of metal tapered down to a tiny, fine point extremely close to the surface of a sample—so close that electrons from the sample can hop over to the conducting tip, or vice versa. By measuring how many electrons make the jump, scientists can learn a lot about the microscopic structure of a material, including where the electrons are on the surface of the sample.

The Butch group sent Madhavan a sample, and Anuva Aishwarya, a graduate student at UIUC who led the study, placed a sample of UTe2 into the scanning tunneling microscope. The team cooled the material just shy of its superconducting temperature, and they stumbled upon another surprise: The electrons didn’t follow the ups and downs of UTe2’s crystal structure. Instead, they clustered together and then apart, forming waves of charge frozen into the surface with a pattern all their own.

These kinds of charge density waves are uncommon but not unprecedented. However, the measurements performed by Ran, Frank or others at QMC didn’t show any indication that a charge density wave might be found in UTe2. To Madhavan and her team, this came out of nowhere.

To try to understand what they were seeing, Aishwarya and her lab mates probed the behavior of these waves in different temperatures and magnetic fields. They found that, in a magnetic field, the charge density wave seemed intimately related to superconductivity itself. As they turned up the field, the charge density wave broke down at precisely the same field strength as superconductivity. This tipped off Madhavan and her collaborators at UIUC that maybe this wave had some relationship to the superconductivity in uranium ditelluride.

If you want to pick out individual electrons, a regular STM is great. But if you want to peer inside the dance patterns of electron couples in a superconductor, you need an STM armed with a special kind of tip—one that is itself a superconductor. The team of Seamus Davis at Cornell University had just such a superconducting tip. They became intrigued by Madhavan’s results and got in on the action. They obtained another sample from the QMC team and stuck it in their specialized STM. They found that the electron pairs behaved similarly to the lone electrons. Here, too, the pairs clustered together and apart, forming a so-called pair density wave with the same beat as the charge density wave observed by Madhavan. This is the first time such a pair density wave has been found in a spin-triplet superconductor.

As with many aspects of UTe2, the origins of the charge and pair density waves remain far from clear. But, Ran comments, these waves are a fairly common feature in unconventional spin-singlet superconductors. This may provide clues for how all these different strange superconductors are connected. “We eventually need to understand unconventional superconductivity overall,” Ran says. “And having this common theme I think is very important for theorists.”

While theorists are hard at work trying to crack the puzzle of unconventional superconductivity, Ran, Butch, and other researchers are continuing to explore all that UTe2 has in store. “It's really rich. It’s a great place to explore,” says Butch. “This one material underscores how little we know about spin triplet physics. It’s as if we are writing textbooks about it right now. So that's actually very exciting.”

Story by Dina Genkina