A Frankenstein of Order and Chaos

Normally the word “chaos” evokes a lack of order: a hectic day, a teenager’s bedroom, tax season. And the physical understanding of chaos is not far off. It’s something that is extremely difficult to predict, like the weather. Chaos allows a small blip (the flutter of a butterfly wing) to grow into a big consequence (a typhoon halfway across the world), which explains why weather forecasts more than a few days into the future can be unreliable. Individual air molecules, which are constantly bouncing around, are also chaotic—it’s nearly impossible to pin down where any single molecule might be at any given moment.

Now, you might wonder why anyone would care about the precise location of a single air molecule. But you might care about a property shared by a whole bunch of molecules, such as their temperature. Perhaps unintuitively, it is the chaotic nature of the molecules that allows them to fill up a room and reach a single temperature. The individual chaos ultimately gives rise to collective order.

Being able to use a single number (the temperature) to describe a bunch of particles bouncing around in some crazy, unpredictable way is extremely convenient, but it doesn’t always happen. So, a team of theoretical physicists at JQI set out to understand when this description applies.Researchers at JQI have discovered a quantum system that is a hybrid of order and chaos. (Credit: geralt/Pixabay)Researchers at JQI have discovered a quantum system that is a hybrid of order and chaos. (Credit: geralt/Pixabay)

"The ambitious goal here is to understand how chaos and the universal tendency of most physical systems to reach thermal equilibrium arises from fundamental laws of physics," says Victor Galitski, a Fellow of the Joint Quantum Institute (JQI).

As a first step towards this ambitious goal, Galitski and two colleagues set out to understand what happens when many particles, each of which is chaotic on its own, get together. For example, the motion of a single puck in an air hockey game, bouncing uninterrupted off the walls, is chaotic. But what happens when a lot of these pucks are let loose onto the table? And furthermore, what would happen if the pucks obey the rules of quantum physics?

In a paper published recently in the journal Physical Review Letters(link is external), the team studied this air hockey problem in the quantum realm. They discovered that the quantum version of the problem (where pucks are really quantum particles like atoms or electrons) was neither ordered nor chaotic, but a little bit of both, according to one common way of measuring chaos. Their theory was general enough to describe a range of physical settings, including molecules in a container, a game of quantum air hockey, and electrons bouncing around in a disordered metal, such as copper wire in your laptop.

“We always thought it was a problem that’s been solved a long time ago in some textbook,” says Yunxiang Liao, a JQI postdoc and the first author on the paper. “It turns out it's a more difficult problem than we imagined, but the results are also more interesting than we imagined.”

One reason this problem has remained unsolved for so long is that once quantum mechanics enters the picture, the usual definitions of chaos don’t apply. Classically, the butterfly effect—tiny changes in initial conditions causing drastic changes down the line—is often used as a definition. But in quantum mechanics, the very notion of initial or final position doesn’t quite make sense. The uncertainty principle says that the position and speed of a quantum particle can’t be precisely known at the same time. So, the particle’s trajectory isn’t very well defined, making it impossible to track how different initial conditions lead to different outcomes.

One tactic for studying quantum chaos is to take something classically chaotic, like a puck bouncing around an air hockey table, and treat it quantum mechanically. Surely, the classical chaos should translate over. And indeed, it does. But when you put more than one quantum puck in, things become less clear.

Classically, if the pucks can bounce off each other, exchanging energy, they will eventually all reach a single temperature, exposing the collective order of the underlying chaos. But if the pucks don’t bump into each other, and instead pass through each other like ghosts, their energies will never change: the hot ones will stay hot, the cold ones will stay cold, and they’ll never reach the same temperature. Since the pucks don’t interact, collective order can’t emerge from the chaos.

The team took this game of ghost air hockey into the quantum mechanical realm expecting the same behavior—chaos for one quantum particle, but no collective order when there are many. To check this hunch, they picked one of the oldest and most widely used (albeit not the most intuitive) tests of quantum chaos.

Quantum particles can’t just have any energy, the available levels are ‘quantized,’ which basically means they are restricted to particular values. Back in the 1970’s, physicists found that if the quantum particles behaved in predictable ways, their energy levels were completely independent of one another—the possible values didn’t tend to bunch up or spread out, on average. But if the quantum particles were chaotic, the energy levels seemed to avoid each other, spreading out in distinctive ways. This energy level repulsion is now often used as one of the definitions of quantum chaos.

Since their hockey pucks didn’t interact, Liao and her collaborators weren’t expecting them to agree on a temperature, meaning that they wouldn’t see any indications of the underlying single-puck chaos. The energy levels, they thought, would not care about each other at all.

Not only did they find theoretical evidence of some level repulsion, a hallmark of quantum chaos, but they also found that some of the levels tended to bunch together rather than repel, a novel phenomenon that they couldn’t quite explain. This deceptively simple problem turned out to be neither ordered nor chaotic, but some curious combination of the two that hadn’t been seen before.

The team was able to uncover this hybrid using an innovative mathematical approach. “In previous numerical studies, researchers were only able to include 20 or 30 particles,” says Liao. “But using our mathematical approach from random matrix theory, we could include 500 or so. And this approach also allows us to calculate the analytic behavior for a very large system.”

Armed with this mathematical framework, and with piqued interest, the researchers are now extending their calculations to gradually allow the hockey pucks to interact little by little. "Our preliminary results indicate that thermalization may happen via spontaneous breaking of reversibility—the past becomes mathematically distinct from the future,” says Galitski. “We see that small disturbances get exponentially magnified and destroy all remaining signatures of order. But this is another story."

Story by Dina Genkina

In addition to Liao and Galitski, Amit Vikram, a JQI graduate student in physics at UMD, was an author on the paper.

Reference Publication
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Original story: https://jqi.umd.edu/news/frankenstein-order-and-chaos

Parker, Jawahery Discuss Findings in Symmetry Magazine

LHCb experiment. Image courtesy of CERN.LHCb experiment. Image courtesy of CERN.In November 2020, the LHCb collaboration announced a major new development, based on data collected during LHC Run 2, confirming and significantly strengthening an anomalous observation in decays of B mesons. 

Postdoc Will Parker and Distinguished University Professor Hassan Jawahery of the UMD flavor physics group recently discussed their work and "matter-antimatter weirdness" in Symmetry magazine. 

The 2020 result followed the LHCb's previous observation of CP violation in decays of D mesons. That finding was rated a Physics World Breakthrough of the Year finalist for 2019.

The Symmetry story is posted here: https://www.symmetrymagazine.org/article/lhcb-finds-more-matter-antimatter-weirdness-in-b-mesons

Enhanced Frequency Doubling Adds to Photonics Toolkit

The digital age has seen electronics, including computer chips, shrink in size at an amazing rate, with ever tinier chips powering devices like smartphones, laptops and even autonomous drones. In the wake of this progress, another miniature technology has been gaining steam: integrated photonics.

Photons, which are the quantum particles of light, have some advantages over electrons, the namesakes of electronics. For some applications, photons offer faster and more accurate information transfer and use less power than electrons. And because on-chip photonics are largely built using the same technology created for the electronics industry, they carry the promise of integrating electronics and photonics on the same chip.

Tiny photonic chips have already been adopted in many places, including telecommunications networks (think fiber optic internet) and large data centers (think interfacing fiber-optics with electronics). Other industries are on the precipice of benefitting from photonics, with self-driving car makers developing(link is external) light-based radar chips. However, many tools that are well-established in traditional optics—things that use lasers, lenses and other bulky equipment—do not yet have a compact photonic analogue. For futuristic tools like light-based quantum computers or portable optical clocks, more work remains to package everything together.

Now, researchers at the Joint Quantum Institute (JQI) have added a new tool to the photonics toolkit: a way to use silicon, the native material for much of digital electronics and photonics, to efficiently double the frequency of laser light. By combining two existing techniques, the team achieved a frequency doubling efficiency 100 times greater than previously experiments with silicon compounds. They detailed their results in a paper published in the journal Nature Photonics(link is external).

Light waves are made up of photons, but they also carry a frequency. Our eyes see a small fraction of these frequencies as the colors of the rainbow, but microwaves, x-rays and radio waves (among others) also inhabit this spectrum. Doubling the frequency of light is one way to convert between these different ranges. In the new work, the team demonstrated a doubling of infrared light—commonly used in optical telecommunications—to red light, the language of very precise atomic clocks.

Frequency doubling is one effect that can occur when light interacts with the medium it’s traveling through, be it air, water or silicon. Depending on the properties of these materials, a little bit of the light can be doubled, tripled, or, in extreme cases, multiplied to even higher degrees, like a musical note also generating a bit of sound one, two, or several octaves up. By choosing the right material, and illuminating it in the right way, researchers can get to the harmonic they need.

Unfortunately, silicon and silicon compounds—the materials of choice for routing light on a chip because of the maturity of silicon manufacturing and the ease of integrating with elA new photonic chip can double the frequency (f) of incoming light using a circular ring 23 microns across. The ring is tailored to generate and hold light at the input frequency and at its second harmonic (2f)—just like piano strings or organ tubes can host harmonics of a single tone. The color indicates crests and troughs of the light field, similar to a piano string’s displacement pattern when it rings. (Credit: Xiyuan Lu/NIST and UMD)A new photonic chip can double the frequency (f) of incoming light using a circular ring 23 microns across. The ring is tailored to generate and hold light at the input frequency and at its second harmonic (2f)—just like piano strings or organ tubes can host harmonics of a single tone. The color indicates crests and troughs of the light field, similar to a piano string’s displacement pattern when it rings. (Credit: Xiyuan Lu/NIST and UMD)ectronics—don’t intrinsically support frequency doubling. The crystal structure is too uniform, meaning it looks the same in all directions. This prohibits the doubling effect, which relies on electrons in the material shifting one way more than another under the influence of light. But once light is confined to a tiny trace on a chip, things become a little less uniform: After all, the air is always nearby, and it doesn’t look at all like a silicon crystal. So, a tiny amount of frequency doubled light does get generated, but usually it is not enough to be useful.

In the new work, a team led by Adjunct Professor Kartik Srinivasan, a Fellow of the National Institute of Standards and Technology (NIST), and NIST and UMD postdoctoral researcher Xiyuan Lu, combined two previously explored techniques to build on this tiny effect, generating 100 times more frequency doubled light than any previous silicon experiments. Additionally, their doubling occurred with an efficiency of 22%, appreciable enough to be useful in applications.

The first trick was to capture the light in a resonator, making the light go round and round and triggering the tiny doubling effect over and over again. To achieve this, the researchers first routed near-infrared laser light into an optical fiber. The fiber then shot the light into a silicon nitride waveguide printed on a silicon chip. This waveguide led to another waveguide, which was wrapped into a circle just 23 microns in diameter. The circular resonator, which was engineered to capture the incoming light and circulate it around, allowed a tiny bit of frequency doubling to happen over and over again. Another straight waveguide, on the other edge of the resonator, was tuned to carry away the frequency-doubled light.

The second trick was to make the silicon less uniform by biasing it with an electric field. Luckily, no external field was actually needed—the tiny amount of frequency doubled light, combined with the original infrared pump light, caused the electrons in the resonator to gather at the edges, creating a constant electric field. This field greatly enhanced the frequency doubling capacity of the silicon nitride.

“It’s a feedback process,” says Srinivasan, “because a little bit of frequency doubled light and pump light start to create the constant electric field, making the frequency doubling process stronger, which in turn creates more frequency doubled light. So both the pump light and the frequency doubled light are circulating around in this ring, and there’s this huge ability to take this thing that started out as extremely weak, and then actually make it a pretty strong effect.”

Getting both of these effects to work in the same device wasn’t easy. Not only does the resonator ring need to be exactly the right size to trap the pump and frequency doubled light, the light also needs to stack up in the right way in the resonator. To achieve this, detailed simulations and precise manufacturing in a clean room are necessary. But once such an accurate device is fabricated, all you need to do is send in pump light, and observe frequency doubled light at the output.

“To enable efficient interaction between light and the material, light of different colors has to live a long time and also move at exactly the same speed,” says Lu, “Our device implements these two key factors into photo-induced frequency doubling, which significantly boosts the power efficiency of this process.”

This device is another step in a long quest to achieve a portable, ultra-precise atomic clock. “These optical clocks are these amazing timekeeping devices, but usually they're in a big lab,” says Srinivasan. “If it could be in a small package it could go on cars or drones or other vehicles. Timing underlies a lot of important navigation applications, and for the most part, now, people rely upon GPS signals. But there are all sorts of possibilities that there might be something in the way, and you can’t acquire those signals, or somebody spoofs the signal. So, having portable timing instruments that could really give you accurate and precise time for long stretches before you need a synchronization signal from GPS is meaningful.”

Although it’s not the star of the show, frequency doubling is a necessary component in optical atomic clocks. These clocks produce an extremely regular beat, but at optical frequencies—hundreds of trillions of light field oscillations per second. Conventional electronics can’t interface with that signal directly, so to bring this precision down to an intelligible frequency (mere billions of oscillations per second) scientists use frequency combs—laser sources with frequency ‘teeth’ at perfectly regular intervals, an invention that won the 2005 Nobel Prize in physics(link is external).

To be useful, these frequency combs need to be calibrated—each tooth in the comb needs to be labeled with a specific frequency value. The simplest and most common way to calibrate them is to take the lowest tooth in the comb, frequency double it, and compare to the highest tooth: this gives the frequency of the lowest tooth. Along with a simple measurement of the spacing between teeth, scientists can use this to deduce the exact frequency of each tooth.

Recently, several pieces of the on-chip atomic clocks, including tiny atomic vapor cells and on-chip frequency combs, have been achieved in silicon-based photonics. However, the frequency doubling calibration was previously done with bulky optics or using materials that are less compatible with silicon. “At least conceptually,” says Srinivasan, “we’re one step closer to a calibrated frequency comb in a really compact package. There's still work to be done to really be able to put these things together, but we’re closer to a compact optical atomic clock than we were before.”

Original story by Dina Genkina: https://jqi.umd.edu/news/enhanced-frequency-doubling-adds-photonics-toolkit

In addition to Srinivasan and Lu, this paper had 3 additional co-authors: Gregory Moille, a postdoctoral researcher at JQI and NIST; Ashutosh Rao, a postdoctoral researcher in chemistry and biochemistry at UMD and NIST; and Daron A. Westly, a research scientist at NIST

Research Contact: Kartik Srinivasan (This email address is being protected from spambots. You need JavaScript enabled to view it.)

Kollár Receives Air Force Young Investigator Grant

Assistant Professor 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.

Kollár plans to develop a new breed of superconducting devices for studying quantum computing and quantum simulation. The devices will build upon an already successful platform—superconducting qubits connected together by photonic cavities—to create new interactions between qubits and new ways of connecting qubits together.Air Force Office of Scientific Research

“These systems realize artificial photonic materials for microwave photons with unprecedented levels of versatility and control,” says Kollár. “They can even be used to make lattices which cannot be found in nature, including things as exotic as lattices in curved hyperbolic spaces. Thanks to the generous support of the Air Force Office of Scientific Research, we can now truly embark on harnessing this effect for new types of interactions and spin models.”

The YIP received more than 215 proposals this year, for research into everything from basic physics to machine learning and network science. Xiaodi Wu, a Fellow of the Joint Center for Quantum Information and Computer Science and an assistant professor of computer science at UMD, was also awarded a YIP grant this year.

Original story by Chris Cesare: https://jqi.umd.edu/news/kollar-receives-air-force-young-investigator-grant