A Fresh Perspective on Ergodicity Breaking Through Soccer Balls, Footballs, and Quantum Physics

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A Fresh Perspective on Ergodicity Breaking Through Soccer Balls, Footballs, and Quantum Physics

A study focusing on a C60 molecule, or buckyball, was conducted to comprehend its potential to break ergodicity. Image credit: Steven Burrows/Jun Ye and David Nesbitt

Scientists noticed extraordinary patterns of ergodicity breaking in the C60 molecule’s rotations, without symmetry breaking, by utilizing advanced infrared spectroscopy techniques. These findings shed new light on quantum system behavior and open the door to further research at the molecular level.

The study, led by JILA and NIST Fellow Jun Ye and fellow scientists David Nesbitt, researchers from the University of Nevada, Reno, and Harvard University, uncovered new instances of ergodicity breaking in C60. This molecule, made of 60 carbon atoms arranged in a pattern resembling a soccer ball (20 hexagons and 12 pentagons), showed ergodicity breaking in its rotations. The team surprisingly discovered that this breaking occurs without breaking symmetry and can toggle on and off as the rotation speed increases. Understanding these breaks is vital in developing better materials for energy and heat transfer. The results were published in the journal Science on August 17.

Many common systems, such as heat spreading in a pan or smoke filling a room, display “ergodicity,” meaning the equal distribution of matter or energy over time across all parts of the system. Conversely, understanding how systems can disrupt ergodicity, like magnets or superconductors, assists scientists in understanding and crafting unusual states of matter.

Often, ergodicity breaking is linked to “symmetry breaking.” In magnets, for example, the atoms’ magnetic moments align in one direction, either “up” or “down.” These two configurations, despite having the same energy, are separated by an energy barrier. This “symmetry breaking” points to the system adopting a configuration with lesser symmetry than what the governing physical laws would allow. Since the magnet has settled into only one of the equal-energy configurations, ergodicity is also broken.

Understanding Symmetry Breaking with Magnets and Footballs

Lead author and postdoctoral researcher Lee Liu explained rotational ergodicity breaking by using a football’s spiral throw as an analogy. The football’s end-to-end orientation never flips mid-flight, like a magnet, breaking ergodicity and symmetry.

But unlike footballs, isolated molecules must adhere to quantum mechanics. Reorienting a spinning ethylene molecule (a quantum football analog) 180 degrees requires overcoming an energy barrier, and the molecule doesn’t have two distinct orientations. Thus, symmetry and ergodicity are preserved.

Insight into C60 Buckyballs

C60, also known as Buckminsterfullerene or “buckyball,” is a spherical molecule of 60 carbon atoms, arranged like a soccer ball. Its discovery in the 1980s paved new paths in nanotechnology and earned the researchers the 1996 Nobel Prize in Chemistry.

Investigating C60 Through Infrared Spectroscopy

To examine C60’s rotational dynamics, the researchers used a method developed by the Ye group: combining buffer gas cooling and sensitive cavity-enhanced infrared spectroscopy. They used lasers to study C60 molecules, resulting in a highly sensitive infrared spectrum, offering snapshots of the molecule at varying rotation speeds. By piecing these together, they unraveled the complete picture of the molecule’s ergodicity evolution, explained Dina Rosenberg, a postdoctoral researcher in Ye’s group.

The study found that spinning C60 at specific frequencies could make it ergodic or break ergodicity, with unexpected switching behavior. The researchers traced this unique behavior to deformations in the molecule as it rotated.

Unpacking Ergodicity Breaking – The Quantum Behavior of Football, Frisbee, and Soccer

Analyzing the infrared spectrum, the researchers discovered that the rotation rate of C60 determined its structural deformation, similar to how drag race car tires bulge when rotated faster. This sequence of deformations was identified as the reason behind C60’s unique ergodicity transitions.

Breaking Ergodicity Without Breaking Symmetry

In the gas phase, C60 molecules behaved as though isolated, rendering the indistinguishability of each carbon atom crucial. The researchers’ data revealed that the rotation axis never switched between sectors. This rotational isolation was attributed to energy conservation and an energy barrier, resulting in ergodicity breaking without symmetry breaking, a surprising discovery to the scientists.

These findings present an exceptional example of ergodicity breaking without symmetry breaking, offering deeper insights into the quantum mechanics of the system.

The researchers are optimistic that their new technique will uncover more surprises in other molecular species.

Reference: The findings were published in Science on August 17, 2023, under the title “Ergodicity breaking in rapidly rotating C60 fullerenes” by Lee R. Liu and others.
DOI: 10.1126/science.adi6354

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• Science Journal
• NIST (National Institute of Standards and Technology)
• JILA, a joint institute of the University of Colorado Boulder and NIST
• Nobel Prize in Chemistry 1996