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Exploring Black Hole-Level Scrambling in Chemical Reactions

If you threw a message inside a bottle into a black hole, the information within it would become scrambled, even down to the quantum level. Black holes are nature's ultimate information scramblers because this scrambling occurs as rapidly and thoroughly as quantum mechanics allows.

Exploring Black Hole-Level Scrambling in Chemical Reactions
Rice University theorist Peter Wolynes and collaborators at the University of Illinois Urbana-Champaign have shown that molecules can be as formidable at scrambling quantum information as black holes. Image Credit: Martin Gruebele; DeepAI was used in image production

However, a recent study by Theorist Peter Wolynes of Rice University and colleagues at the University of Illinois Urbana-Champaign demonstrates that molecules are just as capable of jumbling up quantum information as black holes.

Researchers have demonstrated that quantum information scrambling occurs in chemical reactions and can almost reach the same quantum mechanical limit as in black holes by combining mathematical techniques from chemical and black hole physics. The study was published in the National Academy of Sciences Proceedings.

This study addresses a long-standing problem in chemical physics, which has to do with the question of how fast quantum information gets scrambled in molecules. When people think about a reaction where two molecules come together, they think the atoms only perform a single motion where a bond is made or a bond is broken.

Peter Wolynes, Theorist, Rice University

Peter Wolynes adds, “But from the quantum mechanical point of view, even a very small molecule is a very complicated system. Much like the orbits in the solar system, a molecule has a huge number of possible styles of motion things we call quantum states. When a chemical reaction takes place, quantum information about the quantum states of the reactants becomes scrambled, and we want to know how information scrambling affects the reaction rate."

Out-of-time-order correlators, or OTOCs, are a type of mathematical tool commonly used in black hole physics to better understand how quantum information is jumbled in chemical reactions.

Wolynes said, “OTOCs were actually invented in a very different context about 55 years ago when they were used to look at how electrons in superconductors are affected by disturbances from an impurity. They’re a very specialized object that is used in the theory of superconductivity. They were next used by physicists in the 1990s studying black holes and string theory.”

OTOCs gauge the extent to which adjusting one component of a quantum system at a specific moment influences the behaviors of other components, offering insights into the speed and efficiency of information propagation within the molecule. They serve as the quantum counterpart to Lyapunov exponents, which quantify unpredictability in classical chaotic systems.

How quickly an OTOC increases with time tells you how quickly information is being scrambled in the quantum system, meaning how many more random looking states are getting accessed. Chemists are very conflicted about scrambling in chemical reactions because scrambling is necessary to get to the reaction goal, but it also messes up your control over the reaction.

Martin Gruebele, Chemist and Study Co-Author, Illinois Urbana-Champaign

Martin Gruebele adds, “Understanding under what circumstances molecules scramble information and under what circumstances they don’t potentially gives us a handle on actually being able to control the reactions better. Knowing OTOCs basically allows us to set limits on when this information is really disappearing out of our control and conversely when we could still harness it to have controlled outcomes.”

Gruebele is part of the joint Rice-Illinois Center for Adapting Flaws as Features, which is funded by the National Science Foundation.

According to classical mechanics, a particle cannot undergo a reaction without sufficient energy to cross an energy barrier. Nevertheless, even in the case of insufficient energy, particles may be able to "tunnel" through this barrier according to quantum mechanics. The computation of OTOCs demonstrated that information could be jumbled at almost the quantum limit, similar to a black hole, by chemical reactions with a low activation energy at low temperatures where tunneling predominates.

Nancy Makri, an Illinois Urbana-Champaign Chemist, studied what happens when the small-scale chemical reaction model is embedded in a larger system that tends to suppress chaotic motion. This larger system could be the vibrations of a large molecule or a solvent. Makri developed path integral methods for this purpose.

In a separate study, we found that large environments tend to make things more regular and suppress the effects that we’re talking about. So we calculated the OTOC for a tunneling system interacting with a large environment, and what we saw was that the scrambling was quenched⎯ a big change in the behavior.

Nancy Makri, Chemist, Illinois Urbana-Champaign

One possible use for the research findings is restricting the ways in which tunneling systems can be utilized to construct qubits for quantum computers. Enhancing the dependability of quantum computers requires reducing information scrambling between interacting tunneling systems. Further applications of the research may include advanced material design and light-driven reactions.

Gruebele concluded, “There’s potential for extending these ideas to processes where you wouldn’t just be tunneling in one particular reaction, but where you’d have multiple tunneling steps because that’s what’s involved in, for example, electron conduction in a lot of the new soft quantum materials like perovskites that are being used to make solar cells and things like that.”

Wolynes is Rice’s D.R. Bullard-Welch Foundation Professor of Science and teaches in multiple disciplines, including Chemistry, Biochemistry and Cell Biology, Physics and Astronomy, and Materials Science and Nanoengineering.

Additionally, he co-directs the Center for Theoretical Biological Physics, which receives funding from the National Science Foundation.

Co-authors include Gruebele, who holds the James R. Eiszner Endowed Chair in Chemistry; Makri, who is the Edward William and Jane Marr Gutgsell Professor and Professor of Chemistry And Physics; Chenghao Zhang, a former graduate student in physics at Illinois Urbana-Champaign, now a postdoc at Pacific Northwest National Lab; and Sohang Kundu, who recently earned his Ph.D. in chemistry from the University of Illinois and is currently a Postdoc at Columbia University.

The research received support from the National Science Foundation and the Bullard-Welch Chair at Rice.

Journal Reference:

Zhang, C., et al., (2024) Quantum information scrambling and chemical reactions. National Academy of Sciences


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