Theorists smooth the way to solving one of quantum mechanics oldest problems: Modeling quantum friction (J. Phys. Chem. Letters)

Researchers at Princeton

From left to right: Herschel Rabitz, Renan Cabrera, Andre Campos and Denys Bondar. Photo credit: C. Todd Reichart

By: Tien Nguyen, Department of Chemistry

Theoretical chemists at Princeton University have pioneered a strategy for modeling quantum friction, or how a particle’s environment drags on it, a vexing problem in quantum mechanics since the birth of the field. The study was published in the Journal of Physical Chemistry Letters.

“It was truly a most challenging research project in terms of technical details and the need to draw upon new ideas,” said Denys Bondar, a research scholar in the Rabitz lab and corresponding author on the work.

Quantum friction may operate at the smallest scale, but its consequences can be observed in everyday life. For example, when fluorescent molecules are excited by light, it’s because of quantum friction that the atoms are returned to rest, releasing photons that we see as fluorescence. Realistically modeling this phenomenon has stumped scientists for almost a century and recently has gained even more attention due to its relevance to quantum computing.

“The reason why this problem couldn’t be solved is that everyone was looking at it through a certain lens,” Bondar said. Previous models attempted to describe quantum friction by considering the quantum system as interacting with a surrounding, larger system. This larger system presents an impossible amount of calculations, so in order to simplify the equations to the pertinent interactions, scientists introduced numerous approximations.

These approximations led to numerous different models that could each only satisfy one or the other of two critical requirements. In particular, they could either produce useful observations about the system, or they could obey the Heisenberg Uncertainty Principle, which states that there is a fundamental limit to the precision with which a particle’s position and momentum can be simultaneous measured. Even famed physicist Werner Heisenberg’s attempt to derive an equation for quantum friction was incompatible with his own uncertainty principle.

The researchers’ approach, called operational dynamic modeling (ODM) and introduced in 2012 by the Rabitz group, led to the first model for quantum friction to satisfy both demands. “To succeed with the problem, we had to literally rethink the physics involved, not merely mathematically but conceptually,” Bondar said.

Bondar and his colleagues focused on the two ultimate requirements for their model – that it should obey the Heisenberg principle and produce real observations – and worked backwards to create the proper model.

“Rather than starting with approximations, Denys and the team built in the proper physics in the beginning,” said Herschel Rabitz, the Charles Phelps Smyth ’16 *17 Professor of Chemistry and co-author on the paper. “The model is built on physical and mathematical truisms that must hold. This distinct approach creates a new rigorous and practical formulation for quantum friction,” he said.

The research team included research scholar Renan Cabrera and Ph.D. student Andre Campos as well as Shaul Mukamel, professor of chemistry at the University of California, Irvine.

Their model opens a way forward to understand not only quantum friction but other dissipative phenomena as well. The researchers are interested in exploring the means to manipulate these forces to their advantage. Other theorists are rapidly taking up the new paradigm of operational dynamic modeling, Rabitz said.

Reflecting on how they arrived at such a novel approach, Bondar recalled the unique circumstances under which he first started working on this problem. After he received the offer to work at Princeton, Bondar spent four months awaiting a US work visa (he is a citizen of the Ukraine) and pondering fundamental physics questions. It was during this time that he first thought of this strategy. “The idea was born out of bureaucracy, but it seems to be holding up,” Bondar said.

Read the full article here:

Bondar, D. I.; Cabrera, R.; Campos, A.; Mukamel, S.; Rabitz, H. A. “Wigner-Lindblad Equations for Quantum Friction.J. Phys. Chem. Lett. 2016, 7, 1632.

This work was supported by the US National Science Foundation CHE 1058644, the US Department of Energy DE-FG02-02ER-15344, and ARO-MURI W911NF-11-1-0268.

Quantum mechanical calculations reveal the hidden states of enzyme active sites (Nature Chemistry)

[2Fe–2S] cluster in front of a leaf. (Image by C. Todd Reichart)

Researchers at Princeton University have reported the first direct observation of the electronic states of iron-sulfur clusters, common to many enzyme active sites. Iron-sulfur cluster in front of a leaf. (Image by C. Todd Reichart)

By Tien Nguyen, Department of Chemistry

Enzymes carry out fundamental biological processes such as photosynthesis, nitrogen fixation and respiration, with the help of clusters of metal atoms as “active” sites. But scientists lack basic information about their function because the states thought to be critical to their chemical abilities cannot be experimentally observed.

Now, researchers at Princeton University have reported the first direct observation of the electronic states of iron-sulfur clusters, common to many enzyme active sites. Published on August 31 in the journal Nature Chemistry, the states were revealed by computing the complicated quantum mechanical behavior of the electrons in the clusters.

“These complexes were thought of as impossible to model, due to the complexity of the quantum mechanics,” said Garnet Chan, the A. Barton Hepburn Professor of Chemistry and corresponding author on the paper.

Iron-sulfur clusters

Caption: (a) [2Fe–2S] clusters (b) [4Fe–4S] (c) Area-law entanglement of the physical states can be used to reduce the complexity of quantum calculations (d) Wavefunctions with area-law entanglement can be written compactly as a tensor network where each tensor (represented here by a circle) denotes an active space orbital and the bonds between adjacent orbitals introduce local entanglement between them. (Source: Garnet Chan)

In these systems, the electrons interact strongly with each other, their movements resembling a complicated dance. To reduce the complexity, the researchers drew on a new understanding, gained from fundamental work in quantum information theory, that the motion of the electrons had a special pattern.

“At first glance, the electrons appear to move in a complicated way, but eventually you realize that they only care about what their immediate neighbors are doing, similar to being in a crowded room. This restriction on their behavior leads to important simplifications: the calculations become very difficult rather than impossible — it’s just on the edge of what can be done,” Chan said.

Using their new method, Chan and coworkers found that iron-sulfur clusters possess an order of magnitude more accessible electronic states than previously reported. The researchers suggested that this unusual richness might explain their ubiquity in biological processes.

This finding, that there are many more available electronic states than previously thought, presents many different chemical possibilities. What if these clusters simultaneously used a combination of mechanisms, instead of the accepted chemical idea that there is one distinct electronic pathway, Chan wondered. To test that idea and learn more about the clusters’ behavior, the researchers plan to extend their calculations to observe a chemical transformation in action.

“If you want to understand why iron-sulfur clusters are a ubiquitous biological motif and how we can create even better synthetic analogs, then you need to know what the electrons are doing,” Chan said. “Now we’ve caught a first glimpse as to what they are getting up to.”

Read the abstract.

Sharma, S.; Sivalingam, K.; Neese, F.; Chan, K.-L. G. “Low-energy spectrum of iron sulfur clusters directly from many-particle quantum mechanics.Nat. Chem. 2014, 6, 927.

This work was supported by the US National Science Foundation (CHE-1265277) and used software developed with the support of OCI-1265278. F.N. and K.S acknowledge financial support from the Max Planck Society, the University of Bonn and the SFB 813 “Chemistry at Spin Centers.”

 

 

When scaling the quantum slopes, veer for the straight path (Physical Review A)

Research image

Princeton University researchers found that the “landscape” for quantum control (above) — a representation of quantum mechanics that allows the dynamics of atoms and molecules to be manipulated — can be unexpectedly simple, which could help scientists realize the next generation of technology by harnessing atoms and molecules to create small but incredibly powerful devices. Scientists achieve quantum control by finding the ideal radiation field (top of the graphic) that leads to the desired response from the system. Like a mountain hiker, a scientist can take a difficult, twisting path that requires frequent stops to evaluate the next step (right path). Or, they can opt for a straighter trail that cuts directly to the summit (left path). The researchers provide in their paper an algorithm that scientists can use to identify the starting point of the straight path to their desired quantum field. (Image courtesy of Arun Nanduri)

By Morgan Kelly, Office of Communications

Like any task, there is an easy and a hard way to control atoms and molecules as quantum systems, which are driven by tailored radiation fields. More efficient methods for manipulating quantum systems could help scientists realize the next generation of technology by harnessing atoms and molecules to create small but incredibly powerful devices such as molecular electronics or quantum computers.

Of course, controlling quantum systems is as painstaking as it sounds, and requires scientists to discover the ideal radiation field that leads to the desired response from the system. Scientists know that reaching that state of quantum nirvana can be a long and expensive slog, but Princeton University researchers have found that the process might be more straightforward than previously thought.

The researchers report in the journal Physical Review A that quantum-control “landscapes” — the path of a system’s response from the initial field to the final desired field — appears to be unexpectedly simple. Although still a mountain of a task, finding a good control radiation field turns out to be very much like climbing a mountain, and scientists need only choose the right path. Like a hiker, a scientist can take a difficult, twisting path that requires frequent stops to evaluate which step to take next. Or, as the Princeton researchers show, they can opt for a straighter trail that cuts directly to the summit.

The researchers observe in their paper that these fast tracks toward the desired control field actually exist, and are scattered all over the landscape. They provide an algorithm that scientists can use to identify the starting point of the straight path to their desired quantum field.

The existence of nearly straight paths to reach the best quantum control was surprising because the landscapes were assumed to be serpentine, explained first author Arun Nanduri, who received his bachelor’s degree in physics from Princeton in 2013 and is working in the laboratory of Herschel Rabitz, Princeton’s Charles Phelps Smyth ’16 *17 Professor of Chemistry.

“We found that not only can you always climb to the top, but you can climb along a simple path to the top,” Nanduri said. “If we could consistently identify where these paths are located, a scientist could efficiently climb the landscape. Looking around for the next good step along an unknown path takes great effort. However, starting along a straight path requires you to look around once, and you can keep walking forward with your eyes closed, as it were.”

Following a straighter path could be a far more efficient way of achieving control of atoms and molecules for a host of applications, including manipulating chemical reactions and operating quantum computers, Nanduri said. The source of much scientific excitement, quantum computers would use “qubits” that can be entangled to potentially give them enormous storage and computational capacities far beyond the capabilities of today’s digital computers.

If the Princeton research helps scientists quickly and easily find the control fields they need, it could also allow them to carry out improved measurements of quantum systems and design new ones, Nanduri said.

“We don’t know if our discovery will directly lead to futuristic quantum devices, but this finding should spur renewed research,” Nanduri said. “If straight paths to good quantum control solutions can be routinely found, it would be remarkable.”

Read the abstract.

Nanduri, Arun, Ashley Donovan, Tak-San Ho, Herschel Rabitz. 2013. Exploring quantum control landscape structure. Physical Review A. Article published: Sept. 30, 2013. DOI: 10.1103/PhysRevA.88.033425

The work was funded by the Program in Plasma Science and Technology at Princeton University, the Army Research Office, and the U.S. Department of Energy.