Buckyballs Play by Quantum Rules

A Full Quantum Measurement of the Buckyball

A water molecule has three atoms—two hydrogens and one oxygen. But stack three water molecules side by side and you’ve got the width of a buckyball, a complex molecule of 60 carbon atoms. Medium in size and large in atom count, the buckyball has long challenged the idea that only small molecules can play by quantum rules.

And last month we learned that the buckyball plays by full quantum rules when the Ye group measured its total quantum state. Specifically, this measurement resolved the rotational states of the buckyball, making it the largest and most complex molecule to be understood at this level.

Big Molecules, Big Results

The structure of the buckyball, or formally buckminsterfullerene, is elegant in its complexity. A round molecule of 60 carbon atoms, it mixes hexagons and pentagons like a soccer ball. According to Dr. Marissa Weichman, a JILA postdoc and coauthor of the recent buckyball publication, this is the most symmetric shape a molecule can take.

Given its 60-atom count, the buckyball is large for the quantum world. But while sometimes difficult, large molecules are worth the effort to study, said Bryan Changala, JILA graduate student and lead author of the recent publication. According to Changala, understanding large molecules could potentially further our understanding of all complex systems.  

“A lot of AMO [atomic, molecular, and optical] experiments are focused on creating, controlling and manipulating quantum many-body systems in complex states,” said Changala. “But a molecule is nature’s own quantum many-body system.”

The Ye group has been pursuing cooling large molecules and performing high resolution spectroscopy for a number of years, starting when Changala was a first-year graduate student.  The first demonstration was achieved in 2016 for molecules such as adamantine (26 atoms).   

While the Ye group are not the first to attempt to study buckyballs with spectroscopy, they are the first to attempt to understand it at such a fine quantum level.  “Previous structural measurements have been done with X-ray diffraction and electron diffraction,” said Changala, “but these are either not done in the gas phase, or they are done warm,” both of which directly limit the resolution.

Cold and Combed

To achieve high-resolution measurements, the Ye group both chilled and combed their buckybulls. The former quieted vibrations, and the latter parsed through fine quantum structure.

“Our frequency comb was the reason we were able to measure this and no one else had before,” said Weichman.

The cavity-enhanced frequency comb, developed by the Ye lab, is a laser that is simultaneously narrow and broad. Like all frequency combs, this laser has a broad spectrum of precise frequency peaks that can quickly comb through molecular transitions. But it is the cavity enhancement of this particular laser that enables the necessary high sensitivity.

But while both of these factors—the cold gas state and the cavity-enhanced frequency comb—are necessary to probe the buckyballs at a high-resolution (rotational-state) level, they alone are not enough to tackle a molecule with so many atoms.

“In a normal molecule, there are can be hundreds to thousands of rotational states,” said Weichman. “But bigger molecules mean denser rotational states.”  For a molecule with as many atoms as the buckyball, Weichman said there can be more than a million rotational states in the ground vibrational state alone.

From Grass to Trees

Even with the cavity-enhanced frequency comb, a million rotational states are too dense to resolve. Weichman likens the signal to an overgrown field of grass, where it is hard to differentiate a single blade from another.

“It’s all moving towards a classical structure,” said Weichman. “where the individual states become so dense that they blur into a continuum.”

But the buckyball is no ordinary large molecule. “It’s perfectly symmetric,” Weichman reminded, “and it is this symmetry of buckyballs that allows us to use small-molecule tools.”

When the research team combed through the buckyball’s spectroscopic signal, they saw not a grass field of fuzzy states, but clear, specific states, “like a forest of trees that were pruned in a very specific way” said Weichman.  

And according to Weichman, this pruning is due to the buckyball having a perfect icosahedral structure. “The atoms are all exactly spaced. It’s not approximate, it’s exact.”

Because of this exact spacing, the atoms are indistinguishable, much like how one hexagon corner on a perfect soccer ball looks just like any other hexagon corner. And when the atoms are indistinguishable, quantum statistics declares many rotation states are forbidden, thereby pruning the forest. In the end, only one for every 60 states remain, said Changala, or a little less than 2%.

In future experiments, the Ye group hopes to observe the spectrum of imperfect buckyballs, in which a single carbon-13 atom replaces a typical carbon-12 atom.

“The indistinguishability would completely disappear, because all of the atoms will now be distinguishable based on their distance and location relative to the impurity. So you would see the spectroscopy signal change from individual trees back to grass,” said Weichman.

This research was published in the January 4th 2019 issue of Science.

The research work was conducted by graduate student Bryan Changala, postdoc Marissa Weichman, and Fellow Dr. Jun Ye. They acknowledge the support of co-authors Kevin Lee and Martin Fermann, of IMRA American Inc., who built the infrared laser necessary for this experiment.

 

Written by Catherine Klauss

Synopsis

JILA researchers have measured for the first time the total quantum (i.e., robovibrational) state of buckminsterfullerene, a carbon molecule of 60 atoms. This benchmark measurement makes an excellent bridge between our macro world and our understanding of quantum mechanics. In particular, our understanding and control of complex many-body quantum systems is furthered by buckminsterfullerene’s many applications. 

Principal Investigators