Topological charges of periodically kicked molecules

The peculiar topological properties of certain forms of matter have been investigated for decades. Now, researchers at the Austrian Institute of Science and Technology (ISTA) have discovered topological properties of simple diatomic molecules driven into rotation by laser pulses.

Scientists apply similar mathematics to describe them as for solid matter systems, thus bridging two different fields of physics. Their findings promise potential applications in chemistry.

Sometimes, unexpected connections can arise between different research fields in physics. This applies to the topological properties of quantum states in rotating molecules.

In a new study, Ph.D. student Volker Karle, postdoc Areg Ghazaryan and professor Mikhail Lemeshko from the Austrian Institute of Science and Technology (ISTA), have now revealed that a simple spinning molecule consisting of only two atoms can have quantum states with topological properties, similar to those occurring in graphene and other topological solid-state materials.

“The interesting thing is that these two systems – a rotating molecule and a solid sheet of graphene made up of millions of carbon atoms – are very different and yet some of their properties can be described by similar mathematics,” explains Karle. “We are building a bridge between the fields of physical chemistry and solid state physics.”

The three researchers published their new findings in the journal Physical Review Letters.

A donut stays a donut

“Topology is the study of the geometrical properties of an object that are not affected by the continuous change of its shape and size. The realization that one can classify quantum states not only by their energy and symmetry but also by their topology has led to a real breakthrough in our understanding of solid-state physics in recent decades,” explains Lemeshko.

“A simple example of a topological property would be a donut. Mathematically, a donut is just a ring with one hole,” adds Karle. “No matter how you stretch or squeeze it, it’s still a donut as long as you don’t do anything as drastic as adding or removing a hole. The property of being a donut is therefore topologically protected from ‘small’ perturbations such as changing its shape or size.”

In systems such as topological insulators, these topological phenomena arise from the effects of millions of atoms interacting with each other. However, Karle, Ghazaryan and Lemeshko have shown that this kind of phenomenon can also be found in much simpler systems such as a single molecule.

Pushing a molecule with laser light

“The system we are studying is a single molecule formed by two atoms bonded together,” says Karle. The researchers created a model that describes what happens to such a molecule that is pushed by short laser pulses to make it spin around the midpoint between the two atoms. “At the right wavelength and timing of the laser pulses, we can create topologically non-trivial quantum states in the molecule that behave like those found in solid-state systems.”

For decades now, scientists have studied the topological properties of many different materials and systems—even leading to a Nobel Prize in 2016. However, finding them in a system like a simple molecule enables new kinds of experiments and applications.

“We envision an experiment where a stream of such molecules is fired from a source and then hit with laser pulses,” says Karle. “Then they fly into a detector where we can study their quantum states in much greater detail than is possible with solid-state systems.” The researchers hope to gain many more insights from future experiments that may lay the foundation for new applications in chemistry.

Reactivity control

Non-trivial topological properties, such as those described in this new paper, could lead to topologically protected quantum states. These are particularly interesting for any application that needs to be resistant to external disturbances such as heat, magnetic fields or material impurities. A well-known example that has garnered much research interest in recent years is quantum computers based on topological quantum bits.

However, the molecules Karle and his colleagues are studying would find different applications. “We hope that this research will allow us to better understand many chemical reactions and may one day lead to new ways of controlling them,” says Lemeshko. “We could use lasers to create topologically protected quantum states in molecules that increase or decrease their reactivity with other chemicals just as we need it. Topological protection would stabilize the molecule’s quantum state that would otherwise disappear quickly.”