Bo Zhen, an assistant professor of physics in the School of Arts and Sciences at the University of Pennsylvania, has been awarded a Young Investigator Grant from the Air Force Office of Scientific Research. Zhen will receive $450,000 for a three-year period to investigate non-Hermitian topological photonics.

​​​​​​​In the past decade, topology, a branch of the mathematics studying the preserved properties of objects under continuous deformations, has received an increasing amount of attention in physics. From a topological point of view, a coffee mug and a donut are the same. Since each object has one hole, it is possible for the donut to morph into a mug through continuous deformations:  one would simply make a depression into one side of the donut to make the mug and shrink the donut's hole to make the mug's handle. This sort of abstraction, Zhen said, gives way to new properties in physics and interesting applications in practice.

“When you design something, you usually think about the geometric aspect of it,” Zhen said. “If we were designing a pipeline to talk to each other, what we would care about is the geometry of the pipe. Along the pipe, we would try to make sure the shape never changes because if you change it somehow, say if you block it by half, there will be back reflection and the transmission will not be perfect. Any imperfection degrades your performance. But it's very hard to keep the geometric aspect to be exactly the same across the whole pipe. So we start to think about whether it is possible to rely on some other property that is much easier to maintain and still protect us from this kind of degradation. One solution is to use the concept of topology and build a new type of transmission line where the exact geometry doesn't matter: we can put as much disorder along the path as we want but the transmission will always be perfect.”

According to Zhen, there are many real-life examples of the topology of a system, rather than its geometric aspects, dominating the performance.

“When we tie our shoelaces in the morning, it's never perfect,” he said. “It's not one particular shape and we don't need to measure the exact dimensions. It’s the topology of the knot that really matters.”

The understanding of this new concept first started in electronic systems through the study of the topological phases of electrons, negatively charged subatomic particles. Zhen, however, is interested in studying photons, particles of light. Because of the fundamental differences between these two particles, there will be very profound differences between the research in these two fields.

One difference is that unlike with electrons, whose quantity is typically believed to remain the same in a system, it’s natural for the researchers to gain or lose light, or photons, in their systems. With photons, one can be constantly in a non-equilibrium state where one gains photons from one part of the system and lose them at another part – one such example is the laser pointer.

“There are two kinds of physics,” Zhen said. “One is where I have a closed box with a fixed number of particles, also called a Hermitian system, and the other is an open system with changing particle numbers, called a non-Hermitian system. In electronics, there’s been a lot of success in the Hermitian setting of topological physics with very interesting results. When you go to the non-Hermitian side, you find completely new states that don't exist in the previous framework. There are exciting opportunities that are unique to this new setting. I'm trying to use real material properties and practical numbers to simulate and design devices that can be implemented in real life.”

One application for this research, Zhen said, is improving chemical or biological sensors to allow them to reach much higher sensitivities so they can detect tiny changes, sometime even down to a single particle, in the environment. These sensors can be used to monitor the level of glucose in blood, determine the drug residue in blood or detect the level of poisonous elements in water. 

“Usually this response to the environment change is linear,” he said. “If the environment changes one part in a million, the resonance will also shift one part in a million. But it turns out that in topological non-Hermitian systems, there’s a particular type of topological state where if the environment changes one part in a million, the state will actually shift by one part in a thousand. That’s a huge improvement compared to before and can give you much better sensitivity.”

Zhen is working to translate the concepts of non-Hermitian topology into a nonlinear setting to make an all-optical switch or logic gate than can be used in optical neural networks for computing and artificial intelligence.

“Using optics to artificial neuron networks is a great substitute to the conventional electronic computation scheme for higher speed and lower energy cost,” Zhen said, “but for this kind of application there has to be one step which is a nonlinear operation. This novel type of all-optical switch will further reduce the energy cost in these kinds of networks.”

Zhen said that he considers Penn to be a great place for this type of research because of its history in the field of topology.

“Penn has a tradition of studying topological aspects of materials,” Zhen said. “It’s home to Charles Kane and Eugene Mele, pioneers in the field of electronic topological insulators. Having them around to discuss a different kind of particle in a different kind of setting is very exciting.”