A tiny defect in a crystal reveals a big quantum surprise

When light strikes a tiny imperfection inside a material such as diamond or silicon carbide, it can transfer energy to electrons and push them into an excited state. These imperfections, known as spin defects, could become valuable building blocks for future quantum technologies, including quantum sensors. Because they can function as stable qubits whose states can be read, scientists are eager to understand exactly how they behave. However, predicting how their energy changes over time has remained a major challenge.

Researchers at the University of Chicago Pritzker School of Molecular Engineering (UChicago PME) have now developed a computational method that provides a more complete picture of what happens when these defects interact with light. Their approach can simulate the entire optical cycle, including a particularly difficult process known as internal conversion.

The findings, published in Physical Review Letters, could help scientists design better materials for quantum technologies. The method may also prove useful for studying materials involved in renewable energy conversion and storage.

"This internal conversion process is not only relevant to spin defects -- it's also related to processes of interest to energy technologies," said Giulia Galli, the Liew Family Professor of Electronic Structure and Simulations in UChicago PME and the Department of Chemistry and the senior author of the study. "That's one of the reasons this work is so exciting."

How Quantum Defects Lose Energy

When a laser excites a spin defect, the defect can return to its original, lower-energy state through several different processes. It might release a photon of light, transition between states with different spins, or transfer its energy into vibrations of the surrounding atoms.

That final pathway, called internal conversion, has been especially difficult for scientists to model accurately. Although the fundamental equations of quantum mechanics can describe the other two processes, calculating how energy is lost through atomic vibrations presents substantial computational obstacles.

"Although the equations are known, it's hard to describe the process accurately because of computational difficulties," said Stefano Villani, a UChicago PME postdoctoral researcher and the study's first author. "You need to account for complex interactions between the electrons and surrounding atoms, and that's challenging in realistic solids represented by models with hundreds or thousands of atoms"

To overcome this problem, Galli, Villani, and Yu Jin combined several computational techniques that their research group had developed over many years. Jin, a former graduate student in Galli's group, is now a postdoctoral scholar at the Flatiron Institute in New York.

The researchers used mathematical descriptions known as many-body wavefunctions to represent the excited states of spin defects. Through exact mathematical derivations, they determined how strongly each excited state interacts with the movements of nearby atoms.

This allowed them to calculate how individual electronic states connect with all the possible vibrational configurations of hundreds of surrounding atoms, rather than having to analyze those configurations individually.

"In the past, a clear mathematical derivation and efficient algorithms were not available," explained Yu Jin. "The new derivation came together after years of work on the optical cycle of spin defects."

The researchers incorporated their new framework into WEST, an open-source simulation program optimized for graphics processing units (GPUs). Galli's group has spent the past decade developing WEST through the Midwest Integrated Center for Computational Materials (MICCoM), which has received funding from the U.S. Department of Energy's Office of Basic Energy Sciences since 2015.

A Surprising Discovery Inside Silicon Carbide

To test their approach, the researchers first examined a nitrogen-vacancy center in diamond, a type of crystal defect widely studied for quantum applications.

Their calculations closely matched recent spectroscopy measurements. For triplet states, internal conversion contributed relatively little to energy loss. In singlet states, however, it was the primary mechanism responsible for releasing energy. Both findings agreed with what scientists had previously expected.

The results changed when the team investigated a divacancy defect in silicon carbide.

Their calculations revealed that internal conversion has a much greater influence on the lifetime of the defect's excited triplet state than earlier models had accounted for. This previously underestimated contribution helped explain a long-standing disagreement between theoretical predictions and experimental observations.

"We were expecting to see an effect, but of a smaller magnitude," Galli said. "What we found is that this internal conversion process turns out to be more important than we thought."

Understanding this unexpected energy-loss pathway could help scientists more accurately predict the behavior of silicon carbide defects and improve their potential use as qubits in future quantum devices.

A New Tool for Quantum Computing and Energy Research

With the framework now available through WEST, researchers at other institutions can begin applying it to their own studies. However, Galli noted that the simulations still demand considerable computing power.

The team is exploring ways to reduce those requirements, including the use of artificial intelligence.

"We are working on ways to integrate machine learning into excited states calculations to further improve the efficiency of our method," Villani said.

Meanwhile, the scientists are expanding their approach to investigate spin defects in silicon, as well as materials used in energy technologies where internal conversion influences how energy is transferred or lost.

By addressing one of the most difficult parts of modeling how spin defects respond to light, the researchers have made it possible to predict their behavior more completely and accurately.

"We provided the missing piece of the puzzle needed to completely describe the optical cycle of spin defects," Galli said. "Our work can now be used to make more accurate predictions about many materials of interest for quantum technologies," added Yu Jin.