The new computational approach developed by the UChicago PME team successfully simulates the entire optical cycle of these defects, including a notoriously difficult process known as internal conversion. The findings, recently published in the scientific journal Physical Review Letters, could significantly aid scientists in designing better materials for upcoming quantum technologies. Furthermore, the methodology may prove exceptionally useful for studying materials involved in renewable energy conversion and storage.
The implications of the research extend far beyond quantum computing alone. "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, who also serves as the senior author of the study. "That’s one of the reasons this work is so exciting."
How Quantum Defects Lose Energy
When a specialized laser excites a spin defect, the defect does not remain in that high-energy state indefinitely. Instead, it must eventually return to its original, lower-energy state through one of several different pathways. It might release a photon of light, transition smoothly between states with different spins, or transfer its internal energy directly into the vibrations of the surrounding atoms.
That final pathway, scientifically referred to as internal conversion, has presented an extraordinary challenge for scientists attempting to model it accurately. Although the fundamental equations of quantum mechanics can adequately describe the other two processes, calculating precisely 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 first author of the study. "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 persistent hurdle, Galli, Villani, and researcher Yu Jin combined several advanced computational techniques that their research group had spent many years developing. Jin, who completed their work as a graduate student in Galli’s group, is now a postdoctoral scholar at the Flatiron Institute in New York City.
Rather than tackling the problem through traditional, inefficient approximations, the researchers utilized sophisticated mathematical descriptions known as many-body wavefunctions to represent the excited states of the spin defects. Through exact mathematical derivations, they determined precisely how strongly each excited state interacts with the ongoing movements of nearby atoms. This clever approach allowed them to calculate how individual electronic states connect with all the possible vibrational configurations of hundreds of surrounding atoms simultaneously, eliminating the need to analyze those complex configurations one by one.
"In the past, a clear mathematical derivation and efficient algorithms were not available," explained Yu Jin, reflecting on the complexity of the project. "The new derivation came together after years of work on the optical cycle of spin defects."
The research team successfully incorporated their novel framework into WEST, an open-source simulation program heavily optimized for graphics processing units, commonly known as GPUs. Galli’s research group has dedicated the past decade to developing and refining WEST through the Midwest Integrated Center for Computational Materials (MICCoM), an initiative that has received continuous funding from the U.S. Department of Energy’s Office of Basic Energy Sciences since 2015.
A Surprising Discovery Inside Silicon Carbide
To rigorously test their newly developed approach, the researchers first examined a nitrogen-vacancy center located inside a diamond, a specific type of crystal defect that has been widely and intensively studied for various quantum applications.
Their complex calculations aligned closely with recent spectroscopy measurements performed by experimentalists. For triplet states, internal conversion contributed relatively little to overall energy loss. In singlet states, however, it emerged as the primary mechanism responsible for releasing energy. Both of these findings matched what scientists had previously expected to see based on theoretical assumptions.
However, the results shifted dramatically when the research team turned their attention to a divacancy defect embedded within silicon carbide.
Their advanced calculations revealed that internal conversion exerts a much greater influence on the lifetime of the defect’s excited triplet state than earlier, more basic models had accounted for. This previously underestimated contribution successfully helped explain a long-standing disagreement that had puzzled researchers for years between theoretical predictions and actual experimental observations.
"We were expecting to see an effect, but of a smaller magnitude," Galli noted. "What we found is that this internal conversion process turns out to be more important than we thought."
Gaining a clear understanding of this unexpected energy-loss pathway could help scientists more accurately predict the real-world behavior of silicon carbide defects and substantially improve their potential use as stable qubits in future quantum computing devices.
A New Tool for Quantum Computing and Energy Research
With the new computational framework now publicly available through the WEST program, researchers at other academic and industrial institutions can begin applying it directly to their own independent studies. However, Galli noted that these intensive simulations still demand considerable computing power to run effectively.
To address this limitation, the research team is already actively exploring various ways to reduce those heavy computational requirements, including the integration of artificial intelligence technologies.
"Estamos working on ways to integrate machine learning into excited states calculations to further improve the efficiency of our method," Villani said.
At the same time, the scientists are steadily expanding their approach to investigate spin defects in pure silicon, as well as examining other materials used in advanced energy technologies where internal conversion heavily influences how energy is transferred or lost.
By successfully addressing one of the most difficult and elusive parts of modeling how spin defects respond to light, the researchers have made it entirely possible to predict their complex behavior much more completely and accurately than ever before.
"We provided the missing piece of the puzzle needed to completely describe the optical cycle of spin defects," Galli concluded. "Our work can now be used to make more accurate predictions about many materials of interest for quantum technologies," added Yu Jin.
