When light strikes a tiny imperfection buried deep inside a crystal material such as diamond or silicon carbide, it transfers energy to electrons, pushing them into an excited state. These atomic-scale imperfections, known as spin defects, have emerged as some of the most promising building blocks for the next generation of quantum technologies, including ultra-sensitive quantum sensors and secure communication networks. Because these defects can function as stable qubits whose quantum states can be precisely initialized, manipulated, and read, scientists around the world are intensely eager to understand exactly how they behave under various physical conditions. Yet, despite decades of rapid advancement in quantum mechanics and materials science, predicting precisely how their energy changes and dissipates over time has remained a formidable and major challenge for researchers.
Now, a team of researchers at the University of Chicago Pritzker School of Molecular Engineering (UChicago PME) has developed a groundbreaking computational method that provides a significantly more complete picture of what happens when these quantum defects interact with light. Their innovative approach successfully simulates the entire optical cycle of these materials, capturing complex pathways including a notoriously difficult process known in physics as internal conversion. The findings, which have been published in the prestigious journal Physical Review Letters, could profoundly help scientists design better, more reliable materials for upcoming quantum technologies. Furthermore, the newly developed computational method may also prove exceptionally useful for studying complex materials involved in renewable energy conversion and storage, broadening its scientific impact.
"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 laser or another light source 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 ground state through several distinct physical processes. Depending on the material and its surrounding atomic environment, the defect might release a photon of light in a process known as luminescence, transition between electronic states with different spin configurations, or transfer its energy directly into the mechanical vibrations of the surrounding crystal lattice atoms.
That final pathway, called internal conversion, has historically been especially difficult for theoretical scientists to model accurately. Although the fundamental equations of quantum mechanics can effectively describe the other two dissipation pathways, calculating precisely how energy is lost through atomic vibrations presents substantial and severe 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 new 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 long-standing computational bottleneck, Galli, Villani, and their colleague Yu Jin combined several advanced computational techniques that their research group had meticulously developed over many years of concerted scientific effort. Jin, a former graduate student in Galli’s research group, is now a postdoctoral scholar at the Flatiron Institute in New York, bringing his expertise to the broader scientific community.
To tackle the problem, the researchers utilized sophisticated mathematical descriptions known as many-body wavefunctions to accurately represent the excited states of the spin defects. Through rigorous and exact mathematical derivations, they determined how strongly each individual excited state interacts with the minute movements of nearby atoms within the crystal structure. This breakthrough allowed them to calculate how individual electronic states connect with all the possible vibrational configurations of hundreds of surrounding atoms simultaneously, eliminating the cumbersome need to analyze those countless configurations individually.
"In the past, a clear mathematical derivation and efficient algorithms were not available," explained Yu Jin, reflecting on the complexity of the theoretical undertaking. "The new derivation came together after years of work on the optical cycle of spin defects."
To make these intensive calculations feasible, the researchers incorporated their new theoretical framework directly into WEST, a powerful, open-source simulation program specifically optimized to run on graphics processing units (GPUs). Galli’s research group has spent the past decade 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 test the validity and robustness of their newly developed approach, the researchers first examined a well-known nitrogen-vacancy center in diamond, a type of crystal defect that has been widely studied for years in quantum applications and sensing. The team’s theoretical calculations closely matched recent, high-precision spectroscopy measurements obtained in laboratories. For the diamond’s triplet states, internal conversion contributed relatively little to overall energy loss. However, in its singlet states, internal conversion acted as the primary mechanism responsible for releasing energy. Both of these findings aligned perfectly with what scientists had previously expected based on empirical observations.
However, the results shifted dramatically when the research team turned their attention to a divacancy defect embedded within silicon carbide, another material of immense interest for semiconductor and quantum industries. Their advanced calculations revealed that internal conversion has a much greater and more decisive influence on the lifetime of the defect’s excited triplet state than earlier, simpler models had ever accounted for. This previously underestimated contribution helped solve and explain a long-standing, frustrating disagreement between theoretical predictions and experimental observations that had puzzled researchers for years.
"We were expecting to see an effect, but of a smaller magnitude," Galli noted regarding the unexpected findings. "What we found is that this internal conversion process turns out to be more important than we thought."
Gaining a precise understanding of this unexpected energy-loss pathway could ultimately help scientists more accurately predict the real-world behavior of silicon carbide defects and substantially improve their potential use as reliable qubits in future quantum computing devices.
A New Tool for Quantum Computing and Energy Research
With the new computational framework now fully available to the scientific community through the WEST software package, researchers at other institutions and laboratories can begin applying it directly to their own materials studies. Nevertheless, Galli pointed out that these advanced simulations still demand considerable computing power due to the sheer scale of the quantum interactions being modeled.
To address this limitation, the research team is already actively exploring various ways to reduce those heavy computational requirements, including the incorporation of cutting-edge artificial intelligence techniques.
"We are working on ways to integrate machine learning into excited states calculations to further improve the efficiency of our method," Villani said.
In the meantime, the scientists are actively expanding their computational approach to investigate spin defects in pure silicon, as well as complex materials utilized in renewable energy technologies where internal conversion plays a critical role in determining how energy is transferred, transformed, or lost.
By successfully addressing one of the most notoriously difficult parts of modeling how spin defects respond to light, the researchers have cleared a major path, making it possible to predict the behavior of quantum materials 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 said. "Our work can now be used to make more accurate predictions about many materials of interest for quantum technologies," added Yu Jin.
