Because spin defects can function as stable qubits whose fundamental states can be reliably read, scientists around the world are deeply eager to understand their precise behavioral patterns. However, accurately predicting how their energy levels shift and change over time has remained a formidable hurdle in the field of materials science. The new computational approach developed by the UChicago PME team successfully simulates the entire optical cycle of these defects, closing a long-standing knowledge gap by illuminating a notoriously difficult process called internal conversion.
The findings, which have been published in the journal Physical Review Letters, could significantly aid scientists in designing superior materials tailored for quantum applications. Furthermore, the newly formulated computational method holds profound promise beyond quantum computing, potentially proving useful for the study of complex 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, 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 external light source excites a spin defect, the defect does not remain in that high-energy state indefinitely. Instead, it eventually returns to its original, lower-energy state through several distinct pathways. Depending on the material and the specific configuration of the defect, it might release a photon of light in a process akin to fluorescence, transition between electronic states with different spin characteristics, or transfer its energy directly into the mechanical vibrations of the surrounding crystal lattice of atoms.
That final pathway—internal conversion, where electronic energy is transformed into atomic vibrations—has historically proven exceptionally difficult for computational scientists to model with high accuracy. Although the fundamental equations of quantum mechanics are well-established and capable of describing the radiative release of photons and spin transitions, calculating how energy is dissipated through atomic vibrations presents immense computational obstacles.
"Although the equations are known, it’s hard to describe the process accurately because of computational difficulties," explained 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 tackle this complex problem, Galli, Villani, and former UChicago graduate student Yu Jin combined several sophisticated computational techniques that Galli’s research group had spent many years developing and refining. Jin, who is now a postdoctoral scholar at the Flatiron Institute in New York, worked closely with the team to bridge the gap between theoretical physics and practical simulation.
The research team utilized advanced mathematical descriptions known as many-body wavefunctions to accurately represent the excited states of the spin defects. Through exact and rigorous mathematical derivations, they were able to determine the precise strength of the interaction between each excited electronic state and the dynamic movements of nearby atoms. This analytical breakthrough allowed them to calculate how individual electronic states connect with all the possible vibrational configurations of hundreds of surrounding atoms simultaneously, circumventing the need to analyze those countless configurations individually.
"In the past, a clear mathematical derivation and efficient algorithms were not available," Yu Jin explained, reflecting on the complexity of the project. "The new derivation came together after years of work on the optical cycle of spin defects."
To make these resource-intensive calculations feasible, the researchers integrated their newly established theoretical framework directly into WEST, an open-source simulation program specifically optimized to run on high-performance graphics processing units (GPUs). Galli’s research group has dedicated the past decade to developing and optimizing the WEST software 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 and validate their novel computational approach, the research team first applied the method to a well-known system: a nitrogen-vacancy center embedded inside a diamond crystal. Nitrogen-vacancy centers in diamond are among the most thoroughly studied crystal defects in the entire field of quantum information science.
The team’s calculations yielded results that matched recent, high-precision spectroscopy measurements with remarkable accuracy. For triplet states within the diamond defect, internal conversion contributed relatively little to overall energy loss. Conversely, for singlet states, internal conversion emerged as the primary mechanism responsible for releasing energy. Both of these specific findings aligned closely with what scientists had previously hypothesized and expected based on empirical observations.
However, the predictive power of the new framework truly revealed its worth when the team shifted their focus from diamond to investigate a divacancy defect inside silicon carbide, a wide-bandgap semiconductor material that has recently gained immense traction in the quantum technology sector.
To the researchers’ surprise, their calculations demonstrated that internal conversion exerts a much greater influence on the lifetime of the defect’s excited triplet state than any previous models had ever accounted for. This previously underestimated energy-loss contribution successfully resolved a long-standing disagreement that had puzzled researchers for years, bridging the gap between theoretical predictions and experimental observations that had stubbornly refused to align.
"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 precise understanding of this unexpected energy-loss pathway is expected to help scientists more accurately model and predict the behavior of silicon carbide defects, ultimately paving the way for improved performance when these materials are deployed as qubits in future quantum hardware and sensing devices.
A New Tool for Quantum Computing and Energy Research
With the new computational framework now publicly available through the WEST software package, researchers at other academic institutions and industrial laboratories can begin applying these advanced tools to their own materials science studies. Nevertheless, Galli pointed out that these sophisticated simulations still demand a substantial amount of computational power, reflecting the inherent complexity of quantum-scale interactions in condensed matter.
To address this ongoing challenge, the research team is actively exploring ways to lower these computational demands, including the implementation of artificial intelligence and machine learning techniques.
"Estamos working on ways to integrate machine learning into excited states calculations to further improve the efficiency of our method," Villani said, highlighting the future trajectory of the project.
At the same time, the scientists are broadening the scope of their research to investigate spin defects in pure silicon—a cornerstone material of the modern semiconductor industry—as well as other specialized materials utilized in advanced energy technologies, where internal conversion heavily influences how energy is captured, transferred, or lost.
By successfully addressing one of the most stubborn and difficult bottlenecks in modeling how spin defects respond to light, the UChicago PME researchers have unlocked a more complete and accurate way to forecast the behavior of these quantum-ready materials.
"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.
