When light strikes a tiny imperfection tucked deep inside a material like diamond or silicon carbide, it triggers a remarkable chain of events. Photons transfer their energy directly to electrons, pushing them from their resting state into an excited, energetic condition. These microscopic imperfections, known scientifically as spin defects, have emerged as some of the most valuable building blocks for the future of quantum technologies. Because they can function as stable qubits—the fundamental units of quantum information—whose quantum states can be precisely read and manipulated, scientists around the world are intensely eager to understand exactly how they behave under real-world conditions.
Yet, for all their promise, predicting how the energy of these spin defects changes over time has remained a formidable hurdle. Accurately modeling their dynamic behavior has long challenged researchers striving to harness them for advanced quantum sensors and communication devices.
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 far more complete picture of what happens when these critical defects interact with light. Their innovative approach successfully simulates the entire optical cycle of a spin defect, a feat that includes modeling a notoriously difficult and complex physical process known as internal conversion.
The findings, recently published in the prestigious journal Physical Review Letters, could significantly help scientists design and engineer superior materials for the next generation of quantum technologies. Furthermore, because internal conversion is a fundamental physical mechanism, this newly developed computational method may also prove broadly useful for studying materials involved in renewable energy conversion and storage, opening doors to advances across multiple high-tech industries.
"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 served as the senior author of the study. "That’s one of the reasons this work is so exciting."
How Quantum Defects Lose Energy
To fully grasp the magnitude of the researchers’ accomplishment, one must understand the complex lifecycle of a spin defect when it is stimulated. 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 ground state. It accomplishes this return journey through several distinct pathways. It might release a photon of light through luminescence, transition rapidly between states possessing different spin configurations, or transfer its energy directly into the mechanical vibrations of the surrounding atomic lattice.
It is that final pathway—known formally as internal conversion—that has historically presented the steepest barrier to scientists attempting to build accurate theoretical models. Although the fundamental equations of quantum mechanics have long been established to describe radiative emission and spin transitions, calculating how energy is lost through atomic vibrations presents staggering 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 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 bypass this computational bottleneck, Galli, Villani, and their colleague Yu Jin chose to combine several advanced computational techniques that their research group had meticulously developed over many years of concerted study. Jin, a former graduate student working within Galli’s laboratory, is now a postdoctoral scholar at the Flatiron Institute in New York, bringing the methods he helped forge to a broader scientific audience.
Instead of tackling the problem using brute-force calculations that quickly overwhelm even the most powerful supercomputers, the researchers employed sophisticated 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 precisely how strongly each individual excited state interacts with the minute movements of nearby atoms in the crystal lattice.
This strategic breakthrough allowed them to calculate how individual electronic states connect smoothly with all the possible vibrational configurations of hundreds of surrounding atoms simultaneously, eliminating the tedious and inefficient necessity of analyzing those complex configurations individually.
"In the past, a clear mathematical derivation and efficient algorithms were not available," explained Yu Jin, reflecting on the arduous path required to reach this milestone. "The new derivation came together after years of work on the optical cycle of spin defects."
To make these intensive calculations practical, the researchers incorporated their brand-new theoretical framework directly into WEST, an advanced, open-source simulation program specifically optimized to run on high-performance 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), a collaborative hub that has received steady 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 minted computational approach, the research team first examined a nitrogen-vacancy center embedded inside diamond, a crystal defect that has been widely studied and characterized for a variety of emerging quantum applications.
When they ran the simulations, the resulting calculations closely matched recent, highly accurate spectroscopy measurements performed in laboratories. For triplet states in the diamond defect, internal conversion contributed relatively little to overall energy loss. However, for singlet states, internal conversion emerged as the primary mechanism responsible for releasing energy. Both of these key findings aligned neatly with what scientists had previously hypothesized and expected to see.
However, the scientific narrative took a dramatic and unexpected turn when the team shifted their analytical focus to a divacancy defect located within silicon carbide, another semiconductor material heavily favored for robust electronics and quantum research.
To their initial surprise, the team’s meticulous calculations revealed that internal conversion exerts a vastly greater influence on the lifetime of the defect’s excited triplet state than any earlier, simplified models had ever accounted for. This previously underestimated contribution from atomic vibrations ultimately helped explain and resolve a long-standing 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. "What we found is that this internal conversion process turns out to be more important than we thought."
Gaining a precise understanding of this unexpectedly potent energy-loss pathway could allow scientists to much more accurately predict the real-world behavior of silicon carbide defects, thereby improving their viability and performance as reliable qubits in future quantum computing devices.
A New Tool for Quantum Computing and Energy Research
With the new computational framework now officially made available to the scientific community through the open-source WEST platform, researchers at other institutions and laboratories can begin applying it directly to their own specialized studies. Nevertheless, Galli pointed out that these sophisticated simulations still demand a considerable amount of raw computing power due to the sheer complexity of the underlying quantum mechanical interactions.
To address this ongoing challenge, the team is already actively exploring innovative ways to reduce those computational requirements, including the integration of modern artificial intelligence techniques into their software pipeline.
"Estamos trabajando en formas de integrar el aprendizaje automático en los cálculos de estados excitados para mejorar aún más la eficiencia de nuestro método," said Villani, noting the international and collaborative nature of the effort. Translated to their ongoing research priorities, the group is aggressively working on ways to weave machine learning into excited-state calculations to streamline workflows.
Meanwhile, the scientists are already expanding their methodological approach to investigate spin defects in pure silicon, as well as examining a broader range of complex materials utilized in energy technologies where internal conversion plays a critical role in dictating how energy is transferred or lost.
By successfully tackling and solving one of the most notoriously difficult aspects of modeling how spin defects respond to light, the researchers have cleared a major roadblock, making it possible to predict the behavior of advanced 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 concluded, summarizing the significance of the achievement. "Our work can now be used to make more accurate predictions about many materials of interest for quantum technologies," added Yu Jin.
