The newly devised computational approach successfully simulates the entire optical cycle of these defects, including a notoriously difficult mechanism known as internal conversion. The study’s findings, which have been officially published in the academic journal Physical Review Letters, could profoundly help scientists design vastly superior materials tailored for advanced quantum applications. Beyond the realm of quantum computing and sensing, this innovative method may also prove exceptionally useful for studying complex materials heavily involved in renewable energy conversion and storage technologies.
"This internal conversion process is not only relevant to spin defects — it’s also related to processes of interest to energy technologies," explained 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 research study. "That’s one of the reasons this work is so exciting."
How Quantum Defects Lose Energy
When a high-powered laser or another light source excites a spin defect, the defect does not remain in that high-energy configuration indefinitely. Instead, it eventually returns to its original, lower-energy ground state through several distinct physical pathways. It might directly release a photon of light, transition seamlessly between electronic states with different spin characteristics, or transfer its energy directly into the rapid mechanical vibrations of the surrounding atomic lattice.
That final pathway, formally called internal conversion, has historically been exceptionally difficult for theoretical physicists and chemists to model with high accuracy. Although the fundamental mathematical equations of quantum mechanics are well understood and can adequately describe the other two relaxation processes, calculating precisely how energy is lost through microscopic atomic vibrations presents massive computational obstacles.
"Although the equations are known, it’s hard to describe the process accurately because of computational difficulties," noted Stefano Villani, a UChicago PME postdoctoral researcher and the primary 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 finally overcome this long-standing bottleneck, Galli, Villani, and their colleague Yu Jin strategically combined several powerful computational techniques that their specialized research group had meticulously developed over many years. Jin, who previously worked as a graduate student within Galli’s laboratory group, is currently employed as a postdoctoral scholar at the Flatiron Institute located in New York City.
To tackle the problem, the research team utilized sophisticated mathematical descriptions known as many-body wavefunctions to accurately represent the complex excited states of the spin defects. Through exact and rigorous mathematical derivations, they determined with high fidelity how strongly each distinct excited state interacts with the thermal movements and oscillations of nearby atoms.
This analytical breakthrough allowed them to calculate seamlessly how individual electronic states connect directly with all the possible vibrational configurations of hundreds of surrounding atoms, entirely bypassing the need to analyze those countless configurations individually in a piecemeal fashion.
"In the past, a clear mathematical derivation and efficient algorithms were not available," explained Yu Jin, describing the technical hurdle the team faced. "The new derivation came together after years of work on the optical cycle of spin defects."
The researchers then incorporated their newly formulated theoretical framework directly into WEST, an advanced, open-source simulation program specifically optimized to run on high-performance graphics processing units (GPUs). Members of Galli’s research group have spent the past decade developing and refining the WEST software package through the Midwest Integrated Center for Computational Materials (MICCoM), an initiative that has received continuous financial support 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 established approach in a practical scenario, the researchers first examined a well-known nitrogen-vacancy center embedded within a diamond crystal, which represents a type of crystal defect that has been extensively studied for various quantum technology applications.
When they ran their models, their theoretical calculations closely matched recent, highly precise spectroscopy measurements. For the material’s triplet states, internal conversion contributed relatively little to the overall energy loss experienced by the system. However, in the case of singlet states, internal conversion acted as the primary physical mechanism responsible for releasing energy. Both of these specific findings aligned neatly with what physicists had previously expected to see.
However, the results shifted dramatically when the research team turned their attention to investigating a divacancy defect located inside a crystal of silicon carbide.
Their intricate calculations unexpectedly revealed that internal conversion exerts a much greater influence on the lifetime of the defect’s excited triplet state than any earlier theoretical models had ever accounted for. This previously underestimated contribution successfully helped explain a long-standing, frustrating disagreement that had persisted for years between theoretical predictions and actual experimental observations in the laboratory.
"We were expecting to see an effect, but of a smaller magnitude," Professor Galli remarked. "What we found is that this internal conversion process turns out to be more important than we thought."
Gaining a clear understanding of this previously underappreciated energy-loss pathway could significantly help scientists more accurately predict the complex behavior of silicon carbide defects and substantially improve their potential utility to act as stable, reliable qubits in future quantum computing devices.
A New Tool for Quantum Computing and Energy Research
With the comprehensive framework now publicly available through the WEST simulation software, researchers working at other academic institutions and laboratories can begin applying the tool to their own independent studies. Nevertheless, Professor Galli noted that running these advanced simulations still demands a considerable amount of high-end computing power.
To make the technology even more accessible and efficient, the team is actively exploring various ways to reduce those heavy computational requirements, including the integration of artificial intelligence and advanced data analytics.
"Estamos working on ways to integrate machine learning into excited states calculations to further improve the efficiency of our method," Villani said, outlining the future trajectory of the project.
Meanwhile, the scientists are steadily expanding their computational approach to investigate spin defects located in bulk silicon, as well as examining other specialized materials heavily utilized in clean energy technologies where internal conversion critically influences how energy is successfully transferred or inadvertently lost.
By successfully addressing one of the most notoriously difficult aspects of modeling how spin defects respond dynamically to light, the research team has made it fundamentally possible to predict their overall behavior with a much higher degree of completeness and precision.
"We provided the missing piece of the puzzle needed to completely describe the optical cycle of spin defects," Professor Galli concluded. "Our work can now be used to make more accurate predictions about many materials of interest for quantum technologies," added Yu Jin.
