Quantum calculations reveal how quantum defects lose energy
When light hits a tiny defect embedded in a solid material like diamond or silicon carbide, it can kick the defect’s electrons into an excited state. These spin defects have the potential to be used as stable, readable qubits for quantum technologies, for example quantum sensing. But modeling the full physics of their energetics over time—a key step in developing spin defects into new technologies—is a challenging task.
Now, researchers at the University of Chicago Pritzker School of Molecular Engineering (UChicago PME) have built a computational framework that captures the full optical cycle of such spin defects, including the prediction of internal conversion, a process particularly hard to model. Their results, published in Physical Review Letters, shed light on how to use the defects in the design of quantum materials and could also be applied to a different class of systems used 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 and the senior author of the study. “That’s one of the reasons this work is so exciting.”
How a defect relaxes
When a spin defect is excited with a laser, it can relax back to the ground state along several pathways: by emitting a photon of light, by jumping between states with different spins, or through a process called internal conversion in which energy dissipates as atomic vibrations rather than light. Physicists have used the fundamental equations of quantum mechanics to describe the first two processes, but up to now internal conversion has been harder to predict.
“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 study’s first author. “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”.”
Galli, Villani, and Yu Jin, a former graduate student in the Galli group and now postdoctoral scholar at the Flatiron Institute in New York, coupled several methods developed in the group over the years and arrived at a new formulation to describe internal conversion processes. They described a defect’s excited state with many-body wavefunctions, and found a way to calculate how strongly each excited state is coupled to atomic motion, through exact mathematical derivations. By doing so, they could calculate how each of a defect’s states is coupled to all the vibrational configurations of hundreds of nearby atoms, rather than just computing one at a time.
“In the past, a clear mathematical derivation and efficient algorithms were not available”, explained Yu Jin. “The new derivation came together after years of work on the optical cycle of spin defects”.
The team implemented the framework in the WEST code, an open-source, GPU-optimized simulation code that Galli’s group has developed over the past decade within the Midwest Integrated Center for Computational Materials (MICCoM), funded by the U.S. Department of Energy’s Office of Basic Energy Sciences, since 2015.
A surprise in silicon carbide
When the team applied the new framework to a nitrogen-vacancy center in diamond, the predictions matched up with recent spectroscopy measurements. When triplet states are involved, internal conversion plays little role in the defect’s energy loss, while for singlet states, it is the dominant pathway by which the state loses energy—both observations consistent with previous assumptions.
When they carried out the same calculations on a divacancy in silicon carbide, the results were more surprising. They showed that internal conversion makes a substantial, previously overlooked contribution to the defect’s triplet excited-state lifetime, resolving a long-standing discrepancy between predictions and experiments.
“We were expecting to see an effect, but of a smaller magnitude,” Galli said. “What we found is that this internal conversion process turns out to be more important than we thought.”
Those results could inform the development of this type of defect as qubits, the researchers said.
Extending the framework
Because the new framework is already built into the WEST code, other labs can now begin using it. However, Galli cautioned that it requires substantial computational resources.
“We are working on ways to integrate machine learning into excited states calculations to further improve the efficiency of our method,” Villani said.
As they work to lower its computational costs, the team is also extending the framework to spin defects in silicon and to energy materials where internal conversion plays an important role.
“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.
Reference First-principles calculations of internal conversion processes in spin defects
Stefano Paolo Villani, Yu Jin, and Giulia Galli