Quantum framework resolves energy loss mystery in crystal defects

A long-standing discrepancy between theoretical predictions and experimental observations regarding energy loss in crystal defects has been resolved by a new computational framework. Researchers at the University of Chicago Pritzker School of Molecular Engineering (UChicago PME) developed a method that captures the full optical cycle of these imperfections, including the previously difficult-to-predict process of internal conversion.

The role of internal conversion

Tiny flaws in crystals, such as those found in diamond or silicon carbide, are potential building blocks for quantum sensors. When a laser excites electrons at these sites, the energy does not always return as light. As the defect relaxes toward its lowest-energy ground state, it may emit a photon, transition between states with different electron spins, or release energy through vibrations of surrounding atoms.

These spin defects could function as stable, readable qubits, the fundamental units holding information in quantum technologies. Developing them requires a complete understanding of the excitation and relaxation cycle. While physicists have successfully used quantum mechanics to describe light emission and spin-state transitions, predicting energy loss through atomic vibrations—known as internal conversion—has remained challenging.

Resolving silicon carbide mismatch

The study, published in Physical Review Letters, demonstrates how accounting for internal conversion resolves a specific mismatch concerning a divacancy in silicon carbide. This defect consists of two neighboring missing atoms. The team’s calculations revealed that internal conversion makes a substantial, previously overlooked contribution to the lifetime of the defect's triplet excited state.

Including this factor brought theoretical predictions into agreement with experimental data, potentially informing efforts to utilize this type of defect as a qubit. “We were expecting to see an effect, but of a smaller magnitude,” said Giulia Galli, the Liew Family Professor of Electronic Structure and Simulations in UChicago PME and the Department of Chemistry, who served as the study’s senior author. “What we found is that this internal conversion process turns out to be more important than we thought.”

Validating nitrogen-vacancy centers

For nitrogen-vacancy centers in diamond, where a nitrogen atom sits beside a missing carbon atom, the framework’s predictions aligned with recent spectroscopy measurements. Internal conversion contributed little to energy loss involving triplet states but dominated energy loss from singlet states. These categories describe different arrangements of the electrons’ combined spin, and both results matched previous assumptions.

“We provided the missing piece of the puzzle needed to completely describe the optical cycle of spin defects,” Galli stated.

Overcoming computational barriers

The primary obstacle to calculating internal conversion was computational rather than a lack of fundamental equations. “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 and Villani collaborated with Yu Jin, a former graduate student in Galli’s group now working as a postdoctoral scholar at the Flatiron Institute in New York. They combined several methods previously developed within the group to address these challenges.

Methodology and implementation

The researchers described the defect’s excited states using many-body wavefunctions, mathematical descriptions that account for interacting electrons. Exact mathematical derivations allowed them to calculate how strongly each excited state couples to atomic motion. This formulation accounts for the coupling between each defect state and all vibrational configurations of hundreds of nearby atoms simultaneously, rather than calculating those configurations one at a time.

“In the past, a clear mathematical derivation and efficient algorithms were not available,” Jin explained. “The new derivation came together after years of work on the optical cycle of spin defects.”

The team implemented the framework in WEST, an open-source simulation code optimized for graphics processing units (GPUs). Galli’s group has developed WEST over the past decade within the Midwest Integrated Center for Computational Materials (MICCoM), which has received funding from the U.S. Department of Energy’s Office of Basic Energy Sciences since 2015. With the framework already incorporated into the code, other laboratories can begin using it.

Broader applications and future work

“Our work can now be used to make more accurate predictions about many materials of interest for quantum technologies,” Jin said. Galli added that the relevance extends beyond spin defects: “This internal conversion process is not only relevant to spin defects—it’s also related to processes of interest to energy technologies. That’s one of the reasons this work is so exciting.”

However, access to the code does not eliminate the high computational demands. Galli cautioned that the framework still requires substantial resources. “We are working on ways to integrate machine learning into excited states calculations to further improve the efficiency of our method,” Villani said.

Alongside efforts to lower costs, the team is extending the framework to spin defects in silicon and to a different class of materials used in renewable energy conversion and storage, where internal conversion plays an important role.