Scientists Measure Quantum Metric Tensor in Black Phosphorus

Understanding Quantum Distance and Its Significance

Quantum distance is a concept that measures the similarity between two quantum states. When the quantum distance is one, it indicates that the two quantum states are identical. Conversely, a quantum distance of zero suggests that the states are completely opposite. While this idea has been part of theoretical physics for a long time, its importance has grown significantly in recent years within the field of physics.

In recent years, many experimental physicists have attempted to measure the quantum distance of electrons in real solid-state materials. However, directly measuring the quantum distance and the associated quantum metric tensor—another key geometric quantity in modern physics—has remained a challenge.

The quantum metric tensor plays a crucial role in explaining various physical phenomena in solids. Therefore, developing an effective method for its direct measurement is essential. A recent breakthrough in both theoretical and experimental quantum physics has addressed this challenge.

An international team of researchers from the Republic of Korea and the U.S., led by Keun Su Kim, an Underwood Distinguished Professor of Physics at Yonsei University, has reported the first experimental measurement of the quantum distance. Their findings were published in the journal Science on 5 June 2025.

This research involved close collaboration between an experimental group led by Prof. Kim with Yoonah Chung and Soobin Park at Yonsei University and a theory group led by Professor Bohm-Jung Yang with Sunje Kim and Yuting Qian at Seoul National University.

According to Prof. Kim, the theory group identified black phosphorus as an ideal material for studying the quantum distance due to its structural simplicity. Based on this insight, the experimental group measured the quantum distance of electrons in black phosphorus using the momentum space distribution of the pseudospin texture of the valence band. This was achieved through the polarization dependence of angle-resolved photoemission spectroscopy and synchrotron radiation via the Advanced Light Source in the U.S.

This approach enabled the researchers to successfully measure the full quantum metric tensors of Bloch electrons in solids in black phosphorus for the first time.

Measuring the quantum distance is fundamental not only for understanding anomalous quantum phenomena in solids, such as superconductors, but also for advancing quantum science and technologies. For instance, precise measurements of quantum distances could help develop fault-tolerant quantum computation technologies.

Understanding materials at the quantum mechanical level is essential, and the quantum distance serves as a cornerstone for comprehending complex quantum phenomena in solids. This research is expected to lead to better semiconductor technologies, higher transition-temperature superconductors, and superior quantum computers compared to conventional ones.

Overall, this work is anticipated to provide insights into quantum geometric responses across a wide range of crystalline systems. It could ultimately pave the way for a future driven by quantum technologies.

For more details, refer to the study by Sunje Kim et al., titled "Direct measurement of the quantum metric tensor in solids," published in Science (2025). The DOI for the study is 10.1126/science.ado6049.