First direct measurement of quantum distance in strong materials

An worldwide workforce led by Keun Su Kim at Yonsei University has directly measured the quantum metric tensor, additionally known as the quantum distance, in an actual materials for the primary time. Using angle-resolved photoemission spectroscopy (ARPES) on the U.S. Advanced Light Source, researchers mapped how electrons in black phosphorus work together with mild and reconstructed the total quantum metric tensor of its valence band. Their findings, published in Science on June 5, 2025, mix theoretical work by Bohm-Jung Yang’s group at Seoul National University with experimental measurements by Kim’s group at Yonsei.

The quantum metric quantifies how related or totally different two quantum states are—a quantum distance of 1 means states are an identical, whereas zero signifies they’re reverse. The quantum metric plays an important role in flat-band superconductors by enhancing the transition temperature. Physicists launched this idea many years in the past, however measuring it in solids has been difficult; earlier experiments had been restricted to synthetic techniques comparable to nitrogen-vacancy heart qubits.

Why quantum distance issues

The quantum metric seems in various phenomena throughout condensed-matter physics. It pertains to quantum fluctuations, dissipative responses, and performs roles in quantum part transitions, orbital magnetism, localization and superfluidity. In quantum data concept, it’s equal to the quantum Fisher data, a measure of multipartite entanglement.

Recent theoretical work confirmed the metric contributes to superconductivity: quantum geometry contributes to the coherence length and will clarify latest observations in flat band techniques. The geometric superfluid weight may even survive when the bands turn into utterly flat and is responsible for the enhanced transition temperature of flat-band superconductors. These connections make the metric a key parameter for understanding emergent habits in supplies and designing fault-tolerant quantum applied sciences.

Black phosphorus as a testbed

Black phosphorus is essentially the most steady allotrope of phosphorus and varieties a layered crystal with sturdy intrinsic in-plane anisotropy. Thin black-phosphorus movies exhibit high Hall mobilities—about 1,000 cm²/V·s alongside the light-mass x path and 600 cm²/V·s alongside the heavy-mass y path at 120 Okay. Field-effect transistors fabricated from 5 nm black-phosphorus flakes obtain on–off present ratios above 10⁵ with affordable mobility at room temperature. Yang’s concept group discovered that one of many elemental layered crystals, black phosphorus, is a perfect materials to review the quantum distance of electrons owing to its structural simplicity.

In November 2024, researchers from MIT and Seoul National University reported a reconstruction technique for extracting the quantum geometric tensor from ARPES measurements. Researchers outlined a strategy to measure the momentum-resolved QGT of solids utilizing angle-resolved photoemission spectroscopy (ARPES). That method combines two complementary analyses of polarization- and spin-resolved ARPES information to find out each the quantum distance and the Berry curvature. Riccardo Comin of MIT informed researchers that the tactic permits extraction of details about the electron wavefunction, not simply its vitality bands. The Yonsei experiment builds on this technique by making use of it to black phosphorus’s easy band construction.

Results and implications

During measurements on the Advanced Light Source, the workforce used polarized mild to probe the pseudospin texture of black phosphorus’s valence band. By analyzing the momentum-resolved pseudospin textures of valence electrons in black phosphorus, they had been capable of reconstruct the quantum metric tensor with unprecedented precision. The end result gives direct experimental proof for the quantum metric in a strong and serves as a benchmark for future research.

According to Kim, “Measuring the quantum distance is fundamentally important not only to understand anomalous quantum phenomena in solids, including special ones such as superconductors, but also to advance our quantum science and technologies.” The workforce expects the method to assist develop next-generation semiconductors, high-temperature superconductors and improved quantum computer systems.

While the measurement represents an necessary demonstration, it isn’t a direct blueprint for a quantum laptop. The quantum metric is certainly one of a number of portions governing digital habits, and harnessing it to construct units would require appreciable engineering.

Recent quantum computing developments present regular however measured progress. IBM’s 2025 roadmap targets techniques with hundreds of qubits, whereas industry revenue exceeded $1 billion in 2025. However, classical simulation of IBM’s 127-qubit Eagle processor experiments with better accuracy than the quantum machine itself achieved utilizing tensor community algorithms on a laptop computer laptop demonstrates that quantum benefit stays elusive for a lot of issues.

By making an summary amount experimentally tangible, the Yonsei examine gives a brand new software for probing quantum geometry and highlights the rising interaction between supplies science and quantum data. The work demonstrates that theoretical constructs as soon as thought-about mere abstractions might be translated into measurable portions, enriching our empirical understanding of quantum techniques.

The analysis paper “Direct measurement of the quantum metric tensor in solids” seems in Science (DOI: 10.1126/science.ado6049).