Scientists measure quantum distance in a solid for the first time ever

Scientists have, for the first time, experimentally measured the full quantum metric tensor of electrons in a real solid crystal, using black phosphorus. Quantum distance, a theoretical concept describing how similar or different two quantum states are, had long eluded direct measurement in materials due to the difficulty of capturing the subtle quantum geometry of electrons. By employing angle-resolved photoemission spectroscopy (ARPES) combined with synchrotron radiation at the Advanced Light Source, the researchers mapped the pseudospin texture of electrons in black phosphorus, enabling them to reconstruct the quantum distance and the full quantum metric tensor of Bloch electrons within the crystal. This breakthrough is significant because understanding quantum distances and the quantum metric tensor can illuminate anomalous quantum phenomena in solids, such as high-temperature superconductivity and resistance-free electrical conduction. Moreover, precise knowledge of quantum geometry is crucial for advancing quantum technologies, including the development of fault-tolerant quantum computers. While the current demonstration is limited to black phosphorus, the approach opens new avenues for exploring