Tunable vacuum-field control of fractional and integer quantum Hall phases.

In quantum mechanics, empty space is not void but is characterized by vacuum-field fluctuations, which underlie phenomena such as the Lamb shift, spontaneous emission, and the Casimir effect. Due to their quantitatively small relative contributions in free-space atomic physics, they were traditionally overlooked in solid-state systems. Recently, however, the interplay between electronic correlations and quantum electrodynamical effects in low-dimensional systems has become a rapidly advancing area in condensed matter physics, with substantial implications for quantum materials and device engineering. High-mobility two-dimensional electron gases in the quantum Hall regime offer an ideal platform to investigate how vacuum electromagnetic fields affect strongly correlated electronic states. Here we demonstrate that adjusting the coupling strength between a two-dimensional electron gas and the vacuum fields of a hovering split-ring resonator leads to a significant reduction in exchange splitting at odd-integer filling factors, along with an enhancement of fractional quantum Hall gaps at filling factors 4/3, 5/3 and 7/5. Theoretical analysis indicates that these effects stem from an effective long-range attractive interaction mediated by virtual cavity photons in regions with strong vacuum electric field gradients. Our findings uncover a new mechanism by which cavity vacuum fields can reshape electronic correlations in quantum Hall systems, establishing a new approach for manipulating correlated quantum phases in low-dimensional materials and paving the way for engineering tailored many-body interactions in compact devices.