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 shift¹, spontaneous emission, and the Casimir effect². 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^3-5, with substantial implications for quantum materials and device engineering. High-mobility two-dimensional electron gases in the quantum Hall regime⁶ 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.