Cavity-Vacuum-Induced Chiral Spin Liquids in Kagome Lattices: Tuning and Probing Topological Quantum Phases via Cavity Quantum Electrodynamics

Topological phases in frustrated quantum magnetic systems have captivated researchers for decades, with the chiral spin liquid (CSL) standing out as one of the most compelling examples. Featured by long-range entanglement, topological order, and exotic fractional excitations, the CSL has inspired extensive exploration for practical realizations. In this work, we demonstrate that CSLs can emerge in a kagome lattice driven by vacuum quantum fluctuations over the non-interacting vacuum within a single-mode gyrotropic cavity. The gyrotropic cavity imprints quantum fluctuations with time-reversal symmetry breaking and stabilizes a robust CSL phase without external laser excitation. Moreover, we identify experimentally accessible observables - such as average photon number and transport properties - that reveal connections between photon dynamics and the emergent chiral order. Our findings establish a novel pathway for creating, controlling, and probing topological and symmetry-breaking quantum phases in strongly correlated systems.