Chiral Vacuum Engineering of Quantum Hall Matter

We reveal that a chiral cavity distinguishes the resonant and antiresonant interactions between a two-dimensional electron gas and the cavity vacuum. For co-rotating helicities, the modes anticross, exhibiting vacuum Rabi splitting, and retain a bare vacuum ground state. For counter-rotating helicities, the modes cross, acquiring vacuum-mediated energy shifts and a two-mode squeezed ground state. We trace the origin of these observations to the SU(2) and SU(1,1) symmetries of the respective Hamiltonians and present their spectroscopic signatures in chiral photonic crystal cavities. We further predict that cavity chirality produces a handedness-dependent correction to Hall resistivity at finite polariton broadening, while such a correction is not present in an achiral cavity. For the longitudinal resistivity, we find an asymmetric response of the Shubnikov--de Haas oscillations for the different helicities. Finally, we present an experimentally accessible route for detecting the squeezed ground state through current fluctuations. Parameters based on a recently demonstrated terahertz chiral cavity place these effects within experimental reach.