Decoupling ultrastrong Rabi splitting from quantum vacuum dressing in a chiral cavity
Polariton formation and quantum vacuum dressing are usually regarded as intertwined consequences of ultrastrong light--matter coupling. Here we show that they can be selectively controlled through the relative direction of rotation of the cavity field and the matter excitation. We consider cyclotron resonance coupled to a chiral cavity supporting a single circularly polarized mode. We quantize the electromagnetic field within the cavity, derive from first principles the Hamiltonian, and investigate how mode hybridization and vacuum dressing are rendered as we tune the magnetic field. When the cavity field co-rotates with the cyclotron motion, energy is exchanged resonantly between light and matter, producing a large Rabi splitting and conventional polaritons, while the ground state remains the bare vacuum. Reversing the magnetic field makes the cyclotron motion counter-rotating with the cavity field. The same cavity mode then couples through anomalous processes that create and annihilate light and matter excitations in pairs: the conventional polaritonic anticrossing disappears, while the ground state acquires squeezing and virtual excitations. Our results show that spectral hybridization and quantum vacuum dressing are distinct manifestations of ultrastrong coupling, offering an additional degree of freedom for engineering cavity quantum materials.