Cavity-Modified Zeeman Effect via Spin-Polariton Formation

We study the electronic spin Zeeman effect for an effective spin-$1/2$-system subject to both strong coupling to a low-frequency optical cavity and an external static magnetic field. Specifically, we address the interplay between the cavity magnetic field component in a cavity Zeeman interaction and the canonical spin Zeeman interaction from the perspective of an effective spin-polariton Hamiltonian. The latter is derived from the minimal coupling Pauli-Fierz Hamiltonian beyond the common dipole approximation via first-order quasi-degenerate perturbation theory. We find the spin Zeeman effect to be modified in the presence of the cavity field due to the formation of spin-polariton states, which result from an intricate interplay of cavity and external magnetic fields in our model. Spin-polariton signatures are discussed in the context of electron paramagnetic resonance (EPR) spectroscopy along with cavity-induced modifications of the electronic g-factor.