Optical and magnetic control of orbital flat bands in a polariton Lieb lattice

We study the magneto-optical response of exciton polaritons in p-orbital flat bands in a two-dimensional Lieb lattice of semiconductor microcavity pillars. At low excitation density, we detail the influence of an external magnetic field on the exciton component, which enables magnetic tuning of the flat-band states. In the high-density regime, one can induce a spin population imbalance by circularly polarized pumping leading to an effective nonlinear Zeeman splitting. We show how the interplay between the symmetry of the orbital wave function, photonic spin-orbit coupling, and real and effective Zeeman splittings gives rise to real-space flat-band patterns with tilted orbital wave functions in the regime of dynamical polariton condensation. These results demonstrate the ability to optically and magnetically manipulate the spatial, spectral, and polarization properties of polariton condensates in the flat energy bands of a Lieb lattice.