Realization of Hofstadter's butterfly and a one-way edge mode in a polaritonic system

We present a scheme to generate an artificial gauge field for the system of neutral bosons, represented by polaritons in micropillars arranged into a square lattice. The splitting between the two polarizations of the micropillars breaks the time-reversal symmetry (TRS) and results in the effective phase-dependent hopping between cavities. This can allow for engineering a nonzero flux on the plaquette, corresponding to an artificial magnetic field. Changing the phase, we observe a characteristic Hofstadter's butterfly pattern and the appearance of chiral edge states for a finite-size structure. For long-lived polaritons, we show that the propagation of wave packets at the edge is robust against disorder. Moreover, given the inherent driven-dissipative nature of polariton lattices, we find that the system can exhibit topological lasing, recently discovered for active ring cavity arrays. The results point to a static way to realize artificial magnetic field in neutral spinful systems, avoiding the periodic modulation of the parameters or strong spin-orbit interaction. Ultimately, the described system can allow for high-power topological single-mode lasing which is robust to imperfections.