Driving emergent gauge fields in non-linear optical resonators – Ngauge

Nonlinear optics is a mature field harboring a plethora of discoveries alongside technological applications. Due to the abundance of modes in optics devices, much of the discoveries are spearheaded by experimental exploration of the exotic responses that arise under different driving schemes. In general, the theoretical analysis of such systems is based on linear response, when one knows how to solve all the relevant modes, or on the direct numerical simulation of non-linear regimes, which is very expensive from the computational point of view when the number of degrees of freedom exceeds 3. The recent progress made by Oded Zilberberg's group at the University of Konstanz in exploiting the "Harmonic Balance" method to solve all stationary states of reasonably large nonlinear optical systems (with up to 10 modes) greatly expands the possibilities for exploring such nonlinear physics. Specifically, the method can identify limit cycles as potential stationary states of a driven system under an expanded ansatz. In this project, we propose to couple theory and experiments, and to use this theoretical approach to study ensembles of coupled non-linear resonators, and experimentally observe the new steady states that we will predict. The optical experiments will be carried out on arrays of coupled semiconductor cavities where we will engineer collective polariton modes. The team of Jacqueline Bloch has developed an exquisite control over such lattices and their study by advanced non-linear optical spectroscopy. This will enable the experimental demonstration of these new stationary states. Among the exciting consequences of the emerging gauge freedom of limit cycles, we envision the appearance of a geometric phase during the establishment of limit cycles, and the possibility of realizing a non-linear topological pump.