Limit Cycles in a Photonic Dimer with Tuneable Non-Hermitian Interactions
Interactions govern the emergence of collective behaviour in classical and quantum many-body systems. While conservative interactions are well known to generate nonlinear phenomena ranging from self-trapping to pattern formation, it remains largely unexplored whether purely dissipative -- i.e., non-Hermitian -- interactions can give rise to similarly rich dynamics and nontrivial system states. Here, we experimentally realise tuneable non-Hermitian interactions in two coupled condensates of light confined within a dye-filled double-well microcavity. Local coupling to molecular reservoirs generates the effective dissipative photon interactions. We show that the interplay between coherent tunnelling and interactions stabilises limit-cycle oscillations, a hallmark of nonlinear dynamics traditionally associated with Hermitian nonlinearities. By tuning the reservoir coupling, we map out the dynamical phase diagram comprising stable fixed points and limit cycles, thereby demonstrating direct control over the interaction strength. Our experimentally validated model reveals both supercritical and subcritical Hopf bifurcations, giving rise to hysteresis, bistability and excitability. These results validate dissipative interactions as a mechanism for organising collective nonlinear dynamics in driven-dissipative systems and pave the way towards exploring nonequilibrium many-body physics through controlled dissipation.