Abstract
Coupled many-body quantum systems exhibit rich emergent physics with diverse stationary and dynamical behaviours. By engineering platforms with tunable and distinct coupling mechanisms, new insights emerge into the collective behaviour of coupled many body systems. Particles can be exchanged via evanescent or ballistic coupling: the former, based on proximity, yields large spectral splitting, while the latter requires strict phase-matching, analogous to phase-coupled harmonic oscillators and has a smaller impact on the energy landscape. We demonstrate an all-optically tunable quantum fluid dimer based on exciton-polariton condensates in a photonic crystal waveguide with hyperbolic (saddle-like) dispersion. Varying the dimer's angle relative to the grating tunes the coupling from evanescent to ballistic. We directly observe spectral features and mass flow shaped by the saddle dispersion. This work highlights photonic crystals as powerful platforms to explore condensed matter phenomena lying at the interface between delay-coupled nonlinear oscillators and tight binding physics.