Dirac exciton-polariton condensates in photonic crystal gratings

Bound states in the continuum have recently been utilized in photonic crystal gratings to achieve strong coupling and ultralow power-driven condensation of bosonic exciton-polariton quasiparticles with atypical Dirac-like features in their dispersion relation. Here, we develop the single- and many-body theory of these new effective relativistic exciton-polaritons modes and describe their mean field condensation dynamics facilitated by the interplay between protection from the radiative continuum and negative-mass pump induced optical trapping. Our theory accounts for many tunable grating parameters giving full control over the diffractive coupling properties between guided polaritons and the radiative continuum previously unexplored in the context of driven condensation. In particular, we discover stable cyclical condensate solutions mimicking a driven-dissipative analog of the zitterbewegung effect characterized by coherent superposition of both ballistic (rapid phase front) and trapped (slow phase front) polariton waves. Finally, important distinctions are drawn between the concepts of near field and far field in the photonic grating, clarifying recent experimental observations on the emission characteristics of these long lived nonlinear Dirac polaritons.