Multicomponent Kardar-Parisi-Zhang universality in degenerate coupled condensates

Abstract Gapless phase modes in non-equilibrium condensates fall within the Kardar-Parisi-Zhang (KPZ) universality class, but key single-component symmetries do not clearly generalise to the multicomponent case. We discuss the phase diagram of coupled KPZ equations describing the low-energy theory of a $${{\mathbb{Z}}}_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> degenerate driven-dissipative condensate with global U (1) × U (1) symmetry. In the homogeneous condensate regime, a dynamical renormalisation group (RG) analysis in one dimension reveals that coupled stochastic complex Ginsburg-Landau equations exhibit an emergent stationary distribution, enforcing the KPZ dynamical exponent z = 3/2 and roughness exponent χ = 1/2 for both components. In specific parameter regimes relevant to polaritons, the RG fixed point offers a transformation to decoupled KPZ equations. By tuning the intercomponent coupling, the system offers non-KPZ regimes, including a fragmentation transition, and a non-thermal spacetime vortex phase driven by the KPZ non-linear terms. Our findings have broad implications for experiments and understanding multicomponent KPZ systems in the long-wavelength limit.