The origin of KPZ-scaling in arrays of polariton condensates

Abstract

This work investigates the origin of Kardar-Parisi-Zhang (KPZ) scaling in the phase dynamics of one-dimensional and two-dimensional polariton condensates. We demonstrate that the key mechanism leading to the observed power laws for the first-order correlation function $g^{(1)}$ is the fluctuation of the population of Goldstone modes, which arise due to the spontaneous breaking of $U(1)$ symmetry. Numerical simulations and analytical theory confirm that the critical exponents describing the KPZ universality class directly follow from the dynamics of Goldstone excitations. Our results establish a direct connection between the microscopic parameters of arrays of exciton-polariton condensates and the coherent properties of the light they emit.

Figures (4)

• Figure 1: (a) The calculated single polariton dispersion (blue) and the characteristic dispersion of a Nambu-Goldstone mode (orange) of a bosonic condensate of exciton-polaritons in a linear chain of micropillars (shown schematically in the right bottom part) (b) The two-dimensional dispersion of Nambu-Goldstone modes in a triangular periodic array of exciton-polariton condensates schematically shown at the left bottom corner. The inset compares the dispersions of single polariton and Nambu-Goldstone modes plotted along the $\Gamma$-K trajectory in a Brillouin zone. In both panels, the chemical potential of the polariton condensate is taken to be $\mu=0.4$ µ eV.
• Figure 2: The time-dependent first-order correlation function $g^{(1)}(\Delta x=0, \Delta t)$ (a) and spatial correlation function $g^{(1)}(\Delta x, \Delta t=0)$ (b) calculated for a one-dimensional periodic array of exciton-polariton condensates. Insets are showing the same data in log-log scale fitted with KPZ dependencies \ref{['eq:Ct']} and \ref{['eq:Cr']}. KPZ regions are marked with hatched grey areas.
• Figure 3: The time-dependent first-order correlation function $g^{(1)}(\Delta x=0, \Delta t)$ (a) and spatial correlation function $g^{(1)}(\Delta x, \Delta t=0)$ (b) calculated for a two-dimensional periodic array of exciton-polariton condensates. Insets show the same data in log-log scale fitted with analytic KPZ dependencies \ref{['eq:Ct']} and \ref{['eq:Cr']}. KPZ-regions are selected as hatched grey areas.
• Figure 4: The time-dependent first-order correlation function $g^{(1)}(\Delta x=0, \Delta t)$ of a one-dimensional chain of exciton-polariton condensates calculated for different interaction energies $\mu$: 3 µ eV (blue), 4 µ eV (orange) and 5 µ eV (green). KPZ-regions are marked with red lines and hatched areas of the corresponding color.