Driven-dissipative turbulence in exciton-polariton quantum fluids

TL;DR

The paper tackles driven-dissipative 2D quantum turbulence in exciton-polariton fluids by comparing phase-imprinting tile patterns to conventional spoon-stirring for vortex injection. It shows that Tile-8 imprinting reproduces key turbulence signatures, including vortex clustering and an incompressible kinetic energy spectrum with a Kolmogorov-like $\sim k^{-5/3}$ range for clustered vortices, validating a practical imprinting route for experiments. The work further analyzes the impact of finite lifetimes and gain/loss fluctuations, finding turbulence can persist as long as density depletion remains modest and modulation timescales are suitably matched to lifetimes. These results establish actionable guidelines for realizing and studying quantum turbulence in polariton condensates using phase-imprinting schemes and inform experimental protocols that leverage periodic pumping above and below threshold.

Abstract

The present paper is devoted to comprehensive theoretical studies of exction-polariton quantum fluids specificities in the optics of their utilization for quantum turbulence research. We show that a non-trivial implementation of time-varying potential for excitation of quantum fluid (injection of quantized vortices) via the stirring procedure can be efficiently substituted with resonant excitation-based phase-imprinting techniques. The most efficient phase pattern corresponds to imprinting of tiles with randomly oriented plane waves in each. The resulting turbulent flows, spatial vortex distributions, and clustering statistics resemble those for the case of a conventional spoon-stirring scheme. We quantify the limitations on the lifetime and density depletion for the development and sustainability of quantum turbulence. The yield is the necessity to prevent the density depletion for more than one order of magnitude. Finally, we demonstrate that turbulence is robust with respect to alternating gain and loss at a certain range of modulation parameters, which corresponds to laser operating above and below condensation threshold.

Figures (16)

• Figure 1: Snapshots of condensate wave function to illustrate the various employed quantum fluid excitation schemes. For the rotating-spoon method, density and phase fields are respectively shown in panels a) and b) (one can see the spoon potential stirring the initially homogeneous system). While, for the imprinting-strategies the characteristic field is the wave function phase at initial time moment $t=0$ ps. Tile-imprinting strategies (with 8x8 grid of $32~\mu$m tiles) are illustrated in c) for Tile-8 scheme (plane wave wavelength $\lambda = 8~\mu$m) and in d) for Tile-4 ($\lambda = 4~\mu$m). Finally, snapshots e) and f) show the initial imprinted phase pattern for pixel-imprinting technique, with pixel sizes 8 $\mu$m (Pixel-8) and 4 $\mu$m (Pixel-4) respectively
• Figure 2: Results of vortex detection followed by clustering algorithm for spoon-stirring (a,b) and Tile-8 (c,d) excitation. The vortices of opposite signs are denoted with yellow and blue inner circles in density field images (panels a and c). Vortices belonging to the clusters carry outer circles of the corresponding colors. Green outer circles show the dipoles. Vorticity field is shown in panels b) and d).
• Figure 3: Histograms for vortex statistics results obtained for all excitation strategies. Panel a) is shows single vortices (red bar parts), vortices in dipoles (blue) and clustered vortices (green) in the beginning of the analysis phase (left of paired bars) and in the end of the analysis phase (right of paired bars). Particle lifetime is set $\tau=1.89\ ns$. Panel b) focuses on Tile-8 phase imprinting strategy and spoon-stirring strategy giving details on the number of vortices belonging to clusters of various sizes. The data in panel b) corresponds to the beginning of the analysis phase and thus to the left counterparts of the paired columns in panel a).
• Figure 4: Panel a). Results of the Incompressible Kinetic Energy (IKE) spectra semi-analytical calculation (Eq. \ref{['eq: analyt_IKE']}) for all excitation strategies at the beginning of the analysis phase (approximately 2.3 ns). Solid curves are for full vortex distributions and curve with dots is for clustered vortices only. Guides for eye are given for characteristic exponents: -3 (vortex core), -1 (dipole), -5/3 (clustered vortices). Panels b) presents the comparison of full IKE spectra obtained semi-analytically and numerically and IKE spectra obtained semi-analytically for clustered vortices for Tile-8 excitation. Panel c) is the same for the spoon-stirring approach.
• Figure 5: Time evolution of quantum fluid density (a) and total number of vortices (b) for various values of quantum fluid lifetime $\tau$ for Tile-8 excitation. The cross markers in panel a) correspond to the kink in number of vortices.