Emergence of Turbulence in a counterflow geometry of 2D Polariton Quantum Fluids

Abstract

We numerically investigate the nonlinear dynamics of a two-dimensional exciton-polariton quantum fluid coherently driven by two counter-propagating laser beams. Using an exciton-photon coupled driven-dissipative Gross-Pitaevskii framework, we identify four distinct regimes-linear, solitonic, turbulent, and superfluid-emerging from the interplay between pump strength, laser detuning, and injected momentum, which together control the balance between kinetic and interaction energies in the quantum fluid. The different regimes are characterized through real-space and momentum-space observables, as well as through the temporal first-order coherence function. We show that turbulence occupies a well-defined and extended region of parameter space, marked by spontaneous vortex nucleation, and a pronounced reduction of temporal coherence, providing a clear signature of nonstationary dynamics. By constructing quantitative phase diagrams, we delineate the transitions between the various regimes and identify multiple pathways connecting solitonic, turbulent, and superfluid behaviors. Finally, we demonstrate that the turbulent regime persists over experimentally realistic parameter ranges compatible with state-of-the-art GaAs-based micro-cavity platforms, establishing counter-propagating polariton flows as a robust and versatile setting for the study of driven-dissipative quantum turbulence in two dimensions.

Figures (10)

• Figure 1: (a) Schematic of the experimental two-dimensional polariton cavity, showing two counter-propagating pump beams and a zoom of the 2D pump intensity profile. The scale bar corresponds to approximately $54\,l_0' \approx 75~\mu\mathrm{m}$. (b) Illustration of the bare exciton and cavity mode dispersions (dashed lines), together with the lower (LP) and upper (UP) polariton dispersions (solid lines). The depicted dispersions correspond to a system with a Rabi splitting of $2\hbar\Omega' = 3.3~\mathrm{meV}$ and an initial $50{:}50$ exciton--photon composition, which occurs when the $k=0$ photon energy equals the exciton energy.
• Figure 2: Four distinct regimes are shown: (a) linear ($F_{\text{inc}} = 10^{-3}$), (b) solitonic ($F_{\text{inc}} = 0.6$), (c) turbulent ($F_{\text{inc}} = 1.2$), and (d) superfluid ($F_{\text{inc}} = 3.7$). For each regime, the top panels display the two-dimensional phase distribution of the photonic field. The middle panels show the two-dimensional photonic density $n_C = |\Psi_C|^2$, with the pump positions indicated in red at the $1/e^2$ contour of its maximum intensity. The bottom panels present $\tilde{n}_C$, the normalized momentum-space distribution of the photonic field in the central region (highlighted by the yellow rectangle in panel a)), obtained from the two-dimensional Fourier transform of the real-space photonic density, $n_C$. The scale bar corresponds to $10\,\mu\mathrm{m}$. Parameters: Rabi splitting $2\hbar\Omega' = 3.3$ meV, pump momenta $k_p = 0.4 \leftrightarrow k_p' = 0.29~\mu\mathrm{m}^{-1}$, laser detuning $\Delta=0.22\leftrightarrow\Delta'=0.18\,\mathrm{meV}$, and loss rates $\gamma = 0.02 \leftrightarrow \gamma' = 0.025~\mathrm{ps}^{-1}$.
• Figure 3: Comparison of excitonic and photonic field densities in our polariton system. Panels (a) and (b) show the spatial profiles of the excitonic and photonic field densities, respectively at a fixed time $t'=1980\,\tau_0'=1643\,\mathrm{ps}$. Both components exhibit the same spatial distribution, but the excitonic density is lower than the photonic one. Panel (c) shows the excitonic fraction $f_X$, which quantifies the matter--light composition of the quasiparticles. The central region (black box) highlights a balanced regime in which the excitonic fraction averages to $0.47$.
• Figure 4: Linear-scale plot of the ratio between interaction and kinetic energy, accompanied by a panel showing the same ratio on a logarithmic ($y$-axis) scale. For each point, the ratio is evaluated over a time interval of $500\,\tau_0' \approx 400~\mathrm{ps}$, long compared to the dynamical timescale, allowing the turbulent dynamics to be properly averaged and removing time dependence. Red points indicate the mean value of the energy ratio for each regime, while black bars represent the standard deviation. Each point corresponds to a single simulation; the same simulations are used in Fig.\ref{['fig:phasediagram']}.
• Figure 5: Phase diagrams of the polariton fluid in the $(F_{\text{inc}},\Delta)$ plane. (a) Phase diagram for the input wavevector $k_p' = 0.4\,l_0'^{-1} = 0.29\,\mu\mathrm{m}^{-1}$. (b) Phase diagram for the input wavevector $k_p' = 0.6\,l_0'^{-1}= 0.43\,\mu\mathrm{m}^{-1}$. The color scale indicates the spatially averaged temporal coherence $g^{(1)}$, which serves as a marker for stationarity and turbulence. Dark regions correspond to stationary regimes (linear, solitonic, superfluid), while bright zones indicate the emergence of turbulence. The zones are placed by hand to give an approximate indication of the different regimes. Each white points are a simulation and yellow points are these used for Fig.\ref{['fig:4regimes']}. Parameters: Rabi splitting $2\hbar\Omega = 3.3$ meV, loss rates $\gamma = 0.02 \leftrightarrow \gamma' = 0.025~\mathrm{ps}^{-1}$, chosen photon wavelength $\lambda = 854~\mathrm{nm}$ and the interaction strength between excitons $\hbar g'_X = 0.003\,\mathrm{meV}\cdot\mu\mathrm{m}^2$.