Single-Shot Flow Spectroscopy of a Polariton Condensate: Kibble-Zurek and Kolmogorov-Like Scaling

TL;DR

We report single-shot interferometric imaging of spontaneous vortex nucleation in a room-temperature organic polariton condensate. Off-axis holography reconstructs phase and flow in each realization, enabling tests of defect formation and turbulent scaling. The mean vortex number scales with pump power above threshold with an exponent $α ≈ 0.5$, consistent with Kibble-Zurek expectations for 2D point defects, and the incompressible kinetic-energy spectrum exhibits a Kolmogorov-like segment, E_inc(k) ∝ k^{-5/3}, signaling emergent turbulence in a quantum fluid of light. This work demonstrates direct single-shot access to phase and flow in driven-dissipative polariton systems, providing a quantitative framework for probing stochastic defect formation and the onset of turbulence in quantum fluids of light.

Abstract

Quantized vortices are fundamental topological excitations of quantum fluids. We report single-shot interferometric measurements of spontaneous vortex nucleation in a room-temperature organic exciton-polariton condensate. From hundreds of independent realizations we find random vortex-core positions and unbiased circulation, consistent with intrinsically stochastic, unpinned defect formation. The mean vortex number scales with pump power above threshold with an exponent consistent with Kibble-Zurek freeze-out in a driven-dissipative condensate. Using reconstructed phase maps we obtain single-shot flow fields, compute the incompressible component, and extract kinetic-energy spectra. Vortex-containing realizations develop a robust Kolmogorov-like segment with Einc(k) proportional to k^(-5/3) over a finite k range, indicating the onset of turbulent spectral scaling in a quantum fluid of light. These results establish single-shot access to phase and flow as a direct route to quantifying stochastic defect formation and emerging turbulence in polariton condensates.

Figures (10)

• Figure 1: Single-shot interferometry and flow reconstruction. Two independent single-shot measurements at the same sample location, shown in panels (a)–(e) and (f)–(j), respectively. (a),(f) Single-shot interferograms, each containing a spontaneously formed vortex (fork-like dislocation in the interference fringes, inset). Green curves trace the fringes as a guide to the eye. (b),(g) Reconstructed real-space phase profiles obtained via an off-axis digital holography algorithm. Yellow arrows indicate the local wavevector field $\mathbf{k}(\mathbf{r},t)=\nabla\phi(\mathbf{r},t)$ in regions where the condensate intensity exceeds 5% of its peak value. Blue and red arrows denote vortex cores with counterclockwise and clockwise circulation, respectively; arrow lengths are proportional to $|\mathbf{k}|$. (c),(h) Reconstructed real-space condensate density profiles. (d),(i) Far-field (momentum-space) intensity distributions reconstructed from (c) and (h), respectively. (e),(j) Experimentally measured far-field intensity images.
• Figure 2: Flow maps. Representative single-shot phase-retrieval results from different sample locations. (a) Vortex core at the interface between two large-scale counter-propagating (or locally rotating) flow domains. (b) Vortex within an approximately co-directional flow. Yellow arrows: reconstructed wavevector (flow) field. Red arrows (insets): overall flow directions of the neighboring domains.
• Figure 3: Vortex (un)pinning at a fixed location. Two single-shot interferograms taken in succession at the same sample spot. (a) Interference fringes showing no vortex (uniform fringe pattern) at the areas highlighted by green curves. (c) Fringes from the immediately following shot, in which a vortex appears (fork-like dislocation). (b),(d) Reconstructed phase maps corresponding to (a) and (c), respectively.
• Figure 4: Kibble--Zurek scaling of vortex number. Average vortex count $n_V$ versus relative pump power. Error bars indicate uncertainty from Poisson statistics. Red line: power-law fit over $2.75 \le (P-P_{\mathrm{thr}})/P_{\mathrm{thr}} \le 4.3$ (SM Fig. \ref{['fig:S3']}), yielding $\alpha\simeq0.5$ as expected for 2D point defects in the mean-field benchmark.
• Figure 5: Incompressible kinetic-energy spectra. Log--log plots of the angle-averaged incompressible spectrum $E_{\rm inc}(k)$ for single-shot realizations containing $N_V=1$ (blue), 2 (green), or 3 (red) vortices. Curves show group-averaged spectra and are vertically offset for clarity. Dashed lines are power-law fits performed over an intermediate-$k$ interval between the system-size scale ($k\sim2\pi/L$) and the optical-resolution scale ($k\sim\pi/\delta r$), showing an approximate $k^{-5/3}$ dependence.