Kibble-Zurek mechanism in a polariton supersolid

TL;DR

This work investigates the Kibble-Zurek mechanism during the formation of a polariton supersolid in a liquid-crystal microcavity with tunable Rashba-Dresselhaus spin-orbit coupling ($\text{RDSOC}$). Using a spinor Gross-Pitaevskii framework that includes relaxation and a two-minima dispersion from the RDSOC, the authors predict two distinct KZM scaling exponents for topological defect density as a function of the quench parameter: $\eta_{KZM,an}=1$ in the slow-quench regime and $\eta_{KZM,an2}=1/3$ in the fast-quench regime, contrasting with the scalar case $\eta_{KZM,scalar}=1/2$. Experimental single-shot polarization-resolved imaging yields a slow-quench exponent $\eta_{KZM,exp}=1.0\pm0.2$, in line with theory and numerical simulations ($\eta_{KZM,num}\approx0.95\pm0.05$; $\eta_{KZM,num2}\approx0.32\pm0.03$ for fast quench). Overall, the work demonstrates a novel KZM scaling in a spin-orbit-coupled photonic supersolid, showing how dispersion engineering via $\text{RDSOC}$ controls defect formation during non-equilibrium condensation with potential implications for supersolid physics and related nonequilibrium phenomena.

Abstract

We study the formation of topological defects via the Kibble-Zurek mechanism in a polariton supersolid in a liquid crystal microcavity with tunable Rashba-Dresselhaus spin-orbit coupling. We predict analytically two different scalings in the slow- and fast-quench regimes, and confirm these predictions numerically. We also present experimental results for the slow-quench regime, demonstrating an original Kibble-Zurek scaling exponent $η_{KZM}=1.0\pm 0.2$

Figures (4)

• Figure 1: Polariton supersolid in a liquid crystal microcavity. a) The microcavity with a polymer and a liquid crystal orientable by electric field. b) The lower polariton branch with Rashba-Dresselhaus spin-orbit coupling (black and red are the two subbands). c) The periodic density profile of a supersolid with a topological defect (quantum vortex) that shows up as a dislocation.
• Figure 2: Experimental KZM scaling in a supersolid. a) Intensity of emission from a supersolid, demonstrating the stripes with a dislocation. b) Phase, extracted from the pattern of the stripes, demonstrating a singularity (quantum vortex). Black arrow shows the phase gradient in (a,b). c) Average number of vortices in a single shot as a function of reduced intensity. Black dots -- experiment, red line -- theory. Error bars correspond to the uncertainty provided by the Poissonian distribution fit.
• Figure 3: KZM scaling of topological defects in a polariton supersolid. a) Results of numerical simulations with slow- and fast-quench asymptotes. b) Slow-quench region for varying the RDSOC constant $\alpha$: the slope of the linear asymptote does not depend on $\alpha$
• Figure S1: Spatial distribution of vortices in experiment. a) Number of vortices observed in each of the pixels. b) Histogram of the frequencies of the number of vortices per pixel together with the Poisson distribution and the theoretically expected uncertainty for a finite sample.