Dicke Superradiance in Extended 2D Quantum Arrays Coupled to Metasurface Bound States in the Continuum

Abstract

Dicke superradiance is a collective phenomenon where the emission from ensembles of quantum emitters is coherently enhanced beyond the sum of each emitter's independent emission. Here, we propose a platform that exploits the delocalised nature of a high-Q, non-local mode supported by a dielectric metasurface (a so-called bound-state-in-the-continuum or BIC) to induce superradiant behaviour within an extended two-dimensional array of distant quantum emitters. We show that these BIC-mediated emitter interactions can span several wavelengths, thus overcoming the traditional subwavelength separation between emitters required in free space. We further show that reaching the idealised Dicke limit is possible in this system, provided that the emitters are coupled to the BIC mode efficiently enough, as quantified through the $β$-factor. Moreover, we demonstrate its experimental viability by analysing its robustness to realistic experimental imperfections. This work puts forward optical metasurfaces supporting BICs as a physically viable platform for realising the upper limits of cooperative emission in physically extended quantum emitter arrays.

Figures (7)

• Figure 1: A schematic of the QE array (red dots)–metasurface (blue scatterers) system. The emitter positions and dipole moment orientations (black arrows) correspond to the configuration giving maximum coupling to the metasurface-BIC mode. For clarity, only an $11\times 11$ region is shown.
• Figure 2: (a)$\mathcal{G}^{(2)}(0,0)$ vs $N$ for a finite metasurface (red dots) and free space (blue dots). Dashed green: analytical single-mode model ($\beta=81.79\%$riley2025metasurfacemediatedquantumentanglementbound). Grey: Dicke [Eq. (\ref{['eq:Dicke_result']})] and independent [Eq. (\ref{['G2 ind Gen']})] limits. (b)$\mathcal{G}^{(2)}(0,0)$ vs lattice constant $d$ for metasurface (red curve) and free space (blue curve). Inset: schematic showing scanning direction for $N=3\times 3$ emitters. Horizontal line indicates the superradiant transition $\mathcal{G}^{(2)}(0,0)=1$.
• Figure 3: (a) Incomplete lattice ($N = 5 \times 5$) with five missing emitters ($\eta = 0.8$). (b) $\mathcal{G}^{(2)}(0,0)$ distributions for $\eta = 0.2, 0.5, 0.8$ for $11 \times 11$ QE lattice; dashed line: full lattice ($\eta = 1$). (c) Positional disorder: emitters (green) displaced within radius $\delta r$ from optimal positions (red). (d) $\mathcal{G}^{(2)}(0,0)$ for $\delta r = 10, 20, 30\,\mathrm{nm}$ ($9 \times 9$ array). (e) Orientation disorder: dipole angles shifted within $\delta\theta$. (f) $\mathcal{G}^{(2)}(0,0)$ for $\delta\theta = 30^\circ, 60^\circ, 90^\circ$ ($3 \times 3$ array); dashed line: aligned dipoles ($\hat{\bm{y}}$).
• Figure 4: Plots showing the convergence of the maximum value of the Purcell Factor (a) Max[$F_P$] and (b) resonant Wavelength as a function of the number of scatterers included in the square lattice. The dashed lines in both plots are numerical fittings using the expressions (a) $\text{Max}[F_p] = F_{p,\infty} + A e^{-B*N}$ and (b) $\lambda = \lambda_\infty + C/N^p$, shown by the grey dashed curves. The infinite limit values, $F_{p,\infty}=13.85$ and $\lambda_\infty=708.71$nm, are indicated by the horizontal dashed line in (a) and (b), respectively. The vertical dashed line indicates the $21\times21$ lattice considered throughout the main text.
• Figure 5: $\mathcal{G}^{(2)}(0,0)$ as a function of the total number of emitters for the finite metasurface (red), infinite metasurface under the single mode approximation in Eq. (\ref{['BIC only G2']})(green), and in free space (blue). As seen previously in Fig. \ref{['Lattice Superraidance']}a, but now with the addition of an emitter lattice with separation $d=800$nm in the presence of the metasurface.