Efficient photon-pair emission from a nanostructured resonator and its theoretical description

Abstract

Spontaneous parametric down-conversion (SPDC) in subwavelength nonlinear nanostructures is emerging as a promising source of quantum light, owing to its intrinsic multifunctionality and ability to generate versatile and complex quantum states. Despite this growing interest, the physical mechanisms governing photon-pair generation in nanostructures remain only partially understood. In particular, experimental investigations of key emission properties in individual resonators, such as spatial directionality and spectral characteristics, are still lacking, and predictive theoretical frameworks with direct experimental validation have not yet been established. Here we measure, for the first time, the spatial and spectral properties of photon pairs generated via SPDC in a lithium-niobate bullseye nanostructured resonator. Both spatial and spectral properties show a resonant behavior, which we describe within an extended quasi-normal-mode theoretical framework. This comparison with the theory is enabled by photon-pair count rates reaching up to 0.45 Hz/mW, to our knowledge, the highest reported to date for a nanostructured resonator. Our results provide new physical insight into SPDC in nanostructures and represent an important step toward predictive design strategies for efficient nanoscale sources of quantum light.

Figures (4)

• Figure 1: Spontaneous parametric down-conversion (SDPC) in a lithium niobate (LN) nanostructured resonator. (a) Conceptual picture of the entangled photon pair generated by the nanoresonator. (b) Near-field distribution (left panel) and far-field radiation pattern $|\mathbf{E}|^2$ (right panel, 3D and polar visualization on the $x-y$ plane) of the chosen quasi-normal mode $\text{QNM}_1$. The black arrows indicate the direction of the electric field inside the resonator. (c) Simulated normalized rate of coincidences as a function of the lateral scaling parameter $F_S$. The factor $F_S$ affects the detuning $\Delta\omega = (\omega_1 - \omega_{\mathrm{deg}})/(2\pi)$ between the eigenfrequency $\omega_1$ of QNM$_1$ and the degenerate angular frequency $\omega_{\mathrm{deg}}$, as well as the spatial overlap $\mathcal{G}_{1,1}$, shown with the green curve. (d) Pump electric field $|E_p(\mathbf{r})|$ inside the resonator, calculated for a plane wave with the intensity $I_0 = 10^9\,\mathrm{W/m^2}$ incident from the resonator side and polarized along the $z$-axis.
• Figure 2: Quasi-normal modes of the nano-resonator and modal-overlap coefficient. (a) Quality factors of all QNMs of the nanostructure, plotted versus the real parts of their eigenfrequencies. Labels indicate the modes exhibiting the largest modal-overlap coefficients $\xi_{m,n}$ across the reported range of frequencies. (b) Modal-overlap coefficients $\xi_{m,n}(\omega_s)$ for the nine QNM pairs with the highest peak values. The vertical dashed line marks the degenerate frequency. The red and blue shaded regions indicate the two frequency collection ranges used in the measurements shown in Fig. \ref{['fig:ExpSim']}. (c) Near-field and far-field distributions of two representative modes, $3$ and $8$, illustrating their different far-field patterns and intensities.
• Figure 3: Experimental implementation of SPDC in the nano-resonator (a) SEM picture of the nano-resonator at an intermediate stage of the nano-fabrication process. (b) Schematic view of the experimental setup. The continuous-wave laser power and polarization are controlled using two half-wave plates (HWPs) and a Glan–Taylor prism, and the beam is focused onto the nano-resonator by lens L1. The emitted light is collimated by lens L2. After spatial filtering, the beam is fed into a single-mode fiber by lens L3, and photon-pair coincidences are recorded using superconducting nanowire single-photon detectors (SNSPDs). Spatial properties are measured both with and without spectral filtering around the degenerate wavelength. Spectral properties are characterized by inserting a dispersive fiber after L3 and by introducing a $2\times$ magnifying system composed of lenses L4 and L5. (c) The distribution of the photon arrival time difference, with an incident power of 10 mW, demonstrating a coincidence peak due to the detection of photon pairs.
• Figure 4: Spatial and spectral properties of emission. (a) Directionality of the emitted photon pairs measured using knife-edge scans. Blue experimental points, fitted by the blue curve, are acquired with a $50$ nm bandpass filter centered at the resonance (degenerate) wavelength. Red points, fitted by the red curve, are acquired with a broader detection bandwidth $1340-1580\,\mathrm{nm}$. The shaded regions represent the simulated knife-edge scans, with the 95% confidence intervals of the fit. The insets show the far-field coincidence count rate distributions for both cases in 3D and in the plane $x-y$, computed with an account for the limited NA of the collection optics and the SMF. (b) Spectrum of the photon pairs. The experimental points are shown in blue and the simulated spectrum, in red. The yellow curve represents the simulated spectrum when a shift of $2 \, \mu m$ between the center of the SPDC emission and the center of the Gaussian mode of the SMF, considered at the tip.