Topological protection of photon-pair generation in nonlinear waveguide arrays

Abstract

Harnessing topological effects offers a promising route to protect quantum states of light from imperfections, potentially enabling more robust platforms for quantum information processing. This capability is particularly relevant for active photonic circuits that generate quantum light directly on-chip. Here, we explore topological effects on photon-pair generation via spontaneous parametric down-conversion (SPDC) in nonlinear waveguide arrays, both theoretically and experimentally. A systematic comparison of homogeneous, trivial, and topological Su-Schrieffer-Heeger arrays reveals that only the topological configuration preserves a stable SPDC resonance spectrum under disorder in the tunnel couplings, with fluctuations in the resonance position reduced by more than one order of magnitude. An analytical model supports our experimental observations by linking this robustness to the band-structure properties of the interacting modes. These findings establish quadratic nonlinear waveguide arrays as a promising platform to explore the interplay of nonlinearity, topology, and disorder in quantum photonic circuits.

Figures (4)

• Figure 1: Working principle of a quadratic nonlinear waveguide array (here implementing the Su–Schrieffer–Heeger model). A monochromatic pump beam at frequency $\omega_p$ is injected into the central waveguide, generating pairs of signal and idler photons through spontaneous parametric down-conversion. These photons can tunnel between adjacent waveguides with coupling constants $C_{n,n+1}$. The resonance spectrum (inset) quantifies the efficiency of this nonlinear process as a function of the pump frequency, and its sensitivity to disorder in the coupling constants is investigated.
• Figure 2: First column: (a) Schematic and (b) band structure of a homogeneous waveguide array. (c) Calculated SPDC resonance spectra in the absence of disorder (black thick line) and for 4 random disorder realizations (thin colored lines) with disorder strength $\Delta = 40\%$. (d) Mean value and standard deviation (error bars) of the spectral overlap between the disordered (300 realizations) and disorder-free cases, as a function of disorder strength. (e) Mean value and standard deviation (error bars) of the resonance-peak shift relative to the disorder-free case, as a function of disorder strength. Second column: same quantities for an array featuring a trivial localized mode at its center, with defect amplitude $\delta = 2C$ (see text). Third column: same quantities for a topological array implementing the Su–Schrieffer–Heeger model with dimerization parameter $K=0.5$. Simulation parameters: all arrays contain 13 waveguides of length $L = 2$ mm, with mean coupling constant $C = 2.5$ mm$^{-1}$, pump coupling parameter $\alpha = 0.2$, and single-waveguide phase mismatch $\Delta\beta^{(0)}(\omega_p) = a(\omega_p - \omega_p^{(0)})$, where $2\pi c /\omega_p^{(0)}=775$ nm and $a \simeq 3$ fs/mm correspond to typical values in our experiments.
• Figure 3: SEM image of a fabricated AlGaAs topological SSH array with an input waveguide for the pump beam. The inset shows a close-up of the alternating short and long spacings between adjacent waveguides, resulting in alternating high and low coupling constants with a dimerization parameter $K = 0.5$.
• Figure 4: (a) Measured SPDC resonance spectra in AlGaAs homogeneous waveguide arrays without disorder (bottom trace) and for various random disorder realizations with amplitude $\Delta = 40\%$. (b) Same measurement for arrays featuring a trivial localized mode at the center, and (c) for topological SSH arrays. All spectra are normalized to 1 and vertically offset for clarity. (d) Experimental fluctuations (standard deviation) of the resonance-peak position for the three types of arrays at disorder strengths $\Delta = 40\%$ (blue bars) and $\Delta = 20\%$ (red bars). (e) Mean pairwise overlap between the SPDC resonance spectra, under the same conditions as in (d).