Accelerated Topological Pumping in Photonic Waveguides Based on Global Adiabatic Criteria

Abstract

Adiabatic topological pumping promises robust transport of energy and information, but its speed is fundamentally limited by the instantaneous adiabatic condition, which demands prohibitively slow parameter variations. Here we develop a paradigm shift from instantaneous to global adiabaticity. We derive a global adiabatic criterion (GAC), which sets an absolute fidelity bound by controlling the root-mean-square value of nonadiabaticity factor. We further introduce a fluctuation-suppression acceleration criterion, which minimizes spatial inhomogeneity and allows us to safely increase the mean nonadiabaticity. Experimentally, we implement this principle in femtosecond-laser-written photonic Su-Schrieffer-Heeger waveguide arrays via scalable power-law coupling modulation. Our accelerated topological pumping achieves >0.95 fidelity over a fivefold reduced device length compared to the conventional scheme, exhibits the predicted linear scaling with the system size, and maintains robust performance across a >400 nm bandwidth. This principle of GAC provides a universal design rule for fast, compact, and robust adiabatic devices across quantum and classical topological platforms.

Figures (4)

• Figure 1: Illustration of acceleration strategy. (a) Schematic diagram of the nonadiabatic factor $Q_{\mathrm{non}}(z)$ affecting topological pumping. The global adiabatic scheme with a higher and flatter $Q_{\mathrm{non}}(z)$ enables fast topological pumping, while the conventional scheme (labeled "conv.") is slow with lower ${\overline Q}_{\mathrm{non}}$ or failed with higher ${\overline Q}_{\mathrm{non}}$. (b) Dimerized SSH model with modulated intracell and intercell hopping rates $J_1(z)$ and $J_2(z)$, implementing topological transport from the left edge state $|\Psi_L\rangle$ to the right $|\Psi_R\rangle$. (c) Bottom panel: schematic of a spatially modulated SSH lattice of photonic waveguides fabricated inside a glass; Top panel: photograph of the fabricated sample of waveguides at the output facet.
• Figure 2: Scalability of GAAC-based topological pumping. (a) Critical device length $L_{0.99}$ (in units of $J_{\text{max}}^{-1}$) required to achieve $\mathcal{F}(L) >0.99$, $\forall L>L_{0.99}$, as a function of $N$. For our strategy (blue), circles: numerical data; Solid line: fitted data. For the conventional scheme (red), squares: numerical data; Dashed line: fitted data. (b) Comparison of minimum energy gaps between our acceleration strategy and the conventional scheme (see Note 4 in SMSM for more details). (c) ${\overline Q}_{\mathrm{non}}$ and $\sigma_Q^2$ versus $L$ and $\alpha$ for $N=13$ based on the global adiabatic criteria and the conventional adiabatic scheme, respectively. (d) Numerical fidelity versus different $L$ and $\alpha$ for $N=13$, calculated by CME. Five ${\mathcal{F}}$-$L$ lines with $\alpha=1$-$5$, as well as the ${\mathcal{F}}$-$L$ line of the conventional pumping, are projected onto the leftmost ${\mathcal{F}}$-$L$ plane for comparison.
• Figure 3: Acceleration performance. (a)-(c) Theoretical (Theo.) light propagation and experimentally measured ("Exp.") light intensity patterns at the output facet for our acceleration strategy and the conventional scheme with sample lengths $L=35$ mm, $55$ mm, and $75$ mm, respectively.
• Figure 4: Broadband performances. (a) Predicted pumping fidelity at $L=55$ mm with input wavelength ranging from $600$ nm to $1000$ nm for our acceleration strategy and the conventional pumping scheme. (b) Measured light intensity patterns at the end facets of two samples working at specified four wavelengths instead of 808 nm.