Multiband Topological Heterojunctions on the Surface Nanoscale Axial Photonics Platform

TL;DR

This work establishes the Surface Nanoscale Axial Photonics (SNAP) platform as a premier medium for analogue Hamiltonian simulation of 1D topological insulators. By fabricating and post-processingから, the authors realize SSH lattices across multiple axial-mode bands and demonstrate a multiband heterojunction between SSH2 and SSH4 configurations, observing both topological edge states and interface modes. They further develop a generalized, multiband topological framework based on relative Bloch phases and sublattice displacements to predict bound and quasi-bound modes at heterojunctions, even when global symmetries are imperfect. The combination of ultra-low loss, angstrom-level precision, and the ability to host multiple axial orders enables complex, scalable AHS experiments and points toward nonlinear and higher-dimensional topology via synthetic dimensions on SNAP.

Abstract

Analogue Hamiltonian simulation (AHS) in photonic systems can be an enticing alternative to direct experimental study of complex Hamiltonian systems as a result of the low cost and high degree of control one can have over the system's properties. Notably, the field of topological photonics has emerged in the last decade primarily by simulating tight-binding models of electrons within topologically nontrivial condensed-matter systems. Optical simulation of topologically nontrivial Hamiltonians requires optical resonators with minimal loss and well-matched frequencies whose intersite coupling can also be precisely controlled. The Surface Nanoscale Axial Photonics (SNAP) platform satisfies all these requirements, exhibiting ultra-low loss operation and sub-angstrom fabrication precision, making it an excellent platform for AHS. In this work, we experimentally demonstrate the first topologically nontrivial photonic SNAP devices by coupling together axial modes of adjacent SNAP microresonators to form a variety of Su-Schrieffer-Heeger (SSH) lattices. The devices manifest numerous distinct topological band structures corresponding to each axial mode of the microresonators, enabling us to observe behavior both close to and far from the topological-trivial phase transition. We further expand the scope of topological SNAP systems to contain not just higher-order generalizations of SSH lattices, but junctions between multiband lattices with dissimilar topological phases created by coupling up to 21 uniform and well-matched SNAP microresonators. Analyzing such "heterojunctions" necessitated our development of generalized topological polarization methods. We thus demonstrate the exceptional promise of the SNAP platform for AHS of 1D topological insulators, and also open the door to the potential for simulating >2 dimensional systems by utilizing nonlinear interactions.

Figures (8)

• Figure 1: (a) Visualization of the CO$_2$ laser annealing fabrication process and the tapered optical microfiber scanning method (feature sizes not to scale). (b) A "polymer" depiction of an SSH2 lattice with 10 sites and staggered couplings $v_1$ and $v_2$. Unit cells are labeled by an integer $n\in \{0,1,\ldots,5\}$, with the depicted structure having 4 full unit cells and 2 half unit cells. Each of the sites within are labeled by an integer $s=1,2$. Spectrograms from a (c) computational model and (d) experimental data of the above SNAP device presenting several axial orders corresponding to the band structure of lattices analogous to that of (b). Blue lines represent the estimated ERV profile along the fiber axis and thus an optical potential. Red arrows point to locations of loss-inducing localized defects.
• Figure 2: (a) Computed spectrogram of two adjacent sites with $\Delta z =115$$\mu$m showcasing hybridization of axial modes (color coded). The $q=1$ fundamental modes are unhybridized, while the high-order modes are almost completely hybridized. (b) Wavelength splitting induced as a function of intersite spacing for $q=1$ to $8$ axial modes of the SNAP resonators. At large $\Delta z$, the expected exponential decay is observed. At small $\Delta z$, a saturation of the wavelength splitting, and hence of the coupling between the sites, is observed.
• Figure 3: Measured (a,b) and model (c, d) spectrograms of 5-site SSH model. Purple rectangle corresponds to focused views (b,d) showing the $q=4$ and $q=5$ axial mode families. The lower-order mode families (higher in resonance wavelength) are too localized to observe coupling between the lattice sites. False color orange overlays highlight topological edge modes for $q=4,5$ and dark (light) green arrows indicate the positive (negative) energy bands.
• Figure 4: Band structure of a (a) SSH2 lattice and of a (b) SSH4 lattice. Upper (lower) bands are red (blue), and inner (outer) bands are dashed (dotted). (c) bare tight-binding Green's function sumetsky_theory_2012 intensity (arb. units) of tight-binding model of a large SSH2 lattice on the left (${v}_{L}(s)=[1,0.5]$, $N=400$ unit cells) conjoined to an SSH4 lattice on the right (${v}_{R}(s)=[1,0.7,1,0.3]$, $N=400$ unit cells). Zero energy topological bound mode are tinted orange, non-zero energy bound modes are tinted green, and yellow arrows indicate the quasi-bound modes. Colored brackets next to the bands indicate the corresponding bands in (a,b). (d) Polymeric diagram of a 21 site lattice. The site on the (dashed purple) domain line can be considered a part of either lattice. (e) Measured spectrogram of a topological heterojunction. An SSH2 lattice ($v_j$ correspond to spacings of 100 $\mu$m and $125$$\mu$m) is conjoined to an SSH4 lattice ($v_j$ correspond to spacings of 100 $\mu$m, 105 $\mu$m, 100 $\mu$m, and 130 $\mu$m). This measured spectrogram closely follows the tight-binding spectrogram in (a) barring the expected local self-coupling shifts, also present in Figs. \ref{['fig:1']} and \ref{['fig:3']}. Arrows and brackets indicate correspondence between modes and bands as in (a-c).
• Figure 5: (a) Measured and (b) Fitted Model Spectrogram of a SNAP resonator comparable to those created in this work.