Waveguide and cavity quantum electrodynamics with topological bowtie modes

We present a theoretical study on photonic topological crystals whose symmetry is governed by quantum valley-Hall topological insulators and whose propagating edge modes are strongly confined due to bowtie geometries. Dielectric bowtie structures exploit the field discontinuities at boundaries between materials with different refractive indices, and here bowties emerge at the topological interface due to the close proximity of two triangular features in the underlying crystal. The topological bowtie mode features a unit-cell mode volume down to $8\times10^{-4}$ cubic wavelengths at the center of the bowtie bridge of width $10~\text{nm}$, and we show that it is possible to use perturbed versions of the unit cells as building blocks for topological heterostructure bowtie cavities with quality factors exceeding $10^7$. Due to the tightly confined bowtie mode, this implies a strongly enhanced light-matter interaction as quantified by a Purcell factor of $3 \times 10^6$.