Topologically Protected Valley-Dependent Quantum Photonic Circuits

Topological photonics has been introduced as a powerful platform for integrated optics, since it can deal with robust light transport, and be further extended to the quantum world. Strikingly, valley-contrasting physics in topological photonic structures contributes to valley-related edge states, their unidirectional coupling, and even valley-dependent wave division in topological junctions. Here, we design and fabricate nanophotonic topological harpoon-shaped beam splitters (HSBSs) based on 120-deg-bending interfaces and demonstrate the first on-chip valley-dependent quantum information process. Two-photon quantum interference, namely, Hong-Ou-Mandel interference with a high visibility of $0.956\pm 0.006$, is realized with our $50/50$ HSBS, which is constructed by two topologically distinct domain walls. Cascading this kind of HSBS together, we also demonstrate a simple quantum photonic circuit and generation of a path-entangled state. Our work shows that the photonic valley state can be used in quantum information processing, and it is possible to realize more complex quantum circuits with valley-dependent photonic topological insulators, which provides a novel method for on-chip quantum information processing.

Figure 1

Topological valley photonic crystal and band structure. (a) Unit cell of valley photonic crystal 1 (VPC1) and VPC2. (b) Distribution of TE1 Berry curvature for VPC1 (left) and VPC2 (right). The peak of the Berry curvature is mainly localized around the $K^{\prime }(K)$ valley, while the sink is around the $K(K^{\prime })$ valley. (c) Bulk band for both VPC1 and VPC2, where the TE-like polarization band gap lies between 1520 and 1600 nm. (d) Dispersion relations of topological interfaces $I_{12}$ and $I_{21}$ (shown in Fig. 2). The green and blue dotted lines correspond to $I_{12}$ and $I_{21}$, respectively. States at the two nonequivalent valleys possess opposite-sign group velocities.

Figure 2

Phase vortex and selective coupling of valley-dependent edge states. (a) Electromagnetic phase vortex inside the unit cells of VPC1 and VPC2 at the TE1 band (simulated results). VPC1 supports clockwise and anticlockwise rotating states at different valleys, with the opposite results for VPC2. (b),(c) Directional edge state transport of the two topologically distinct valley photonic crystals at the $K$ valley. The valley-dependent backward (interface $I_{12}$) or forward (interface $I_{21}$) propagation of the edge states is formed. More cases of directional edge state transport are available in the Supplemental Material [31]. (d) Valley-dependent wave division at a topological junction. Photons are coupled into port $a$ at the $K$ valley (red arrow), then the propagating photons at the junction will couple into port $c/d$ and the coupling to port $b$ (blue arrow) is suppressed.

Figure 3

Transmission spectra of the valley-dependent photonic circuits. (a) Scanning electron microscopy (SEM) image of the harpoon-shaped beam splitter (HSBS). (b) Simulation of the light evolution in our HSBS. (c) SEM image of the valley-dependent photonic circuits. (d) Simulated and (e) measured transmission spectra for the photonic circuits shown in (c). Broadband $50/50$ beam splitters in the band gap range from 1520 to 1600 nm are obtained both theoretically and experimentally.

Figure 4

Topologically protected valley-dependent quantum circuits. (a) Experimental setup for the on-chip HOM interference. TEC, thermoelectric cooler; PBS, polarization beam splitter; HWP, half-wave plate; PC, polarization controllers; TCSPC, time-correlated single photon counting. Two-photon off-chip quantum interference using a fiber beam splitter for (b) the straight topological interface and (c) the $\mathrm{\Omega }$-shaped topological interface. The visibilities are 0.969 and 0.977, respectively. (d) On-chip HOM interference for the harpoon-shaped beam splitter (HSBS), with a visibility of $0.956\pm 0.006$. Coincidence measurements are performed between port $c$ and port $f$. (e) Coincidence measurements between port $f$ and port $g$ of the quantum circuit. We obtain an interference curve with a peak pattern. The interference visibility is $0.999\pm 0.049$. The error bars are all calculated by assuming Poisson statistics.