Biphoton entanglement of topologically distinct modes

The robust generation and manipulation of entangled multiphoton states on chip has an essential role in quantum computation and communication. Lattice topology has emerged as a means of protecting photonic states from disorder, but entanglement across different topologies remains unexplored. We report biphoton entanglement between topologically distinct spatial modes in a bipartite array of silicon waveguides. The results highlight topology as an additional degree of freedom for entanglement and open avenues for investigating information teleportation between trivial and topological modes.

Figure 1

Bipartite array of silicon waveguides that is complementary metal-oxide semiconductor (CMOS) compatible, and experimental setup. (a) Pulses from a mode-locked laser are coupled into the center of a short-short defect of the array, whose five center waveguides are fanned out and coupled to individual tunable filters and polarization controllers before being detected with single-photon detectors and a time-correlation circuit. Inset: Scanning electron microscope (SEM) image of a portion of the array. (b) Detail of the short-short defect. (c) Schematic of degenerate spontaneous four-wave mixing.

Figure 2

Simulations of classical and quantum dynamics. (a) Amplitude distributions of the three eigenmodes colocalized at the short-short defect. (b) Normalized pump intensity, showing beating between two trivial modes. (c) Biphoton probabilities, showing beating between the topological and the two trivial modes. (d)–(f) Spatial biphoton probabilities and (g)–(i) biphoton population of localized eigenmodes at propagation points A–C, respectively. Topo., topological; Wg., waveguide.

Figure 3

Experimentally measured correlated photon counts (left) and simulated biphoton probabilities (right) at the lattice output with (a) $\delta =0$, (b) $\delta =0.2$, and (c) $\delta =0.4$.

Figure 4

(a) Relation between eigenenergy and disorder strength $\delta \in [0,0.5]$. The zero-energy topological mode is robust to disorder. The extended and topological eigenmodes at each level of disorder are plotted in different colors. (b) Average relative weights as probabilities of topological and trivial biphoton eigenmodes, $p_{\text{bi-ph}}$, with respect to the disorder strength.