Quantum Walks of Two-Photon Wannier States in Nonlinear Waveguide Lattices with Floquet-Modulated Coupling

Thouless pumping has been realized both theoretically and experimentally in photonic waveguide lattices with Floquet-modulated coupling, including demonstrations of topological phenomena like integer and fractional quantized motion of solitons in nonlinear lattices. However, these demonstrations were with classical coherent light, which is similar to the dynamics of a single particle in such lattices. On the other hand, two-particle evolution has been observed in atomic and photonic lattices with constant coupling, demonstrating nontrivial quantum correlations, interference, and entanglement. Here we study the dynamics of two-photon states in nonlinear waveguide lattices with Floquet-modulated coupling. We predict a band-dependent evolution and localization of two-photon Wannier states that cannot be explained in the classical or single-photon regime. Our work shows that the transport of Wannier states through nonlinear waveguide lattices with Floquet-modulated coupling exhibits uniquely different features compared to both classical transport through nonlinear lattices and two-photon quantum transport through constant-coupling and linear lattices. These results have applications for analog quantum simulation and engineering topological systems using photonic devices.