Biphoton topology in a quadratic nonlinear waveguide array under the Su-Schrieffer-Heeger model

We demonstrate the generation of a stable topologically nontrivial biphoton state with a high degree of quantum entanglement by the bosonic Bogoliubov Hamiltonian in a quadratic nonlinear waveguide array (QNWA) under the Su-Schrieffer-Heeger model. Analysis of its energy spectrum and eigenmode spectra verifies that this biphoton state is a topological nontrivial edge state characterized by the nonzero Berry phase at 1/4 and 3/4 fillings. The changes of Berry phase at 1/4 and 3/4 fillings indicate the topological quantum transition. The topological robustness of the biphoton edge state can be demonstrated by the spatial correlation under random disorders in propagation constant of the QNWA. It is also shown that the Renyi entanglement entropy of this topologically nontrivial biphoton state can approach high values. The robustness of this topologically nontrivial property suggests the promising application of this highly entangled biphoton state in quantum computing and information.