Hong-Ou-Mandel interference in a temporal-average-inversion-symmetric chain

We show how to implement a tunable beam splitter and Hong-Ou-Mandel interference in the Su-Schrieffer-Heeger chain by manipulating the topological edge states adiabatically. The boson initially injected in the single end of the chain can be transferred to the double end with a tunable proportion that depends on the dynamical phases accumulated during the adiabatic evolution. We also observe Hong-Ou-Mandel interference via the tunable (50:50) beam splitter and achieve a spatially entangled two-particle NOON state. We demonstrate the robustness of our proposal under chiral- and time-reversal-symmetry-preserving disorder. However, chiral symmetry is scarce for realist systems. Therefore, we demonstrate that Hong-Ou-Mandel interference is robust to inversion-symmetric disorder breaking the chiral symmetry, highlighting the protection of inversion symmetry. More importantly, the inversion symmetry violated by static disorder can be restored for more common situations where disorder becomes time dependent, giving rise to the Hong-Ou-Mandel interference protected by temporal-average-inversion symmetry. Our approach provides an alternative way to study quantum effects in topological matter with potential applications..