Quadrupole topological phases in the zero-dimensional optical cavity

The quadrupole topological insulator, which supports robust corner states, has been recently demonstrated in two-dimensional (2D) spatial lattices. Here, we design the first photonic quadrupole topological insulator in fully synthetic spaces with the utilization of 0D optical cavity. The frequency and orbital angular momentum (OAM) of light are used to form the 2D synthetic spaces. Four degenerate polarization states are mapped to the internal lattice sites within the unit cell. By suitably engineering the coupling between cavity modes with different frequencies, OAMs and polarizations, the ideal synthetic quadrupole topological insulator is obtained. By using the robust synthetic corner states, we present the possibility for the realization of topological transportation of multi-photon entangled states. Our designed synthetic photonic quadrupole insulator proposes a unique platform to investigate higher-order topological phases in lower-dimensional systems and possesses potential applications in quantum information and optical communication.