Generation of frequency entanglement by rotating Doppler effect

We propose a method to generate the frequency entanglement, allowing a continuous generation of entangled two-photon states in a hybrid degree of freedom by post-manipulation. Our method is based on type-II spontaneous parametric down-conversion in a nonlinear crystal and the rotation Doppler effect by rotating the q-plates, without preset discrete frequency entanglement. This allows the arbitrary modification of frequency entangled photons in a wide frequency range at room temperature, offering enhanced flexibility for quantum information tasks and quantum metrology. We also analyze the entanglement state by a combined calculation for the joint spectrum and Hong-Ou-Mandel interference of the two photons, which can be used to reconstruct a restricted density matrix in the frequency space.