Topological protection of continuous frequency entangled biphoton states

Abstract

Topological quantum optics that manipulates the topological protection of quantum states has attracted special interests in recent years. Here we demonstrate valley photonic crystals implementing topologically protected transport of the continuous frequency entangled biphoton states. We numerically simulate the nonlinear four-wave mixing interaction of topological valley kink states propagating along the interface between two valley photonic crystals. We theoretically clarify that the signal and idler photons generated from the four-wave mixing interaction are continuous frequency entangled. The numerical simulation results imply that the entangled biphoton states are robust against the sharp bends and scattering, giving clear evidence of topological protection of entangled photon pairs. Our proposal paves a concrete way to perform topological protection of entangled quantum states operating at telecommunication wavelengths.

Generation of Quantum Optical Frequency Combs in Topological Resonators

“…More importantly, there is no input for the idler, therefore, the excitation of idler modes indicates the generation of simulated FWM processes. [ 30 ]…”

“…For simplified simulation, it used an equivalent refractive index of silicon as n = 2.965 in 2D configuration to effectively simulate realistic VPCs. [30,34,49] The FWM process governed by the third-order nonlinear polarizations of silicon can be described by…”

“…For simplified simulation, it used an equivalent refractive index of silicon as $$n=2.965$$ in 2D configuration to effectively simulate realistic VPCs. [ 30,34,49 ] The FWM process governed by the third‐order nonlinear polarizations of silicon can be described by $$$$\begin{equation} \mathbf {P}_{p}{\left(\omega _{s}+\omega _{i}-\omega _{p}\right)}=6\varepsilon _{0}\chi ^{(3)}E_{s}E_{i}E_{p}^{*} \end{equation}$$$$ $$$$\begin{equation} \mathbf {P}_{s}{\left(\omega _{p}+\omega _{p}-\omega _{i}\right)}=3\varepsilon _{0}\chi ^{(3)}E_{p}E_{p}E_{i}^{*} \end{equation}$$$$ $$$$\begin{equation} \mathbf {P}_{i}{\left(\omega _{p}+\omega _{p}-\omega _{s}\right)}=3\varepsilon _{0}\chi ^{(3)}E_{p}E_{p}E_{s}^{*} \end{equation}$$$$where $$\mathbf {P}_{p,s,i}$$ and $$E_{p,s,i}$$ are the polarizations and electric field of the pump, signal, and idler, respectively. The third‐order nonlinearity of silicon was take as …”

“…More importantly, there is no input for the idler, therefore, the excitation of idler modes indicates the generation of simulated FWM processes. [30] For the perfect triangular cavity, the frequencies of the pump, signal, and idler are chosen as f s = 192.31 THz, f p = 191.52 THz, and f i = 190.73 THz, respectively. As shown in Figure 4, the field profiles of resonator modes at the idler frequency give clear evidence of the simulated FWM process.…”

“…Subsequently, emergent advances in topological quantum photonics have been proposed, including topological single quantum emitters, [25][26][27] topological quantum interference, [28] and even topological entangled states. [29][30][31] However, the production of quantum frequency combs with high-dimensional entanglement generated in a super-compact topological device remains significantly challenging.…”