Nonlinear tunneling and robust energy transfer in sum frequency generation

Based on the counter-diabatic protocol in quantum physics and the quasi-phase-matching method in nonlinear optics, we present a method of achieving robust energy transfer between the sum frequency and signal fields in an optical crystal system by adding a counter-diabatic field (CDF). Adding the CDF does not loosen the adiabatic condition, but rather separates the single original diabatic step into two so that the system remains adiabatic. The two resulting diabatic steps exhibit nonlinear tunneling, where the second step is the inverse of the first one. Moreover, we predict the fabrication of a nonlinear optical crystal with quasi-periodicity in terms of the CDF. Not only does this work provide a solid theoretical foundation for the design of nonlinear optical devices, but it also elucidates physical processes that can be applied in many areas of modern science, ranging from quantum information processing and coherent manipulation of quantum systems to high-precision measurements.