Efficient Broadband Frequency Conversion via Shortcuts to Adiabaticity

Abstract

The method of adiabatic frequency conversion, in analogy with a two-level atomic system, has been put forward recently and verified experimentally to achieve robust frequency mixing processes such as sum and difference frequency generation. Here a comparative study of efficient frequency mixing using various techniques of shortcuts to adiabaticity such as counter-diabatic driving and invariant-based inverse engineering is presented. It is shown here that it is possible to perform sum frequency generation by properly designing the poling structure of a periodically poled crystal and the coupling between the input lights and the crystal. The required crystal length for frequency conversion significantly decreases beyond the adiabatic limit. This approach significantly improves the robustness of the process against the variation in temperature as well as the signal frequency. By introducing a single parameter control technique with constant coupling and combining with the inverse engineering, perturbation theory, and optimal control, it is shown that the phase mismatch can be further optimized with respect to the fluctuations of input wavelength and crystal temperature that results into a novel experimentally realizable mixing scheme.