  The method of adiabatic frequency conversion, in analogy with the 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 we present a comparative study of efficient frequency mixing
using various techniques of shortcuts to adiabaticity (STA) such as
counter-diabatic driving and invariant-based inverse engineering. We show 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 is significantly decreases beyond the adiabatic limit. Our 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, we show 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.

Quantum Physics;Optics