High efficiency in Mode Selective Frequency Conversion for Optical Quantum Information Processing

Mode selective Frequency conversion (FC) is an enabling process in many quantum information protocols \footnote{B. Brecht et al. Phys. Rev. X {\bf 5}, 041017 (2015)}. Recently, it has been observed that upconversion efficiencies in single-photon, mode-selective FC are limited to around 80\% \footnote{B. Brecht et al. Phys. Rev. A {\bf 90}, 030302 (2014)}. In this contribution we show that these limits can be understood as time ordering corrections (TOCs) that modify the joint conversion amplitude of the process \footnote{N. Quesada et al. Phys. Rev. A {\bf 90}, 063840 (2014).}. Furthermore we show, using a simple scaling argument, that recently proposed cascaded FC protocols \footnote{D.V. Reddy et al. Opt. Lett. {\bf 39}, 2924-2927 (2014).} that overcome the aforementioned limitations act as ``attenuators'' of the TOCs. This observation allows us to argue that very similar cascaded architectures can be used to attenuate TOCs in photon generation via spontaneous parametric down-conversion\footnote{N. Quesada et al., Phys. Rev. Lett. {\bf 114}, 093903 (2015).}. Finally, by using the Magnus expansion, we argue that the TOCs, which are usually considered detrimental for FC efficiency, can also be used to increase the efficiency of conversion in partially mode selective FC.