Spectral Effects of Strong Chi-2 Non-Linearity for Quantum Processing

TL;DR

This paper models the spectral effects of strong chi-2 non-linearity in crystals, revealing how dispersion impacts quantum measurement and gate performance, and proposes conditions to mitigate spectral entanglement.

Contribution

It introduces a Dyson series approach to model spectral effects in strong chi-2 non-linear crystals and identifies a periodic poling regime where entanglement can be minimized.

Findings

Dyson series expansion captures spectral entanglement effects.

Periodic poling can suppress unwanted spectral entanglement.

Spectral effects influence Bell measurements and quantum gate performance.

Abstract

Optical $\chi^{(2)}$ non-linearity can be used for parametric amplification and producing down-converted entangled photon pairs that have broad applications. It is known that weak non-linear media exhibit dispersion and produce a frequency response. It is therefore of interest to know how spectral effects of a strong $\chi^{(2)}$ crystal affect the performance. Here we model the spectral effects of the dispersion of a strong $\chi^{(2)}$ crystal and illustrate how this affects its ability to perform Bell measurements and influence the performance of a quantum gates that employ such a Bell measurement. We show that a Dyson series expansion of the unitary operator is necessary in general, leading to unwanted spectral entanglement. We identify a limiting situation employing periodic poling, in which a Taylor series expansion is a good approximation and this entanglement can be removed.