Spectral effects of strong χ⁽²⁾ nonlinearity for quantum processing

Optical χ⁽²⁾ nonlinearity can be used for parametric amplification and producing down-converted entangled photon pairs that have broad applications. It is known that weak nonlinear media exhibit dispersion and produce a frequency response. It is therefore of interest to know how spectral effects of a strong χ⁽²⁾ crystal affect the performance. Here we model the spectral effects of the dispersion of a strong χ⁽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.