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Effects of nonlinear phase modulation on quantum frequency conversion using four-wave mixing Bragg scattering

Recently, we solved the coupled-mode equations for Bragg scattering (BS) in the low- and high-conversion regimes, but without the effects of nonlinear phase modulation (NPM). We now present solutions and Green functions in the low-conversion regime that include NPM. We find that NPM does not change the lowest-order conversion efficiency, but prevents complete separability (freedom from temporal entanglement). This problem is overcome to some degree by pre-chirping the pumps, which mitigates the effects of NPM. We conclude that arbitrary reshaping of the output modes and nearly complete separability are still possible, even when the effects of NPM are included. Finally, the effects of using different input signals are considered, and we conclude that using the natural input modes of the system drastically increases the efficiency.