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arXiv:1707.03363 · Physical Review A

Effect of self- and cross-phase modulation on photon pairs generated by spontaneous four-wave mixing in integrated optical waveguides

Gary F. Sinclair, Mark G. Thompson

Published Dec 27, 2016• 17 citations
arXivHTMLPDF

Abstract

A time-domain approach using the momentum operator is used to model spontaneous four-wave mixing in a lossless nonlinear waveguide. The effects of self- and cross-phase modulation on the photon-pair production rate and heralded photon purity are investigated. We show that in the special case where only one half of the photon-pair state is filtered the generation rate and purity of the heralded photons are unmodified by the presence of self- and cross-phase modulation. The significance of this special case arises when we consider heralded single-photon sources, where future schemes are likely to only filter the herald photon to ensure a high heralding efficiency is maintained.

DOI
10.1103/physreva.94.063855

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A time-domain approach using the momentum operator is used to model spontaneous four-wave mixing in a lossless nonlinear waveguide. The effects of self- and cross-phase modulation on the photon-pair production rate and heralded photon purity are investigated. We show that in the special case where only one half of the photon-pair state is filtered the generation rate and purity of the heralded photons are unmodified by the presence of self- and cross-phase modulation. The significance of this special case arises when we consider heralded single-photon sources, where future schemes are likely to only filter the herald photon to ensure a high heralding efficiency is maintained.
We consider the effect of self-phase modulation and cross-phase modulation on the joint spectral amplitude of photon pairs generated by spontaneous four-wave mixing. In particular, the purity of a heralded photon from a pair is considered in the context of schemes that aim to maximize the purity and minimize correlation in the joint spectral amplitude using birefringent phase matching and short pump pulses. We find that nonlinear phase-modulation effects will be detrimental and will limit the quantum interference visibility that can be achieved at a given generation rate. An approximate expression for the joint spectral amplitude with phase modulation is found by considering the group velocity walk-off between each photon and the pump but neglecting the group-velocity dispersion at each wavelength. The group-velocity dispersion can also be included with a numerical calculation, and it is shown that it has only a small effect on the purity for the realistic parameters considered.
We present a general model, based on a Hamiltonian approach, for the joint quantum state of photon pairs generated through pulsed spontaneous four-wave mixing, including nonlinear phase modulation and a finite material response time. For the case of a silica fiber, it is found that the pair-production rate depends weakly on the waveguide temperature, due to higher-order Raman scattering events, and more strongly on pump-pair frequency detuning. From the analytical model, a numerical scheme is derived, based on the well-known split-step method. This scheme allows computation of joint states where nontrivial effects are included, such as group-velocity dispersion and Raman scattering. In this work, the numerical model is used to study the impact of the noninstantaneous response on the prefiltering purity of heralded single photons. We find that for pump pulses shorter than 1 ps, a significant detuning-dependent change in quantum-mechanical purity may be observed in silica. This shows that Raman scattering not only introduces noise, but can also drastically change the spectral correlations in photon pairs when pumped with short pulses.
We investigate theoretically the spontaneous four-wave mixing (FWM) process that occurs in optical waveguides, as a source of quantum correlated photon-pairs. We consider that the waveguide used to implement the spontaneous FWM process presents a high value of nonlinear parameter, γ = 93.4 W-1m-1, and a non-negligible value of loss coefficient, α = 133.3 dB/m. Moreover, the theoretical model also consider the Raman scattering that inevitably accompanies the FWM process, and generates time-uncorrelated (noise) photon pairs. We use the coincident-to-accidental ratio (CAR) as a figure of merit of the photon pair source, and we were able to observe a CAR of the order of 65 in a high loss regime. After, we use the time-correlated photon pairs generated by the spontaneous FWM process to implement a heralded single photon source at waveguide output. In this scenario, the detection of one photon of the pair heralds the presence of the other photon. The quality of the source was studied by the evaluation of the second order coherence function for one photon of the pair conditioned by the detection of its twin photon. We observe that the presence of a high loss coefficient tends to improve the quality of the photon source, when compared with the lossless regime, even considering the Raman noise photons. We obtain a value for the conditional second order coherence function of the order of 0.11 in absence of loss, and a value of 0.03 for a loss coefficient of 133.3 dB/m.
We study the preparation of heralded single-photon states using dual-pump spontaneous four-wave mixing. The dual-pump configuration, which in our case employs cross-polarized pumps, allows for a gradual variation of the nonlinear interaction strength enabled by a birefringence-induced walk-off between the pump pulses. The scheme enables the preparation of highly pure heralded single-photon states, and proves to be extremely robust against the effect of nonlinear phase modulation at the required photon-pair production rates.
We model the spectral quantum-mechanical purity of heralded single photons from a photon-pair source based on nondegenerate spontaneous four-wave mixing taking the impact of distributed dispersion fluctuations into account. The considered photon-pair-generation scheme utilizes pump-pulse walk-off to produce pure heralded photons and phase matching is achieved through the dispersion properties of distinct spatial modes in a few-mode silica step-index fiber. We show that fiber-core-radius fluctuations in general severely impact the single-photon purity. Furthermore, by optimizing the fiber design we show that generation of single photons with very high spectral purity is feasible even in the presence of large core-radius fluctuations. At the same time, contamination from spontaneous Raman scattering is greatly mitigated by separating the single-photon frequency by more than 32 THz from the pump frequency.