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arXiv:2110.03110 · New Journal of Physics

Complete conversion between one and two photons in nonlinear waveguides: theory of dispersion engineering

Alexander S. Solntsev, S. Batalov, Nathan K. Langford, Andrey A. Sukhorukov

Published May 25, 2022• 4 citations
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Abstract

Abstract High-efficiency photon-pair production is a long-sought-after goal for many optical quantum technologies, and coherent photon conversion (CPC) processes are promising candidates for achieving this. We show theoretically how to control coherent conversion between a narrow-band pump photon and broadband photon pairs in nonlinear optical waveguides by tailoring frequency dispersion for broadband quantum frequency mixing. We reveal that complete deterministic conversion as well as pump-photon revival can be achieved at a finite propagation distance. We also find that high conversion efficiencies can be realised robustly over long propagation distances. These results demonstrate that dispersion engineering is a promising way to tune and optimise the CPC process.

DOI
10.1088/1367-2630/ac7348

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Abstract High-efficiency photon-pair production is a long-sought-after goal for many optical quantum technologies, and coherent photon conversion (CPC) processes are promising candidates for achieving this. We show theoretically how to control coherent conversion between a narrow-band pump photon and broadband photon pairs in nonlinear optical waveguides by tailoring frequency dispersion for broadband quantum frequency mixing. We reveal that complete deterministic conversion as well as pump-photon revival can be achieved at a finite propagation distance. We also find that high conversion efficiencies can be realised robustly over long propagation distances. These results demonstrate that dispersion engineering is a promising way to tune and optimise the CPC process.
Engineering and controlling well-defined states of light for quantum information applications is of increasing importance as the complexity of quantum systems grows. For example, in quantum networks, high multi-photon interference visibility requires properly devised pure photon sources. In this paper, we present a theoretical model for a spontaneous parametric down conversion source based on an integrated cavity-waveguide, where single narrow-band, possibly distinct, resonant modes for the idler and the signal fields can be generated. This mode selection takes advantage of the clustering effect, due to the intrinsic dispersion of the nonlinear material. We show that, by engineering the clustering effect in an integrated cavity-waveguide and by using a standard detector, one can efficiently generate heralded pure single photons even with a continuous-wave pumping mode. The photon source proposed in this paper is extremely flexible and could easily be adapted to a wide variety of wavelengths and applications, such as long-distance quantum communication.
In this Letter we demonstrate frequency conversion in the single-photon regime through Bragg-scattering four-wave mixing with near-unit efficiency in a 750 m long commercially available dispersion-engineered highly nonlinear fiber, where all photons and pump laser frequencies are in the low-loss telecommunications band. We achieve 99.1%±4.9% downconversion and 98.0%±5.0% upconversion of photons by 12 nm using a weak coherent state with an average input of 0.27 photons per detection gate window.
This thesis presents an analysis of photon pairs generated via either spontaneous parametric downconversion or spontaneous four-wave mixing in channel waveguides as well as in microring resonators side-coupled to channel waveguides. The state of photons exiting a particular device is calculated within a general Hamiltonian formalism that simplifies the link between quantum nonlinear optics experiments and classical nonlinear optics experiments. This state contains information regarding photon pair production efficiency as well as modal and spectral correlations between the two photons, characterized by a two-dimensional spectral distribution function called the biphoton wave function.\n\nIn the limit of a low probability of pair production, photon pair production fficiencies are cast into forms resembling corresponding well-known classical nonlinear optical frequency conversion efficiencies, making it easy to see what plays the role of a classical “seed” field in an un-seeded (quantum) process. This also allows photon pair production efficiencies to be calculated based on the results of classical nonlinear optical experiments. It is further calculated that, unless enerated photons are collected over a very narrow frequency range, their generation efficiency does not scale the same way with device length in a channel waveguide, or resonance quality factor in a microring resonator, as might be expected from the corresponding classical frequency conversion efficiency. Although calculations do not include self- or cross-phase modulation, nor two-photon absorption\nor free-carrier absorption, it is calculated that their neglect is justified in the low pair production probability limit. Linear (scattering) loss is also neglected, though partially addressed in the final chapter of this thesis.\n\nBiphoton wave functions are calculated explicitly, such that their shape and orientation, including approximate analytic expressions for their widths, can easily be determined. This further allows estimation of the suitability of their associated photon pairs for various quantum information processing applications. As an alternative to dispersion engineering a channel waveguide photon pair source, it is calculated that microring resonators can very naturally produce nearly spectrally uncorrelated photon pairs, which behave very much like idealized single-mode photons and are thus useful for applications involving the interference of photons from multiple sources.
Full control over the spatiotemporal structure of quantum states of light is an important goal in quantum optics, to generate, for instance, single-mode quantum pulses or to encode information on multiple modes, enhancing channel capacities. Quantum light pulses feature an inherent, rich spectral broadband-mode structure. In recent years, exploring the use of integrated optics as well as source engineering has led to a deep understanding of the pulse-mode structure of guided quantum states of light. In addition, several groups have started to investigate the manipulation of quantum states by means of single-photon frequency conversion. In this paper, we explore new routes towards complete control of the inherent pulse-modes of ultrafast pulsed quantum states by employing specifically designed nonlinear waveguides with adapted dispersion properties. Starting from our recently proposed quantum pulse gate (QPG), we further generalize the concept of spatiospectral engineering for arbitrary χ (2) -based quantum processes. We analyse the sum-frequency generation-based QPG and introduce the difference-frequency generation-based quantum pulse shaper (QPS). Together, these versatile and robust integrated optical devices allow for arbitrary manipulations of the pulse-mode structure of ultrafast pulsed quantum states. The QPG can be utilized to select an arbitrary pulse mode from a multimode input state, whereas the QPS enables the generation of specific pulse modes from an input wavepacket with a Gaussian-shaped spectrum.