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Developing a quantum light source that carries more than one bit per photon is pivotal for expanding quantum information applications. Characterizing a high-dimensional multiple-degree-of-freedom source at the single-photon level is challenging due to the large parameter space as well as limited emission rates and detection efficiencies. Here, we characterize photon pairs generated in optical fiber in the transverse-mode and frequency degrees of freedom by applying stimulated emission in both degrees of freedom while detecting in one of them at a time. This method may be useful in the quantum state estimation and optimization of various photon-pair source platforms in which complicated correlations across multiple degrees of freedom may be present., Comment: 14 pages, 5 figures; supplemental document 6 pages, 5 figures

The purpose of this tutorial paper is to present a broad overview of photon-pair generation through the spontaneous four wave mixing (SFWM) process in optical fibers. Progress in optical fiber technology means that today we have at our disposal a wide variety of types of fiber, which together with the fact that SFWM uses two pump fields, implies a truly remarkable versatility in the resulting possible photon-pair properties. We discuss how the interplay of the frequency, transverse mode, and polarization degrees of freedom, the first linked to the latter two through fiber dispersion, leads to interesting entanglement properties both in individual degrees of freedom and also permitting hybrid and hyper entanglement in combinations of degrees of freedom. This tutorial covers methods for photon pair factorability, frequency tunability, and SFWM bandwidth control, the effect of frequency non-degenerate and counter-propagating pumps, as well methods for characterizing photon pairs generated in optical fibers., Comment: 21 pages, 9 figures

The emission of light of an efficient single-photon emitter (SPE) should have a high-count rate into a well-defined spatio-temporal mode along with an accessible numerical aperture (NA) to increase the light extraction efficiency that is required for effective coupling into optical waveguides. Based on a previously developed experimental approach to fabricate hybrid Fabry-Perot microcavities (Further information is available [F. Ortiz-Huerta et al, Opt.Express 26, 33245 (2018)]), we managed to find analytical and finite-difference time-domain (FDTD) values for the, experimentally achievable, geometrical parameters of a hybrid plano-concave microcavity that enhances the spontaneous emission (i.e. Purcell enhancement) of color centers in two-dimensional (2D) hexagonal boron nitride (hBN) while simultaneously limiting the NA of the emitter. Paraxial approximation and a transfer matrix model are used to find the spotsize of the fundamental Gaussian mode and the resonant modes of our microcavity, respectively. A Purcell enhancement of 6 is found for a SPE (i.e. in-plane dipole) hosted by a 2D hBN layer inside the hybrid plano-concave microcavity., Comment: 5 pages, 8 figures

In this work we experimentally demonstrate a photon-pair source with correlations in the frequency and polarization degrees of freedom. We base our source on the spontaneous four-wave mixing (SFWM) process in a photonic crystal fiber. We show theoretically that the two-photon state is the coherent superposition of up to six distinct SFWM processes, each corresponding to a distinct combination of polarizations for the four waves involved and giving rise to an energy-conserving pair of peaks. Our experimental measurements, both in terms of single and coincidence counts, confirm the presence of these pairs of peaks, while we also present related numerical simulations with excellent experiment-theory agreement. We explicitly show how the pump frequency and polarization may be used to effectively control the signal-idler photon-pair properties, defining which of the six processes can participate in the overall two-photon state and at which optical frequencies. We analyze the signal-idler correlations in frequency and polarization, and in terms of fiber characterization, we input the SFWM-peak experimental data into a genetic algorithm which successfully predicts the values of the parameters that characterize the fiber cross section, as well as predict the particular SFWM process associated with a given pair of peaks. We believe our work will help advance the exploitation of photon-pair correlations in the frequency and polarization degrees of freedom., Comment: 12 pages, 7 figures

We study the process of seeded, or stimulated, third-order parametric down-conversion, as an extension of our previous work on spontaneous parametric downconversion (TOSPDC). We present general expressions for the spectra and throughputs expected for the cases where the seed field or fields overlap either only one or two of the TOSPDC modes, and also allow for both pump and seed to be either monochromatic or pulsed. We present a numerical study for a particular source design, showing that doubly-overlapped seeding can lead to a considerably greater generated flux as compared with singly-overlapped seeding. We furthermore show that doubly-overlapped seeding permits stimulated emission tomography for the reconstruction of the three-photon TOSPDC joint spectral intensity. We hope that our work will guide future experimental efforts based on the process of third-order parametric downconversion., Comment: 14 pages, 6 figures. To be published in Physical Review A

In this work we propose the generation of a hybrid entangled resource (HER) and its further application in a quantum teleportation scheme from an experimentally feasible point of view. The source for HER preparation is based on the four wave mixing process in a photonic crystal fiber, from which one party of its output bipartite state is used to herald a single photon or a single photon added coherent state. From the heralded state and linear optics the HER is created. In the proposed teleportation protocol Bob uses the HER to teleport qubits with different spectral properties. Bob makes a Bell measurement in the single photon basis and characterizes the scheme with its average quantum teleportation fidelity. Fidelities close to one are expected for qubits in a wide spectral range. The work also includes a discussion about the fidelity dependence on the geometrical properties of the medium through which the HER is generated. An important remark is that no spectral filtering is employed in the heralding process, which emphasizes the feasibility of this scheme without compromising photon flux., Comment: 15 pages, 5 figures

Optical fibers have been considered an optimal platform for third-order parametric down-conversion since they can potentially overcome the weak third-order nonlinearity by their long interaction length. Here we present, in the first part, a theoretical derivation for the conversion rate both in the case of spontaneous generation and in the presence of a seed beam. Then we review three types of optical fibers and we examine their properties in terms of conversion efficiency and practical feasibility.

The ability to determine the joint spectral properties of photon pairs produced by the processes of spontaneous parametric downconversion (SPDC) and spontaneous four wave mixing (SFWM) is crucial for guaranteeing the usability of heralded single photons and polarization-entangled pairs for multi-photon protocols. In this paper, we compare six different techniques that yield either a characterization of the joint spectral intensity or of the closely-related purity of heralded single photons. These six techniques include: i) scanning monochromator measurements, ii) a variant of Fourier transform spectroscopy designed to extract the desired information exploiting a resource-optimized technique, iii) dispersive fibre spectroscopy, iv) stimulated-emission-based measurement, v) measurement of the second-order correlation function $g^{(2)}$ for one of the two photons, and vi) two-source Hong-Ou-Mandel interferometry. We discuss the relative performance of these techniques for the specific cases of a SPDC source designed to be factorable and SFWM sources of varying purity, and compare the techniques' relative advantages and disadvantages.

We introduce a new kind of spontaneous four wave mixing process for the generation of photon pairs, in which the four waves involved counter-propagate in a guided-wave \chi^{(3)} medium; we refer to this process as counter-propagating spontaneous four wave mixing (CP-SFWM). We show that for the simplest CP-SFWM source, in which all waves propagate in the same polarization and transverse mode and in which self- and cross-phase modulation effects are negligible, phasematching is attained automatically regardless of dispersion in the fiber or waveguide. Furthermore, we show that in two distinct versions of this source (both pumps pulsed, or one pump pulsed and the remaining one monochromatic), the two-photon state is automatically factorable provided that the length of the nonlinear medium exceeds a certain threshold, easily achievable in practice since this threshold length tends to be in the range of mm to cm. We also show that if one of the pumps approaches the monochromatic limit, and for a sufficient nonlinear medium length, the bandwidth of one of the two photons in a given pair may be reduced to the level of MHz, compatible with electronic transitions for the implementation of atom-photon interfaces, without the use of optical cavities., Comment: 27 pages, 7 figures, accepted to New Journal of Physics

We report on the generation of an indistinguishable heralded single-photon state, using highly nondegenerate spontaneous parametric downconversion (SPDC). Spectrally factorable photon pairs can be generated by incorporating a broadband pump pulse and a group-velocity matching (GVM) condition in a periodically-poled potassium titanyl phosphate (PPKTP) crystal. The heralding photon is in the near IR, close to the peak detection efficiency of off-the-shelf Si single-photon detectors; meanwhile, the heralded photon is in the telecom L-band where fiber losses are at a minimum. We observe spectral factorability of the SPDC source and consequently high purity (90%) of the produced heralded single photons by several different techniques. Because this source can also realize a high heralding efficiency (> 90%), it would be suitable for time-multiplexing techniques, enabling a pseudo-deterministic single-photon source, a critical resource for optical quantum information and communication technology.

We present an experimental and theoretical study of photon pairs generated by spontaneous four wave mixing (SFWM), based on birefringent phasematching, in a fiber which supports more than one transverse mode. We present SFWM spectra, obtained through single-channel and coincidence photon counting, which exhibit multiple peaks shown here to be the result of multiple SFWM processes associated with different combinations of transverse modes for the pump, signal, and idler waves., Comment: Accepted for publication in Optics Letters

We study the process of co-polarized spontaneous four-wave mixing in single-mode optical fibers, with an emphasis on an analysis of the conversion efficiency. We consider both the monochromatic-pumps and pulsed-pumps regimes, as well as both the degenerate-pumps and non-degenerate-pumps configurations. We present analytical expressions for the conversion efficiency, which are given in terms of double integrals. In the case of pulsed pumps we take these expressions to closed analytical form with the help of certain approximations. We present results of numerical simulations, and compare them to values obtained from our analytical expressions, for the conversion efficiency as a function of several key experimental parameters.

We study the third order spontaneous parametric down conversion (TOSPDC) process, as a means to generate entangled photon triplets. Specifically, we consider thin optical fibers as the nonlinear medium to be used as the basis for TOSPDC in configurations where phase matching is attained through the use of more than one fiber transverse modes. Our analysis in this paper, which follows from our earlier paper Optics Letters 36, 190 (2011), aims to supply experimentalists with the details required in order to design a TOSPDC photon-triplet source. Specifically, our analysis focuses on the photon triplet state, on the rate of emission, and on the TOSPDC phasematching characteristics for the cases of frequency degenerate and frequency nondegenerate TOSPDC.

We study the processes of spontaneous four wave mixing and of third-order spontaneous parametric downconversion in optical fibers, as the basis for the implementation of photon-pair and photon-triplet sources. We present a comparative analysis of the two processes including expressions for the respective quantum states and plots of the joint spectral intensity, a discussion of phasematching characteristics, and expressions for the conversion efficiency. We have also included a comparative study based on numerical results for the conversion efficiency for the two sources, as a function of several key experimental parameters.

We present an experimental proposal for the generation of photon triplets based on third-order spontaneous para- metric downconversion in thin optical fibers. Our analysis includes expressions for the quantum state, which de- scribes the photon triplets and for the generation rate in terms of all experimental parameters. We also present, for a specific source design, numerically calculated generation rates.

We present a study of the spectral properties of photon pairs generated through the process of spontaneous four wave mixing (SFWM) in single mode fiber. Our analysis assumes narrowband pumps, which are allowed to be frequency-degenerate or non-degenerate. Based on this analysis, we derive conditions on the pump frequencies and on the fiber dispersion parameters which guarantee the generation of ultra-broadband photon pairs. Such photon pairs are characterized by: i) a very large degree of entanglement, and ii) a very high degree of temporal synchronization between the signal and idler photons. Through a numerical exercise, we find that the use of photonic crystal fiber (PCF) facilitates the fulfilment of the conditions for ultra-broadband photon pair generation; in particular, the spectral region in which emission occurs can be adjusted to particular needs through an appropriate choice of the PCF parameters. In addition, we present a novel quantum interference effect, resulting from indistinguishable pathways to the same outcome, which can occur when pumping a SFWM source with multiple spectral lines., Comment: 15 pages, 10 figures. To be published in Phys. Rev. A

We study photon pair generation through scalar spontaneous four-wave mixing in single-mode fibre and for frequency-degenerate pumps; we concentrate on source geometries which fulfil full group velocity matching (GVM), i.e. where the pump, signal and idler propagate at identical group velocities. We discuss two experimental techniques which permit the attainment of full GVM, and discuss the resulting two-photon state properties. In particular, we show that full GVM can lead to sources which approach phasematching unconstrained by dispersion and therefore with a remarkably large bandwidth. We also discuss the generation of nearly-factorablestates as an application of full GVM., Comment: 12 pages, 4 figures. To appear in J. Mod. Opt; PQE-2008 special issue