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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

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

The hybrid atoms-cell site entanglement in a one-dimensional Su-Schrieffer-Heeger (SSH) topological insulator with first and second neighbor hopping interaction in space representation of finite chains is analyzed. The geometric phase is calculated by the Resta electric polarization and the entanglement in the atomic basis by the Schmidt number. A relation between entanglement and the topological phase transitions (TPT) is given since the Schmidt number has critical points of maximal entangled (ME) states in the singularities of the geometrical phase. States with second-neighbors have higher entanglement than first-order hopping. The general conditions to produce ME hybrid Bell states and the localization-entanglement relation are given., Comment: 7 pages and 4 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

We study quantum correlations and discord in a bipartite continuous variable hybrid system formed by linear combinations of coherent states $|\alpha\rangle$ and single photon added coherent states (SPACS) of the form $|\psi\rangle_{\text{dp(pa)}}= \mathcal{N}/\sqrt{2} (\hat{a}^\dagger |\alpha\rangle_a |\alpha\rangle_b \pm \hat{b}^\dagger |\alpha\rangle_a |\alpha\rangle_b)$. We stablish a relationship between the quantum discord with a local observable (the quadrature variance for one sub-system) under the influence of scattering and phase fluctuation noise. For the pure states the quantum correlations are characterized by means of measurement induced disturbance (MID) with simultaneous quadrature measurements. In a scenario where homodyne conditional measurements are available we show that the MID provides an easy way to select optimal phases to obtain information of the maximal correlations in the channels. The quantum correlations of these entangled states with channel losses are quantitatively characterized with the quantum discord (QD) with a displaced qubit projector. We observe that as scattering increases, QD decreases monotonically. At the same time for the state $|\psi\rangle_{\text{dp}}$, QD is more resistant to high phase fluctuations when the average photon number $n_0$ is bigger than zero, but if phase fluctuations are low, QD is more resistant if $n_0=0$. For the dp model with scattering, we obtain an analytical expression of the QD as a function of the observable quadrature variance in a local sub-system. This relation allows us to have a way to obtain the degree of QD in the channel by just measuring a local property observable such as the quadrature variance. For the other model this relation still exists but is explored numerically. This relation is an important result that allows to identify quantum processing capabilities in terms of just local observables., Comment: 27 pages, 14 figures

We study the degree of entanglement of arbitrary superpositions of $m,n$ photon-added coherent states (PACS) $|\psi\rangle \propto u |{\alpha},m\rangle |{\beta},n \rangle+ v |{\beta},n\rangle |{\alpha},m\rangle$ using the concurrence, and obtain the general conditions for maximal entanglement. We show that photon addition process can be identified as an entanglement enhancer operation for superpositions of coherent states (SCS). Specifically for the known bipartite positive SCS: $|\psi\rangle \propto |\alpha\rangle_a |-\alpha\rangle_b + |-\alpha\rangle_a |\alpha\rangle_b $ whose entanglement tends to zero for $\alpha \to 0$, can be maximal if al least one photon is added in a subsystem. A full family of maximally entangled PACS is also presented. We also analyzed the decoherence effects in the entangled PACS induced by a simple depolarizing channel. We find that robustness against depolarization is increased by adding photons to the coherent states of the superposition. We obtain the dependence of the critical depolarization $p_{\text{crit}}$ for null entanglement as a function of $m,n, \alpha$ and $\beta $.