We calculate the quantum correlations existing among the three output fields (pump, signal, and idler) of a triply resonant non-degenerate Optical Parametric Oscillator operating above threshold. By applying the standard criteria [P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003)], we show that strong tripartite continuous-variable entanglement is present in this well-known and simple system. Furthermore, since the entanglement is generated directly from a nonlinear process, the three entangled fields can have very different frequencies, opening the way for multicolored quantum information networks.
Pumping a nonlinear crystal by an intense radiation results in the optical parametric generation of photons in two modes (the signal and the idler). The quantized electromagnetic field in these modes is described by a continuous-variable quantum state, which is entangled if the pump is a coherent state produced by a laser. The signal and the idler modes remain populated by photons even if the pump becomes incoherent (dephased by a medium, superposed with a thermal state, or produced by an alternative source such as the superluminescent diode). However, the incoherent pump does effect the entan…
We calculate the bi-photon state generated by spontaneous parametric down conversion in a thin crystal and under collinear phase matching conditions using a pump consisting of any superposition of Laguerre-Gauss modes. The result has no restrictions on the angular or radial momenta or, in particular, on the width of the pump, signal and idler modes. We demonstrate the strong effect of the pump to signal/idler width ratio on the composition of the down-converted entangled fields. Knowledge of the pump to signal/idler width ratio is shown to be essential when calculating the maximally entangled …
The correlation properties of the pump field in spontaneous parametric down-conversion are crucial in determining the degree of entanglement of generated signal and idler photons. We find theoretically that continuous-variable entanglement of the transverse positions and momenta of these photons can be achieved only if the coherence of the pump beam is sufficiently high. The positions of signal and idler photons are found to be correlated, even for an incoherent pump. However, the momenta of the signal and idler photons are not anti-correlated, even though transverse momentum is conserved.
Most investigations of multipartite entanglement have been concerned with temporal modes of the electromagnetic field, and have neglected its spatial structure. We present a simple model which allows to generate tripartite entanglement between spatial modes by parametric down-conversion with two symmetrically-tilted plane waves serving as a pump. The characteristics of this entanglement are investigated. We also discuss the generalization of our scheme to 2N+1-partite entanglement using 2N symmetrically-tilted plane pump waves. Another interesting feature is the possibility of entanglement loc…
We demonstrate an optical-fiber based source of polarization entangled photon-pairs with improved quality and efficiency, which has been integrated with off-the-shelf telecom components and is, therefore, well suited for quantum communication applications in the 1550 nm telecom band. Polarization entanglement is produced by simultaneously pumping a loop of standard dispersion-shifted fiber with two orthogonally-polarized pump pulses, one propagating in the clockwise and the other in the counter-clockwise direction. We characterize this source by investigating two-photon interference between th…
Possibilities of generation of lower order and higher order intermodal entanglement in 87Rb 5S-5P-5D hyperfine manifold are rigorously investigated using Sen-Mandal perturbative technique by showing the equivalence of the system with the four-wave mixing (FWM) process. The investigation has revealed that for a set of experimentally realizable/relevant parameters we can observe lower order and higher order intermodal entanglement between pump and signal modes, signal and idler modes, and idler and pump modes in a FWM process associated with the 87Rb 5S-5P-5D hyperfine manifold. In addition, tri…
We present a quantum-theoretical treatment of biphoton generation in single-resonant type-II parametric down-conversion. The nonlinear medium is continuously pumped and is placed inside a cavity which is resonant for the signal field, but nonresonant for the idler deflected by an intra-cavity polarizing beam splitter. The intensity of the classical pump is assumed to be sufficiently low in order to yield a biphoton production rate that is small compared to the cavity loss rate. Explicit expressions are derived for the rate of biphoton generation and for the biphoton wave function. The output s…
Coherent, purely-dispersive three-wave mixing systems in optics and superconducting microwave circuits can be operated as parametric amplifiers, generating from a pump wave at one frequency amplified signal and idler waves at lower frequencies. Here we demonstrate the reciprocal process using a Josephson amplifier in which coherently imposed signal and idler beams up-convert to the pump frequency. For signal and idler beams strong enough to significantly deplete the pump, we show that this reciprocal process ("coherent cancellation") leads to large, phase-sensitive modulation and even enhancem…
Quantum correlations between bright pump, signal, and idler beams produced by an optical parametric oscillator, all with different frequencies, are experimentally demonstrated. We show that the degree of entanglement between signal and idler fields is improved by using information of pump fluctuations. This is the first observation of three-color optical quantum correlations.
We study the properties of bi-squeezed tripartite Gaussian states created by two spontaneous parametric down-conversion processes that share a common idler. We give a complete description of the quantum correlations across of all partitions, as well as of the genuine multipartite entanglement, obtaining analytical expressions for most of the quantities of interest. We find that the state contains genuine tripartite entanglement, in addition to the bipartite entanglement among the modes that are directly squeezed. We also investigate the effect of homodyne detection of the photons in the common…
The process of cascaded downconversion and sum-frequency generation inside an optical cavity has been predicted to be a potential source of three-mode continuous-variable entanglement. When the cavity is pumped by two fields, the threshold properties have been analysed, showing that these are more complicated than in well-known processes such as optical parametric oscillation. When there is only a single pumping field, the entanglement properties have been calculated using a linearised fluctuation analysis, but without any consideration of the threshold properties or critical operating points …
Uncertainty in the determination of emission angles of signal and idler photons is investigated. The role of divergence of the pump beam, width of the pump spectrum, and size of the crystal is elucidated. Experimental data obtained by an iCCD camera are in a good agreement with a numerical model that provides angular and spectral characteristics of the signal and idler fields.
We experimentally investigate quadrature correlations between pump, signal, and idler fields in an above-threshold optical parametric oscillator. We observe new quantum correlations among the pump and signal or idler beams, as well as among the pump and a combined quadrature of signal and idler beams. A further investigation of unforeseen classical noise observed in this system is presented, which hinders the observation of the recently predicted tripartite entanglement. In spite of this noise, current results approach the limit required to demonstrate three-color entanglement.
We present a fiber-based source of polarization-entangled photon pairs that is well suited for quantum communication applications in the 1.5$μ$m band of standard telecommunication fiber. Quantum-correlated signal and idler photon pairs are produced when a nonlinear-fiber Sagnac interferometer is pumped in the anomalous-dispersion region of the fiber. Recently, we have demonstrated nonclassical properties of such photon pairs by using Geiger-mode InGaAs/InP avalanche photodiodes. Polarization entanglement in the photon pairs can be created by pumping the Sagnac interferometer with two orthogona…
We study the chronocyclic character, i.e. the joint temporal and spectral properties, of the single-photon constituents of photon pairs generated by spontaneous parametric down conversion. In particular we study how single photon properties, including purity and single-photon chirp, depend on photon pair properties, including the type of signal-idler spectral and correlations and the level of pump chirp.
Intense spatio-spectral twin beams generated in the regime with pump depletion are analyzed applying a suggested quantum model that treats the signal, idler and pump fields in the same way. The model assumes the signal and idler fields in the form of the generalized superposition of signal and noise and reveals nonzero signal coherent components in both fields, contrary to the models developed earlier. The influence of coherent components on the properties of intense twin beams is elucidated. The interference pattern formed in the process of sum-frequency generation and that of the Hong-Ou-Man…
Using the correlated signal and idler photon pairs generated in a dispersion shifted fiber by a pulsed pump, we measure the quantum efficiency of a InGaAs/InP avalanche photodiode-based single photon detector. Since the collection efficiency of photon pairs is a key parameter to correctly deduce the quantum efficiency, we carefully characterize the collection efficiency by studying correlation dependence of photon pairs upon the spectra of pump, signal and idler photons. This study allows us to obtain quantum efficiency of the single photon detector by using photon pairs with various kinds of …
We present a fiber based source of polarization-entangled photon pairs that is well suited for quantum communication applications in the 1550nm band of standard fiber-optic telecommunications. Polarization entanglement is created by pumping a nonlinear-fiber Sagnac interferometer with two time-delayed orthogonally-polarized pump pulses and subsequently removing the time distinguishability by passing the parametrically scattered signal-idler photon pairs through a piece of birefringent fiber. Coincidence detection of the signal-idler photons yields biphoton interference with visibility greater …
We experimentally demonstrate the nonclassical photon number correlations expected in tripartite continuous variable states obtained by parametric processes. Our scheme involves a single nonlinear crystal, where two interlinked parametric interactions take place simultaneously, and represents a bright and compact source of a sub-shot-noise tripartite light field. We analyze the effects of the pump intensities on the numbers of detected photons and on the amount of noise reduction in some details, thus demonstrating a good agreement between the experimental data and a single-mode theoretical de…
By utilizing the nondegenerate optical parametric amplifier, the quantum state transfer from a pump state with high frequency to a signal state of lower frequency is studied theoretically. The noiseless state transfer is characterized by frequency conversion efficiency and noise figure. It is shown that the quantum state can be well preserved during the frequency conversion as long as the optical parametric amplifier is operated far below the threshold, and meanwhile injected with an input idler field with a power density about ten times greater than that of the pump. The dependence of the noi…
We examine one asymmetric adnd two fully symmetric Gaussian continuous-variable systems in terms of their tripartite and bipartite entanglement properties. We treat pure states and are able to find analytic solutions using the undepleted pump approximation for the Hamiltonian models, and standard beamsplitter relations for a model that mixes the outputs of optical parametric oscillators. Our two symmetric systems exhibit perfect tripartite correlations, but only in the unphysical limit of infinite squeezing. For more realistic squeezing parameters, all three systems exhibit both tripartite and…
We investigate the effect of the cumulative phase on the photon statistics of the three-mode state whose evolution is described by the trilinear Hamiltonian $\hat{H}_{I}=i\hbarκ\big(\hat{a}\hat{b}\hat{c}^{\dagger}-\hat{a}^{\dagger}\hat{b}^{\dagger}c\big)$, wherein the pump is taken to be quantized (and prepared in a coherent state) and the signal and idler modes are initially seeded with coherent states. We provide a brief review of the two-mode squeezed coherent states generated by non-degenerate coherently-stimulated parametric down-conversion, whereby the nonlinear crystal is driven by a st…
A photonic crystal fiber based source of photon pairs in symmetric factorable state is experimentally demonstrated. The idler and signal photons, with almost the same bandwidth, are centering at 807.5 nm and 1364.1 nm, respectively. The property of the spectral de-correlation is confirmed by measuring the correlation dependence of photon pairs upon the spectra of pump, signal and idler photons.
In the process of spontaneous parametric downconversion, photons from a pump field are converted to signal and idler photon pairs in a nonlinear crystal. The reversed process, or upconversion of these pairs back to single photons in a second crystal, is also possible. Here, we present experimental measurements of the upconversion rate with a controlled time delay introduced between the signal and idler photons. As a function of delay, this rate presents a full width at half maximum of 27.9 fs under our experimental conditions, and we further demonstrate that group delay dispersion of the photo…
We performed an experiment to observe the storages of an input probe field and an idler field generated through an off-axis four-wave mixing (FWM) process via a double-lambda configuration in a cold atomic ensemble. We analyzed the underlying physics in detail and found that the retrieved idler field came from two parts if there was no single-photon detuning for pump pulse: part 1 was from the collective atomic spin (the input probe field, the coupling field and the pump field combined to generate the idle field through FWM, then the idler was stored through electromagnetically induced transpa…
Temporal coherence of individual signal or idler beam, determined by the spectral correlation property of photon pairs, is important for realizing quantum interference among independent sources. To understand the effect of chirp on the temporal coherence property, two series of experiments are investigated by introducing different amount of chirp into either the pulsed pump or individual signal (idler) beam. In the first one, based on spontaneous four wave mixing in a piece of optical fiber, the intensity correlation function of the filtered individual signal beam, which characterizes the degr…
We propose an application of quantum temporal imaging to restoring the indistinguishability of the signal and the idler photons produced in type-II spontaneous parametric down-conversion with a pulsed broadband pump. It is known that in this case, the signal and the idler photons have different spectral and temporal properties. This effect deteriorates their indistinguishability and the visibility of the Hong-Ou-Mandel interference, respectively. We demonstrate that inserting a time lens in one arm of the interferometer and choosing properly its magnification factor restores perfect indistingu…
The influence of the phase fluctuation of the pump laser on the phase-correlation between the signal and idler modes of the output fields from as non-degenerate optical parametric oscillator operating above oscillation threshold was experimentally investigated. The noise spectra of the intensity-difference and the phase-sum of the entangled optical beams were measured with a pair of unbalanced fiber Match-Zehnder interferometers specifically designed. The experimental results proved the previously theoretical prediction and are in reasonable agreement with the calculation based on semiclassica…
We present a full quantum analysis of resonant forward four-wave mixing based on electromagnetically induced transparency (EIT). In particular, we study the regime of efficient nonlinear conversion with low-intensity fields that has been predicted from a semiclassical analysis. We derive an effective nonlinear interaction Hamiltonian in the adiabatic limit. In contrast to conventional nonlinear optics this Hamiltonian does not have a power expansion in the fields and the conversion length increases with the input power. We analyze the stationary wave-mixing process in the forward scattering co…
We analyze the process of photon-pair generation via spontaneous parametric down-conversion in a quadratic nonlinear asymmetric waveguide coupler. The two waveguides have different geometry, such that light coupling only occurs within a narrow bandwidth of one of the generated (signal) photon modes, while the other (idler) photon together with the pump stay localized in one (driven) arm of the coupler. We demonstrate that such a setup represents a powerful and flexible tool for engineering spectral properties of generated photon pairs. Mode hybridization and dispersion of coupling can be utili…
We demonstrate efficient generation of collinearly propagating, highly nondegenerate photon pairs in a periodically-poled lithium niobate cw parametric downconverter with an inferred pair generation rate of 1.4*10^7/s/mW of pump power. Detection of an 800-nm signal photon triggers a thermoelectrically-cooled 20%-efficient InGaAs avalanche photodiode for the detection of the 1600-nm conjugate idler photon. Using single-mode fibers as spatial mode filters, we obtain a signal-conditioned idler-detection probability of about 3.1%.
Measurement of photon-number statistics of fields composed of photon pairs generated in spontaneous parametric downcoversion pumped by strong ultrashort pulses is described. Final detection quantum efficiencies, noises as well as possible loss of one or both photons from a pair are taken into account. Measured data provided by an intensified single-photon CCD camera are analyzed along the developed model. The joint signal-idler photon-number distribution is obtained using the expectation maximization algorithm. Covariance of the signal and idler photon-numbers equals 80 %. Statistics of the ge…
A nonlinear planar waveguide pumped by a beam orthogonal to its surface may serve as a versatile source of photon pairs. Changing pump-pulse duration, pump-beam transverse width, and angular decomposition of pump-beam frequencies characteristics of a photon pair including spectral widths of signal and idler fields, their time durations as well as degree of entanglement of two fields can be changed significantly. Using the measured spectral widths of the down-converted fields and width of a coincidence-count dip in a Hong-Ou-Mandel interferometer entropy of entanglement can be determined.
In this paper we investigate several properties of the full signal-idler-pump mode quantum state generated by a triply resonant non-degenerate Optical Parametric Oscillator operating above threshold, with an injected wave on the signal and idler modes in order to lock the phase diffusion process. We determine and discuss the spectral purity of this state, which turns out not to be always equal to 1 even though the three interacting modes have been taken into account at the quantum level. We have seen that the purity is essentially dependent on the weak intensity of the injected light and on an…
Coherence properties of the down-converted beams generated in spontaneous parametric down-conversion are investigated in detail using an iCCD camera. Experimental results are compared with those from a theoretical model developed for pulsed pumping with a Gaussian transverse profile. The results allow to tailor the shape of correlation area of the signal and idler photons using pump-field and crystal parameters. As an example, splitting of a correlation area caused by a two-peak pump-field spectrum is experimentally studied.
We report a novel Bell state preparation experiment. High-purity Bell states are prepared by using femtosecond pulse pumped \emph{nondegenerate} collinear spontaneous parametric down-conversion. The use of femtosecond pump pulse {\em does not} result in reduction of quantum interference visibility in our scheme in which post-selection of amplitudes and other traditional mechanisms, such as, using thin nonlinear crystals or narrow-band spectral filters are not used. Another distinct feature of this scheme is that the pump, the signal, and the idler wavelengths are all distinguishable, which is …
We investigated the intensity noise spectra of the single beam of a pump-enhanced continuous-wave (cw) optical parametric oscillator (OPO), which was used to generate quantum correlated twin beams, as a function of the pump power. With a triply (pump-, signal-, and idler-) resonant cavity, the oscillation threshold of our OPO was about 8.5+/-1.3 mW and the measured slope conversion efficiency was 0.72+/-0.02. A twin beams with power of 240 mW were generated at pump power of 350 mW. The relaxation oscillation frequencies, which depend on the pump power, were observed when the pump power of OPO …
We consider novel method for implementation of hybrid entanglement between microscopic and macroscopic states on output of spontaneous parametric down converter through the depletion of the pump wave. The generated signal, idler and pumping fields show weak entanglement. We characterize it and show the limits of applicability of the depleted pump regime. Testing method of the hybrid entanglement is proposed. The hybrid entanglement is tested by conditional generation of maximally entangled states of two qubits and qutrits regardless of its smallness. Possibilities to enhance the hybrid entangl…
The dependence of quantum correlation of twin beams on the pump finesse of an optical parametric oscillator is studied with a semi-classical analysis. It is found that the phase-sum correlation of the output signal and idler beams from an optical parametric oscillator operating above threshold depends on the finesse of the pump field when the spurious pump phase noise generated inside the optical cavity and the excess noise of the input pump field are involved in the Langevin equations. The theoretical calculations can explain the previously experimental results, quantitatively.
Strong correlations between the signal and idler beams imprinted during their generation dominantly determine the properties of twin beams. They are also responsible for the waves in intensity coherence observed in the wave-vector space of a twin beam propagating in a nonlinear crystal in the regime with pump depletion. These waves start to develop at certain twin-beam intensity and move from the signal and idler beam centers towards their tails. They manifest themselves via the change of coherence volume monitored in the far field by the measurement of local modified $ \bar{g}^{(2)} $ functio…
We study a multimode optomechanical system where two mechanical oscillators are coupled to an electromagnetic cavity. Previously it has been shown that if the mechanical resonances have nearly equal frequencies, one can make the oscillators to interact via the cavity by strong pumping with a coherent pump tone. One can view the interaction also as emergence of an electromagnetically dark mode which gets asymptotically decoupled from the cavity and has a linewidth much smaller than that of the bare cavity. The narrow linewidth and long lifetime of the dark mode could be advantageous for example…
We consider a scheme of multiplexed cold atomic ensembles that generate a frequency-entangled biphoton state with controllable entropy of entanglement. The biphoton state consists of a telecommunication photon (signal) immediately followed by an infrared one (idler) via four-wave mixing with two classical pump fields. Multiplexing the atomic ensembles with frequency and phase-shifted signal and idler emissions, we can manipulate and control the spectral property of the biphoton state. Mapping out the entropy of entanglement in the scheme provides the optimal configuration for entanglement reso…
We experimentally investigate the parametric down-conversion process in a nonlinear bulk crystal, driven by two non-collinear pump modes. The experiment shows the emergence of bright hot-spots in modes shared by the two pumps, in analogy with the phenomenology recently observed in 2D nonlinear photonic crystals. By exploiting the spatial walk-off between the two extraordinary pump modes we have been able to recreate a peculiar resonance condition, reported by a local enhancement of the parametric gain, which corresponds to a transition from a three-mode to a four-mode coupling. From a quantum …
We analyze the amplification processes occurring in a nonlinear fiber, either driven with one or two pumps. After determining the solution for the signal and idler fields resulting from these amplification processes, we analyze the physical transformations that these fields undergo. To this aim, we use a Bloch-Messiah decomposition for the symplectic transformation governing the fields evolution. Although conceptually equivalent to other works in this area [McKinstrie and Karlsson, Opt. Expr. 21, 1374 (2013)], this analysis is intended to be particularly simple, gathering results spread in the…
Heralded single photon sources are the most commonly used sources for optical quantum technology applications. There is strong demand for accurate prediction of their spectral features and temporal correlations with ever increasing precision. This is particularly important in connection with the intrinsically stochastic photon-pair generation process in heralded sources. Here we present a complete theoretical description of the temporal correlation of a signal-idler, signal-signal and signal-signal-idler coincidences of photons generated by continuous wave pumped cavity-enhanced spontaneous pa…
In this paper, we address the issue of the generation of non-degenerate cross-polarization-entangled photon pairs using type-II periodically poled lithium niobate. We show that, by an appropriate engineering of the quasi-phase-matching grating, it is possible to simultaneously satisfy the conditions for two spontaneous parametric down-conversion processes, namely ordinary pump photon down-conversion to either extraordinary signal and ordinary idler paired photons, or to ordinary signal and extraordinary idler paired photons. In contrast to single type-II phase-matching, these two processes, wh…
We propose and analyse analogs of optical cavities for atoms using three-well inline Bose-Hubbard models with pumping and losses. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show a qualitative dependence on the choice of damped well. The systems we analyse remain far from equilibrium, although most do enter a steady-state regime. We find quadrature squeezing, bipartite and tripartite inseparability and entanglement, and states exhibiting the EPR paradox, depending on the parameter regimes. We also discover situations where the mean-…
We have used an ultra-low threshold continuous-wave Optical Parametric Oscillator (OPO) to reduce the quantum fluctuations of the reflected pump beam below the shot noise limit. The OPO consisted of a triply resonant cavity containing a Periodically-Poled Lithium Niobate crystal pumped by a Nd:YAG laser and giving signal and idler wavelengths close to 2.12 microns and a threshold as low as 300 microwatts. We detected the quantum fluctuations of the pump beam reflected by the OPO using a slightly modified homodyne detection technique. The measured noise reduction was 30 % (inferred noise reduct…
We show that scalable multipartite entanglement among light fields may be generated by optical parametric oscillators (OPO). The tripartite entanglement existent among the three bright beams produced by a single OPO -- pump, signal, and idler -- is scalable to a system of many OPOs by pumping them in cascade with the same optical field. This latter serves as an entanglement distributor. The special case of two OPOs is studied, as it is shown that the resulting five bright beams share genuine multipartite entanglement. In addition, the structure of entanglement distribution among the fields can…
We review some recent experiments based upon multimode two-photon interference of photon pairs created by spontaneous parametric down-conversion. The new element provided by these experiments is the inclusion of the transverse spatial profiles of the pump, signal and idler fields. We discuss multimode Hong-Ou-Mandel interference, and show that the transverse profile of the pump beam can be manipulated in order to control two-photon interference. We present the basic theory and experimental results as well as several applications to the field of quantum information.
We present a theoretical study of ghost imaging based on correlated beams arising from parametric down-conversion, and which uses balanced homodyne detection to measure both the signal and idler fields. We analytically show that the signal-idler correlations contain the full amplitude and phase information about an object located in the signal path, both in the near-field and the far-field case. To this end we discuss how to optimize the optical setups in the two imaging paths, including the crucial point regarding how to engineer the phase of the idler local oscillator as to observe the desir…
Correlated signal and idler photon pairs with small detuning in the telecom band can be generated through spontaneous four-wave mixing in dispersion shift fibers. However, photons originated from other nonlinear processes in optical fibers, such as Raman scattering and self-phase modulation, may contaminate the photon pairs. It has been proved that photons produced by Raman scattering are the background noise of photon pairs. Here we show that photons induced by self-phase modulation of pump pulses are another origin of background noise. After studying the dependence of self-phase modulation i…
We show that in parametric down-conversion the coherence properties of a temporally partially coherent pump field get entirely transferred to the down-converted entangled two-photon field. Under the assumption that the frequency-bandwidth of the down-converted signal-idler photons is much larger than that of the pump, we derive the temporal coherence functions for the down-converted field, for both infinitely-fast and time-averaged detection schemes. We show that in each scheme the coherence function factorizes into two separate coherence functions with one of them carrying the entire statisti…
We theoretically address squeezed light generation through the spontaneous breaking of the rotational invariance occuring in a type I degenerate optical parametric oscillator (DOPO) pumped above threshold. We show that a DOPO with spherical mirrors, in which the signal and idler fields correspond to first order Laguerre-Gauss modes, produces a perfectly squeezed vacuum with the shape of a Hermite-Gauss mode, within the linearized theory. This occurs at any pumping level above threshold, hence the phenomenon is non-critical. Imperfections of the rotational symmetry, due e.g. to cavity anisotrop…
The mismatch between elegant theoretical models and the detailed experimental reality is particularly pronounced in quantum nonlinear interferometry (QNI). In stark contrast to theory, experiments contain pump beams that start in impure states and that are depleted, quantum noise that affects -- and drives -- any otherwise gradual build up of the signal and idler fields, and nonlinear materials that are far from ideal and have a complicated time-dependent dispersive response. Notably, we would normally expect group velocity mismatches to destroy any possibility of measurable or visible entangl…
