We present a theoretical and experimental analysis of the joint effects of the transverse electric field distribution and of the nonlinear crystal characteristics on the properties of photon pairs generated by spontaneous parametric downconversion (SPDC). While it is known that for a sufficiently short crystal the pump electric field distribution fully determines the joint signal-idler properties, for longer crystals the nonlinear crystal properties also play an important role. In this paper we present experimental measurements of the angular spectrum (AS) and of the conditional angular spectrum (CAS) of photon pairs produced by spontaneous parametric downconversion (SPDC), carried out through spatially-resolved photon counting. In our experiment we control whether or not the source operates in the short-crystal regime through the degree of pump focusing, and explicitly show how the AS and CAS measurements differ in these two regimes. Our theory provides an understanding of the boundary between these two regimes and also predicts the corresponding differing behaviors.
The temperature dependence of the refractive indices of potassium titanyl phosphate (KTP) are shown to enable quasi-phasematched type II spontaneous parametric downconversion (SPDC) with low temperature sensitivity. Calculations show the effect to be maximised for emission of photons at around 1165nm, as well as producing potentially useful regions for wavelengths throughout the telecommunications bands. We demonstrate the effect experimentally, observing temperature-insensitive degenerate emission at 1326nm, within the telecommunications O band. This result has practical applications in the d…
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-overla…
We report a simple scheme for direct generation of frequency-bin entangled photon pairs via spontaneous parametric downconversion. Our fabricated nonlinear optical crystal with two different poling periods can simultaneously satisfy two different, spectrally symmetric nondegenerate quasi-phase-matching conditions, enabling the direct generation of entanglement in two discrete frequency-bin modes. Our produced photon pairs exhibited Hong-Ou-Mandel interference with high-visibility beating oscillations, a signature of two-mode frequency-bin entanglement. Moreover, we demonstrate deterministic en…
We show experimentally how noncollinear geometries in spontaneous parametric downconversion induce ellipticity of the shape of the spatial mode function. The degree of ellipticity depends on the pump beam width, especially for highly focused beams. We also discuss the ellipticity induced by the spectrum of the pump beam.
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 address parametric-downconversion seeded by multimode pseudo-thermal fields. We show that this process may be used to generate multimode pairwise correlated states with entanglement properties that can be tuned by controlling the seed intensities. Multimode pseudo-thermal fields seeded parametric-downconversion represents a novel source of correlated states, which allows one to explore the classical-quantum transition in pairwise correlations and to realize ghost imaging and ghost diffraction in regimes not yet explored by experiments.
We present the first experimental demonstration of ghost imaging realized with intense beams generated by a parametric downconversion interaction seeded with pseudo-thermal light. As expected, the real image of the object is reconstructed satisfying the thin-lens equation. We show that the experimental visibility of the reconstructed image is in accordance with the theoretically expected one.
Spontaneous parametric downconversion is an essential technique in quantum optics experiments. In this paper, various quasi-phase-matching processes in several typical periodically polarized nonlinear materials are analyzed and calculated. Furthermore, a general method for realizing multiple types of quasi-phase-matching in a monolithic material is presented. Finally, a novel design to prepare multiple entangled photon pairs based on the Sagnac interferometer is discussed. This technology can be applied to tiny optical paths in the telecom C band, saving both cost and space.
Parametric downconversion (PDC) is a technique of ubiquitous experimental significance in the production of non-classical, photon-number correlated twin beams. Standard theory of PDC as a two-mode squeezing process predicts and homodyne measurements observe a thermal photon number distribution per beam. Recent experiments have obtained conflicting distributions. In this paper, we explain the observation by an a-priori theoretical model solely based on directly accessible physical quantities. We compare our predictions with experimental data and find excellent agreement.
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.
A class of centrosymmetric molecules support excitons with a well-defined quasi-angular momentum. Cofacial arrangements of these molecules can be engineered so that quantum cutting produces a pair of excitons with angular momenta that are maximally entangled. The Bell state constituents can subsequently travel in opposite directions down molecular chains as ballistic wave packets. This is a direct excitonic analog to the entangled polarization states produced by the spontaneous parametric downconversion of light. As in optical settings, the ability to produce Bell states should enable foundati…
We employ a high quantum efficiency photon number counter to determine the photon number distribution of the output field from a parametric downconverter. The raw photocount data directly demonstrates that the source is nonclassical by forty standard deviations, and correcting for the quantum efficiency yields a direct observation of oscillations in the photon number distribution.
We present a simple treatment for the phenomenon of parametric downconversion considering the coherent scattering of one pump photon into a photon pair by a nonlinear crystal. The energy and momentum entanglement of the quantum state of the generated twin photons are seen as a consequence of the fundamental indistinguishability of the time and the position in which the photon pair is created inside the crystal. We also discuss some consequences of the system entanglement.
In this paper we study photon pairs generated in a nonlinear cavity, composed of a nonlinear crystal surrounded by mirrors, by the process of spontaneous parametric downconversion. We analyze two different regimes: singly-resonant cavities where the signal and idler modes are resonant, and doubly-resonant cavities where the pump mode is also resonant. We present analytic expressions for the joint spectral amplitude in these two cases, and study the reduction in emission bandwidth as the cavity coefficient finesse is increased. We also study the enhancement of the source brightness resulting fr…
We study the conditional preparation of single photons based on parametric downconversion, where the detection of one photon from a given pair heralds the existence of a single photon in the conjugate mode. We derive conditions on the modal characteristics of the photon pairs, which ensure that the conditionally prepared single photons are quantum-mechanically pure. We propose specific experimental techniques that yield photon pairs ideally suited for single-photon conditional preparation.
We report spontaneous parametric downconversion having an unusually wide spectral bandwidth. A collinear type-1 phase-matching configuration is employed with degeneracy near the zero group velocity dispersion frequency. With a spectral width of 1080 nm and degenerate wavelength 1885 nm, the source also emits a high flux of photon pairs constrained to a cone of only 2 degree half-angle. A rigorous theoretical approach is developed that confirms the experimental observations. The source properties are consistent with an ultra-short photon-pair correlation time and, for a narrowband pump, extreme…
We introduce a theoretical framework based on Fano's theory of discrete-continuum interactions to analyze the quantum dynamics of broadband parametric downconversion (PDC) in the few-pump-photon regime of nonlinear quantum nanophotonics. Applying this unified analytic approach to 1D $χ^{(2)}$-nonlinear waveguides, we find a host of remarkable dynamical features due to the coupling of a discrete pump state to the signal continuum, from unit-efficiency (i.e., complete) downconversion when the coupling is dissipative, to Rabi-like oscillations with sub-exponential decay when it is dispersive. The…
We address the pair of conjugated field modes obtained from parametric-downconversion as a convenient system to analyze the quantum-classical transition in the continuous variable regime. We explicitly evaluate intensity correlations, negativity and entanglement for the system in a thermal state and show that a hierarchy of nonclassicality thresholds naturally emerges in terms of thermal and downconversion photon number. We show that the transition from quantum to classical regime may be tuned by controlling the intensities of the seeds and detected by intensity measurements. Besides, we show …
We address the intrinsic multimode nature of the quantum state of light obtained by pulsed spontaneous parametric downconversion and develop a theoretical model based only on experimentally accessible quantities. We exploit the pairwise entanglement as a resource for conditional multimode measurements and derive closed formulas for the detection probability and the density matrix of the conditional states. We present a set of experiments performed to validate our model in different conditions that are in excellent agreement with experimental data. Finally, we evaluate nonGaussianity of the con…
What are the orbital angular momentum correlations between spatially entangled photon pairs generated in spontaneous parametric down-conversion? We show that the answer to this question can be given in two alternative, although complementary, ways. The answer posed in this letter explains satisfactorily the seemingly contradictory results obtained in different experiments, and theoretical approaches.
The use of quantum bits (qubits) in cryptography holds the promise of secure cryptographic quantum key distribution schemes. It is based usually on single-photon polarization states. Unfortunately, the implemented ``qubits'' in the usual weak pulse experiments are not true two-level systems, and quantum key distribution based on these imperfect qubits is totally insecure in the presence of high (realistic) loss rate. In this work, we investigate another potential implementation: qubits generated using a process of parametric downconversion. We find that, to first (two-photon) and second (four-…
For advanced quantum information technology, sources of photon pairs in quantum mechanically factorable states are of great importance for realizing high-fidelity photon-photon quantum gate operations. Here we experimentally demonstrate a technique to produce spectrally factorable photon pairs utilizing multi-order quasi-phase-matching (QPM) conditions in spontaneous parametric downconversion (SPDC). In our scheme, a spatial nonlinearity profile of a nonlinear optical crystal is shaped with current standard poling techniques, and the associated phase-matching function can be approximated to a …
We study the joint spectral properties of photon pairs generated by spontaneous parametric down-conversion in a one-dimensional nonlinear photonic crystal in a collinear, degenerate, type-II geometry. We show that the photonic crystal properties may be exploited to compensate for material dispersion and obtain photon pairs that are nearly factorable, in principle, for arbitrary materials and spectral regions, limited by the ability to fabricate the nonlinear crystal with the required periodic variation in the refractive indices for the ordinary and extraordinary waves.
This paper presents the general Schmidt decomposition of two-photon fields generated in spontaneous parametric down-conversion (SPDC). It discusses in particular the separation of the radial and azimuthal degrees of freedom, the role of projection in modal analysis, and the benefits of collinear phase mismatch. The paper is written in a review style and presents a wealth of numerical results. It aims at emphasising the physics beyond the mathematics, through discussions and graphical representations of key results.
Spontaneous parametric downconversion is the primary source to generate entangled photon pairs in quantum photonics laboratories. Depending on the experimental design, the generated photon pairs can be correlated in the frequency spectrum, polarisation, position-momentum, and spatial modes. Exploring the spatial modes' correlation has hitherto been limited to the polar coordinates' azimuthal angle, and a few attempts to study Walsh modes radial states. Here, we study the full-mode correlation, on a Laguerre-Gauss basis, between photon pairs generated in a type-I crystal. Furthermore, we explor…
Pulsed parametric downconversion (PDC) processes generate photon pairs with a rich spectral-temporal structure, which offer an attractive potential for quantum information and communication applications. In this paper, we investigate the four-dimensional chronocyclic Wigner function of the PDC state, which naturally lends itself to the pulsed characteristics of these states. From this function we derive the conditioned time-bandwidth product of one of the pair photons, a quantity which is not only a valid measure of entanglement between the PDC photons but also allows to highlight a remarkable…
In an experiment reported recently [Phys. Rev. Lett. 100, 133601 (2008)], we demonstrated that, through group velocity matched parametric downconversion, heralded single photons can be generated in pure quantum states without spectral filtering. The technique relies on factorable photon pair production, initially developed theoretically in the strict collinear regime; focusing - required in any experimental implementation - can ruin this factorability. Here we present the numerical model used to design our single photon sources and minimize spectral correlations in the light of such experiment…
It is shown that a highly phase sensitive polarization squeezed (2n-1)-photon state can be generated by subtracting a diagonally polarized photon from the 2n photon component generated in collinear type II downconversion. This polarization wedge state has the interesting property that its photon number distribution in the horizontal and vertical polarizations remains sharply defined for phase shifts of up to 1/n between the circularly polarized components. Phase shifts at the Heisenberg limit are therefore observed as nearly deterministic transfers of a single photon between the horizontal and…
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 f…
Parametric downconversion (PDC) in semiconductor Bragg-reflection waveguides (BRW) is routinely exploited for photon-pair generation in the telecommunication range. Contrary to many conventional PDC sources, BRWs offer possibilities to create spectrally broadband but nevertheless indistinguishable photon pairs in orthogonal polarizations that simultaneously incorporate high frequency entanglement. We explore the characteristics of co-propagating twin beams created in a type-II ridge BRW. Our PDC source is bright and efficient, which serves as a benchmark of its performance and justifies its ex…
In this paper we show that by suitably tailoring the dispersion characteristics of a Bragg reflection waveguide (BRW) mode, it is possible to achieve efficient photon pair generation over a large pump bandwidth while maintaining narrow signal bandwidth. The structure proposed consists of a high index core BRW with a periodically poled GaN core and periodically stratified cladding made up of alternate layers of $Al_{0.02}Ga_{0.98}N$ and $Al_{0.45}Ga_{0.55}N$. Such photon-pair generators should find applications in realizing compact and stable sources for quantum information processing.
We show that the states generated by a three-mode spontaneous parametric downconversion (SPDC) interaction Hamiltonian possess tripartite entanglement of a different nature to other paradigmatic three-mode entangled states generated by the combination of two-mode SPDCs interactions. While two-mode SPDC generates gaussian states whose entanglement can be characterized by standard criteria based on two-mode quantum correlations, these criteria fail to capture the entanglement generated by three-mode SPDC. We use criteria built from three-mode correlation functions to show that the class of state…
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…
Device-independent quantum key distribution (DIQKD) guarantees unconditional security of secret key without making assumptions about the internal workings of the devices used. It does so using the loophole-free violation of a Bell's inequality. The primary challenge in realizing DIQKD in practice is the detection loophole problem that is inherent to photonic tests of Bell's inequalities over lossy channels. We revisit the proposal of Curty and Moroder [Phys. Rev. A 84, 010304(R) (2011)] to use a linear optics-based entanglement-swapping relay (ESR) to counter this problem. We consider realisti…
Optical downconversion is a key resource for generating nonclassical states. Very recently, direct nondegenerate triple-photon spontaneous downconversion (NTPSD) with bright photon triplets and strong third-order correlations has been demonstrated in a superconducting device (2020 Phys. Rev. X 10 011011). Besides, linear and nonlinear tripartite entanglement in this process have also been predicted (2018 Phys. Rev. Lett. 120 043601; 2020 Phys. Rev. Lett. 125 020502). In this paper, we consider the generation of nonclassical optical quantum superpositions and investigate nonlinear quantum steer…
We present a study of the effects of dispersion on the properties of photon pairs generated by type-II, collinear spontaneous parametric downconversion. Specifically, we take into consideration the effects of a chirped pump, as well as of dispersive propagation of the photon pairs. We present expressions for the joint amplitude both in the spectral and temporal domains, as well as for the chronocyclic Wigner function of heralded single photons, which fully characterizes the single photon spectral (temporal) properties. On the one hand, we show that unwanted effects of pump chirp in terms of th…
We interface a spontaneous parametric down conversion (SPDC) crystal and a cold atomic ensemble and demonstrate a highly efficient quantum memory through polarization-encoded single-photon qubits. Specifically, narrowband heralded single photons from a cavity-enhanced SPDC source is stored using cold atomic ensemble, with ~70% storage-and-retrieval efficiency and ~10$μ$s storage time at 50% efficiency. To prevent the degradation after storage, we also manipulate the single-photon wave profile so that the retrieved non-classical nature of single photon is preserved. On the other hand, the dual-…
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…
Spontaneous parametric down-conversion (SPDC) is widely used in quantum applications based on photonic entanglement. The efficiency of photon pair generation is often characterized by means of a $sinc(LΔk/2)$-function, where $L$ is the length of the nonlinear medium and $Δk$ the phase mismatch between the pump and down-converted fields. In theoretical investigations, the \textit{sinc} behavior of the phase mismatch has often been approximated by a Gaussian function $\exp{(-αx^2)}$ in order to derive analytical expressions for the SPDC process. Different values have been chosen in the literatur…
We derive frequency correlation and exit probability expressions for photons generated via spontaneous parametric downconversion (SPDC) in nonlinear waveguides that exhibit linear scattering loss. Such loss is included within a general Hamiltonian formalism by connecting waveguide modes to reservoir modes with a phenomenological coupling Hamiltonian, the parameters of which are later related to the usual loss coefficients. In the limit of a low probability of SPDC pair production, the presence of loss requires that we write the usual lossless generated pair state as a reduced density operator,…
Heralded single photon sources are often implemented using spontaneous parametric downconversion, but their quality can be restricted by optical loss, double pair emission and detector dark counts. Here, we show that the performance of such sources can be improved using cascaded downconversion, by providing a second trigger signal to herald the presence of a single photon, thereby reducing the effects of detector dark counts. We find that for a setup with fixed detectors, an improved heralded second-order correlation function $g^{(2)}$ can always be achieved with cascaded downconversion given …
The distorsion of a spontaneous downconvertion process caused by an auxiliary mode coupled to the idler wave is analyzed. In general, a strong coupling with the auxiliary mode tends to hinder the downconversion in the nonlinear medium. On the other hand, provided that the evolution is disturbed by the presence of a phase mismatch, the coupling may increase the speed of downconversion. These effects are interpreted as being manifestations of quantum Zeno or anti-Zeno effects, respectively, and they are understood by using the dressed modes picture of the device. The possibility of using the cou…
Spontaneous parametric downconversion (SPDC) has been a key enabling technology in exploring quantum phenomena and their applications for decades. For instance, traditional SPDC, which splits a high energy pump photon into two lower energy photons, is a common way to produce entangled photon pairs. Since the early realizations of SPDC, researchers have thought to generalize it to higher order, e.g., to produce entangled photon triplets. However, directly generating photon triplets through a single SPDC process has remained elusive. Here, using a flux-pumped superconducting parametric cavity, w…
Optical parametric downconversion has proven to be a valuable source of nonclassical light. The process is inherently able to produce twin beam correlations along with individual intensity squeezing of either parametric beam, when pumped far above threshold. Here, we present for the first time the direct observation of intensity squeezing of -1.2 dB of each of the individual parametric beams in parametric downconversion by use of a high quality whispering gallery mode disk resonator. In addition we observed twin beam quantum correlations of -2.7 dB with this cavity. Such resonators feature str…
Coherence-domain imaging systems can be operated in a single-photon counting mode, offering low detector noise; this in turn leads to increased sensitivity for weak light sources and weakly reflecting samples. We have demonstrated that excellent axial resolution can be obtained in a photon-counting coherence domain imaging (CDI) system that uses light generated via spontaneous parametric down-conversion (SPDC) in a chirped periodically poled stoichiometric lithium tantalate (chirped-PPSLT) structure, in conjunction with a niobium nitride superconducting single-photon detector (SSPD). The bandw…
The development of new quantum light sources requires robust and convenient methods of characterizing their joint spectral properties. Measuring the joint spectral intensity between a photon pair ignores any correlations in spectral phase which may be responsible for degrading the quality of quantum interference. A fully phase-sensitive characterization tends to require significantly more experimental complexity. Here, we investigate the sensitivity of the frequency-resolved double-pair emission to spectral phase correlations, in particular to the presence of a simple form of correlated phase …
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 sever…
We discuss a novel method of efficiently producing multi-photon states using repeated spontaneous parametric downconversion. Specifically, by attempting downconversion several times, we can pseudo-deterministically add photons to a mode, producing various several-photon states. We discuss both expected performance and experimental limitations.
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 …
Alternative theories to quantum mechanics motivate important fundamental tests of our understanding and descriptions of the smallest physical systems. Here, using spontaneous parametric downconversion as a heralded single-photon source, we place experimental limits on a class of alternative theories, consisting of classical field theories which result in power-dependent normalized correlation functions. In addition, we compare our results with standard quantum mechanical interpretations of our spontaneous parametric downconversion source over an order of magnitude in intensity. Our data match …
