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.
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 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 spectr…
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 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.
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 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 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.
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.
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 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.
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 …
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.
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…
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-…
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.
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…
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…
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 …
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…
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…
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…
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…
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…
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-…
A detailed analysis of the stimulated parametric down-conversion (PDC) process is performed to investigate the effects of the spatiotemporal degrees of freedom. The analysis provides information that would be useful for PDC-based metrology applications. Using a Wigner functional approach, we obtain the parametric down-converted state as the Bogoliubov transformed input state, in terms of Bogoliubov kernel functions. The result is used to consider the case for a coherent state seeding stimulated PDC. We also compute the background which is obtained from spontaneous PDC.
We present a quantum optics approach for describing stimulated parametric down conversion in the two type-I crystal "sandwich" configuration, which allows for parametric interaction of vector vortex beams. We analyze the conditions for which phase conjugation of the seed vector beam occurs. We then use two strategies for defining generalized Stokes parameters to describe phase conjugation of vector vortex beams. These allow for geometrical representations, such as higher-order Poincaré spheres. Our results are useful for description and design of stimulated and spontaneous parametric down conv…
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,…
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…
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…
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…
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 …
The advanced-wave picture is "... an intuitive treatment of two-photon correlation with the help of the concept of an effective field acting upon one of the two detectors and formed by parametric conversion of the advanced wave emitted by the second detector ..." [A. V. Belinskii and D. N. Klyshko, JETP 78, 259 (1994)]. This quote from Belinskii and Klyshko nicely describes the concept of the advanced-wave picture; an intuitive tool for designing and predicting results from coincidence-based two-photon experiments. Up to now, the advanced-wave picture has been considered primarily for the case…
We show how stimulated parametric processes can be employed in experiments on beyond the diffraction limit to overcome the problem of low visibility obtained by using spontaneous down conversion operating in the high gain regime. We further show enhancement of the count rate by several orders when stimulated parametric processes are used. Both the two photon counts and the visibility can be controlled by the phase of the stimulating coherent beam.
Stimulated emission of two photons is observed experimentally in the parametric amplification process and is compared to a three-photon interference scheme. We find that the underlying physics of stimulated emission is simply the constructive interference due to photon indistinguishability. So the observed signal enhancement upon the input of photons is a result of multi-photon interference of the input photons and the otherwise spontaneously emitted photon from the amplifier.
We theoretically discuss one-photon and two-photon double-slit interferences for spontaneous and stimulated parametric down-conversions. We show that the two-photon sub-wavelength interference can exist in a general spontaneous parametric down-conversion (SPDC) for both type I and type II crystals. We propose an alternative way to observe sub-wavelength interference by a joint-intensity measurement which occurs for only type I crystal in a higher gain of SPDC. When a signal beam injects into the crystal, it may create two interference patterns by two stimulated down-converted beams, showing no…
Spontaneous parametric down conversion (SPDC) has been largely exploited as a tool for absolute calibration of photon-counting detectors, i.e detectors registering very small photon fluxes. In [J. Opt. Soc. Am. B 23, 2185 (2006)] we derived a method for absolute calibration of analog detectors using SPDC emission at higher photon fluxes, where the beam is seen as a continuum by the detector. Nevertheless intrinsic limitations appear when high-gain regime of SPDC is required to reach even larger photon fluxes. Here we show that stimulated parametric down conversion allow one to avoid this limit…
We address the process of generation of the photon-number entangled states of light in the stimulated nonlinear parametric down conversion process and build the simple model describing the generation, not involving the traditional parametric approximation. The motion equations for the system of pumping and two-mode outgoing field are solved for the case of the strong correlation between two modes, the evolution of the state parameters of the generated modes is obtained. The solution is briefly analyzed for particular types of photon-number entangled states.
Spontaneous parametric down conversion has been largely exploited as a tool for absolute calibration of photon counting detectors, photomultiplier tubes or avalanche photodiodes working in Geiger regime. In this work we investigate the extension of this technique from very low photon flux of photon counting regime to the absolute calibration of analog photodetectors at higher photon flux. Moving toward higher photon rate, i.e. at high gain regime, with the spontaneous parametric down conversion shows intrinsic limitations of the method, while the stimulated parametric down conversion process, …
We introduce a scheme of single photon emission based on four-wave mixing in a three mode system with weak Kerr-type nonlinearity. A highly populated lower energy mode results in strong stimulated scattering of particle pairs out of the central mode, which consequently limits the central mode occupation. Thus, the system can be reduced to a $χ^{(2)}$ nonlinear medium with greatly enhanced interaction constant. As a model setup we consider dipolaritons in semiconductor microcavities. Using the master equation approach we show strong antibunching under continuous wave pump, which largely exceeds…
