Parametric Down-conversion Process Research Articles

Engineering multipartite coupling in doubly pumped parametric down-conversion processes

We investigate the quantum state generated by optical parametric down-conversion in a $\chi^{(2) } $ medium driven by two noncollinear light modes. The analysis shows the emergence of multipartite, namely 3- or 4-partite, entangled states in a subset of the spatio-temporal modes generated by the process. These appear as bright spots against the background fluorescence, providing an interesting analogy with the phenomenology recently observed in two-dimensional nonlinear photonic crystals. We study two realistic setups: i) Non-critical phase-matching in a periodically poled Lithium Tantalate slab, characterized by a 3-mode entangled state among hot spots. ii) A type I setup in a Beta-Barium Borate crystal, where the spatial walk-off between the two pumps can be exploited to make a transition to a quadripartite entangled state. In both cases we show that the properties of the state can be controlled by modulating the relative intensity of two pump waves, making the device a versatile tool for quantum state engineering.

Improving the purity of heralded single-photon sources through spontaneous parametric down-conversion process* *Project supported by the National Key Research and Development Program of China (Grant Nos. 2018YFA0306400 and 2017YFA0304100), the National Natural Science Foundation of China (Grant Nos. 12074194, 11774180, and U19A2075), and the Leading-edge Technology Program of Jiangsu Natural Science Foundation, China (Grant No. BK20192001).

The high-purity single-photon source plays an important role in the field of quantum information. Usually, it is generated through spontaneous parametric down-conversion process. In this paper, we investigate and summarize a few approaches on obtaining single-photon sources with a high purity using either PPKTP or PPLN nonlinear crystals. Moreover, we present improved schemes to increase the purity based on existing work, corresponding applicable conditions and procedures are discussed and analyzed. Besides, we carry out numerical simulations and show that nearly perfect purity can be reached even without using any filters. Therefore, this work might provide valuable references for the generation and application of high purity single-photon sources.

Positive operator-valued measure for two-photon detection via sum-frequency generation

Spontaneous parametric down conversion (PDC), in the perturbative limit, can be considered as a probabilistic splitting of one input photon into two output photons. Conversely, sum-frequency generation (SFG) implements the reverse process of combining two input photons into one. Here we show that a single-photon projective measurement in the temporal-mode basis of the output photon of a two-photon SFG process effects a generalized measurement on the input two-photon state. We describe the positive-operator-valued measure (POVM) associated with such a measurement, and show that its elements are proportional to the two-photon states produced by the time-reversed PDC process. Such a detection acts as a joint measurement on two photons, and is thus an important component of many quantum information processing protocols relying on photonic entanglement. Using the retrodictive approach, we analyze the properties of the two-photon POVM that are relevant for quantum protocols exploiting two-photon states and measurements.

Impact of higher-order optical fiber modes for photon-triplet generation

This paper presents a study of the phasematching properties of the third-order parametric down-conversion process in multimode optical fibers with a step-index profile. Through this process, entangled photon triplets can be generated in the spontaneous regime. We show that phasematching is achieved in a wide range of fiber geometries, provided that the pump field propagates in a higher-order mode. Furthermore, we show the nonlinear coefficient and the absolute emitted flux for each source configuration, evaluated from expressions derived by us in previous theoretical studies concerning the spontaneous and stimulated emission regimes.

Comparative Study of Quantum Features of Radiation Generated by Nondegenerate Down-Conversion

A comparative study of quantum properties associated with coherent correlations between the modes of light generated by a nondegenerate parametric down-conversion process is presented. Particularly, the degree of nonclassicality that can be quantified by logarithmic negativity and quantum discord is compared, and a striking similar tendency is observed. In the same manner, a comparison of the quadrature variance, the smallest eigenvalue of the symplectic matrix and Einstein-Podolsky-Rosen (EPR) steering is made whereby a significant similarity is witnessed. The highest degree of quantum features of the radiation is in general manifested near threshold, whereas the quantifying measure related to the smallest eigenvalue of the symplectic matrix is found to capture a better degree of quantumness. Since each criterion renders only sufficient condition, it is hoped that witnessing consistent outcome across different criteria enhances the chance for experimental verification and practical application.

Interaction of a heralded single photon with nitrogen-vacancy centers in a diamond.

A simple, room-temperature, cavity- and vacuum-free interface for a photon-matter interaction is implemented. In the experiment, a heralded single photon generated by the process of spontaneous parametric down-conversion is absorbed by an ensemble of nitrogen-vacancy color centers. The broad absorption spectrum associated with the phonon sideband solves the mismatch problem of a narrow absorption bandwidth in a typical atomic medium and broadband spectrum of quantum light. The heralded single photon source is tunable in the spectral range 452 - 575 nm, which overlaps well with the absorption spectrum of nitrogen-vacancy centers.

Noise transfer of pump field noise with analysis frequency in a broadband parametric downconversion process

Our previous work had proved pump field noise coupling in the seed field injected optical parametric amplifier (OPA) at a certain analysis frequency. Inspired by this noise coupling mechanism, the frequency dependent squeezing factor due to excess pump noise was experimentally demonstrated. Apart from a reduced squeezing level with an increased noise, the results also prove that a broadband squeezing noise spectrum is not frequency dependent on the amplitude modulated pump field, but limited by the bandwidth of the amplitude modulator and OPA resonator, and the effective measurement is carried out in the frequency range of 2–10 MHz. It provides a guidance to design a broader-bandwidth, higher-level bright squeezed light.

Mid-infrared spectrally-uncorrelated biphotons generation from doped PPLN: a theoretical investigation.

We theoretically investigate the preparation of mid-infrared (MIR) spectrally-uncorrelated biphotons from a spontaneous parametric down-conversion process using doped LN crystals, including MgO doped LN, ZnO doped LN, and In2O3 doped ZnLN with doping ratio from 0 to 7 mol%. The tilt angle of the phase-matching function and the corresponding poling period are calculated under type-II, type-I, and type-0 phase-matching conditions. We also calculate the thermal properties of the doped LN crystals and their performance in Hong-Ou-Mandel interference. It is found that the doping ratio has a substantial impact on the group-velocity-matching (GVM) wavelengths. Especially, the GVM2 wavelength of co-doped InZnLN crystal has a tunable range of 678.7 nm, which is much broader than the tunable range of less than 100 nm achieved by the conventional method of adjusting the temperature. It can be concluded that the doping ratio can be utilized as a degree of freedom to manipulate the biphoton state. The spectrally uncorrelated biphotons can be used to prepare pure single-photon source and entangled photon source, which may have promising applications for quantum-enhanced sensing, imaging, and communications at the MIR range.

Optimal photon pairs for quantum communication protocols

We theoretically investigate the problem of finding optimal characteristics of photon pairs, produced in the spontaneous parametric down-conversion (SPDC) process, for fiber-based quantum communication protocols. By using the accessible setup parameters, the pump pulse duration and the extended phase-matching function width, we minimize the temporal width of SPDC photons within the general scenario. This allows one to perform more effectively the temporal filtering procedure, which aims at reducing the noise acquired by the measurement devices. Moreover, we compare the obtained results with the achievable parameter values for SPDC sources based on beta-Barium Borate crystal. We also investigate the influence of non-zero detection timing jitter. Finally, we apply our optimization strategy to a simple quantum key distribution scheme to show that the full optimization of an SPDC source can potentially extend the maximal security distance by several tens of kilometres, which is around 30% more as compared to previous approaches.

Hot-spots and gain enhancement in a doubly pumped parametric down-conversion process.

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, similar to 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 point of view, this opens the way to the generation of multimode entangled states of light, such as tripartite or quadripartite states, in simple bulk nonlinear sources.

Einstein-Podolsky-Rosen steering in spontaneous parametric down-conversion cascaded with a sum-frequency generation

Einstein-Podolsky-Rosen (EPR) steering has potential applications in quantum information processing. Here the genuine tripartite EPR steering is investigated in cascaded nonlinear process of spontaneous parametric down-conversion cascaded with a sum-frequency generation in an optical cavity for a wide range of the nonlinear parameters. The threshold properties of the cascaded nonlinear precess are also analyzed both below and without threshold regime, respectively. The genuine tripartite EPR steering is demonstrated based on the criteria for genuine multipartite EPR steering. Our scheme of the generation of genuine tripartite EPR steering can be used as a suggestion for the potential experiments and the applications in quantum communication and computation.

Gouy phase of type-I SPDC-generated biphotons

We consider a double Gaussian approximation to describe the wavefunction of twin photons (also called a biphoton) created in a nonlinear crystal via a type-I spontaneous parametric downconversion (SPDC) process. We find that the wavefunction develops a Gouy phase while it propagates, being dependent of the two-photon correlation through the Rayleigh length. We evaluate the covariance matrix and show that the logarithmic negativity, useful in quantifying entanglement in Gaussian states, although Rayleigh-dependent, does not depend on the propagation distance. In addition, we show that the two-photon entanglement can be connected to the biphoton Gouy phase as these quantities are Rayleigh-length-related. Then, we focus the double Gaussian biphoton wavefunction using a thin lens and calculate a Gouy phase that is in reasonable agreement with the experimental data of D. Kawase et al. published in Ref. [1].

Amplification of polarization correlations in Compton scattering of hard x-ray Bell states

The theoretical cross section for Compton scattering of maximally entangled Bell photons has yet to be rigorously confirmed by experiments. Test cases of Bell states for use in Compton scattering experiments can now be expanded given reports of creating all 4 Bell states in the hard x-ray regime by the process of spontaneous parametric down-conversion. We outline an experiment and apply a matrix method to parameterize Compton scattering theory using the phase matching angles. When the azimuths of two hypothetical photon counters are recorded at angles of 0 degrees and 90 degrees, and the ratio of their counting rates determined, azimuthal ratios are expected to be 600 times larger compared to 511 keV Bell photons.

SPDC photon pairs using a spatially anti-symmetric pump beam in a ppLN ridge waveguide

In this paper, we study the possible parametric down-conversion processes in a type II phase-matched, Lithium Niobate ridge waveguide, designed to generate photon pairs in the telecommunication range. A quantum analysis of spontaneous parametric down-conversion (SPDC), first, with a pulsed Gaussian pump beam and second, with a pulsed, spatially anti-symmetric Hermite-Gaussian HG (1,0) pump beam predict the possible down conversion processes in each case. In case of the former, degenerate photon pairs are emitted at 1550 nm with the highest efficiency in the fundamental waveguide mode. While, in case of the latter, non-degenerate photon pairs in different higher-order spatial modes are generated. The joint spectral amplitude (JSA) analysis of these processes, prove that the generated photons pairs having orthogonal polarizations are negatively correlated. With multiple degrees of freedom, like polarization and spatial modes, such photons can be further harnessed towards modal-entangled and hyper-entangled photons for quantum information applications. This study involving the JSA is one of the first kinds, especially, to show the possibility of photon pairs generated in different spatial modes and polarization, after being incident with a spatially anti-symmetric pump beam in a ridge waveguide scenario.

Parametric down-conversion beyond the semiclassical approximation

Using a perturbative approach, we investigate the parametric down-conversion process without the semi-classical approximation. A Wigner functional formalism, which incorporates both the spatiotemproal degrees of freedom and the particle-number degrees of freedom is used to perform the analysis. First, we derive an evolution equation for the down-conversion process in the nonlinear medium. Then we use the perturbative approach to solve the equation. The leading order contribution is equivalent to the semi-classical solution. The next-to-leading order contribution provides a solution that includes the evolution of the pump field as a quantum field.

Molecular Rovibrational Spectroscopy with Undetected Photons via Single-Photon Interferometry

Interferometric spectroscopy with undetected photons (ISUP) utilizing quantum mechanically path-entangled photon pairs has received considerable attention as an optical-measurement platform. Recently, we carried out a proof-of-concept experiment to show that ISUP can be used to measure the transmission spectrum of a Fabry-Perot resonator. Here, we demonstrate that ISUP with dual stimulated parametric down-conversion (StPDC) processes, which allows us to perform infrared rovibrational spectroscopy with visible photons. In our ISUP method, quantum coherence between two independent signal photons from each StPDC crystal is induced by the indistinguishability of conjugate idler fields and results in high visibility of the signal single-photon interferometry at the nondegenerate wavelength. If the seed-beam intensity is imbalanced due to the sample absorption, the corresponding envelope modulation of the interference fringe as a function of the seed-beam frequency reveals the absorption spectrum of the optical sample. As a proof-of-principle experiment, the full rovibrational transmission spectrum at 1550 nm of the hydrogen cyanide (${\mathrm{H}}^{13}{\mathrm{C}}^{14}\mathrm{N}$) molecules in a gas cell is measured from the single-photon interference fringe of the signal fields at 807 nm. We thus anticipate that the single-photon ISUP technique with dual StPDC crystals will find broad use for the development of high-resolution atomic and molecular spectroscopy with undetected photons.

Dependence of the photon statistics of down-converted field-modes on the photon statistics of the pump field-mode

Using the zero time-delay second-order correlation function for studying photon statistics, we investigate how the photon statistics of field-modes generated by the parametric down-conversion (PDC) process depends on the photon statistics of the pump field-mode. We derive general expressions for the zero time-delay second-order correlation function of the down-converted field-modes for both multi-mode and single-mode PDC processes. We further study these expressions in the weak down-conversion limit. We show that for a two-photon two-mode PDC process, in which a pump photon splits into two photons into two separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to twice that of the pump field-mode. Furthermore, for an n -photon n -mode down-conversion process, in which a pump photon splits into n photons into n separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to 2 ( n − 1 ) times that of the pump field- mode. However, in contrast to multi-mode PDC processes, for a single-mode PDC process, in which a pump photon splits into two or more photons into a single mode, the zero time-delay second-order correlation function of the down-converted field-mode is not proportional to that of the pump in the weak down-conversion limit. Nevertheless, we find it to be inversely proportional to the average number of photons in the pump field-mode.

Generation of narrowband counterpropagating polarization-entangled photon pairs based on thin-film lithium niobate on insulator

We propose a scheme for the generation of counterpropagating polarization-entangled photon pairs from a periodically poled lithium niobate on insulator waveguide. The waveguide is designed to enable a special dispersion relationship between the T M 00 and T E 00 modes that allows two concurrent counterpropagating quasi-phase-matching type-II spontaneous parametric downconversion processes with a single reciprocal wave vector. Due to the counterpropagating phase-matching geometry, the source has a narrow bandwidth in the order of several gigahertz. The compact source opens up a new method for integrated photonic technologies.

Interaction of a dipolariton system with squeezed light from a parametric down-conversion process

We investigate the photon statistics of the light transmitted by a dipolariton system in interaction with a squeezed light from a degenerate optical parametric oscillator. We show that the presence of the squeezed photons in the cavity considerably increases the excitonic intensities and leads to a narrowing of the widths and a duplication of the intensity peaks. Our study reveals that the outgoing light exhibits a strong thermally resistant squeezing. Furthermore, it turns out that the weak-coupling regime is favorable to a perfect squeezing depending on the detunings and the strength of the squeezed pump. For a weak coherent driving field, the proposed system presents a bunching effect of the emitted light.

Experimental demonstration of hidden nonlocality with local filters.

The violation of the Bell inequalities implies that quantum mechanics cannot be interpreted using any local hidden variable theory. However, particular quantum states that can originally be described using a local hidden variable model surprisingly exhibit nonlocality by employing local filters before a standard Bell test is performed. This is referred to as hidden nonlocality. In this study, we provide the experimental demonstration of hidden nonlocality through linear optics towards the local states which are put forword by Hirsch et al., PRL 111, 160402 (2013). A class of local states is generated through a spontaneous parametric down-conversion process, and the violation of the Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality is observed by applying local filters. Our experimental results confirm the superiority of local filters, and throw light on deep understanding the intriguing phenomena of hidden nonlocality and local states.