Spontaneous Parametric Down-conversion Process Research Articles

Maximizing the validity of the Gaussian approximation for the biphoton state from parametric down-conversion

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 $sinc(L\Delta k/2)$-function, where $L$ is the length of the nonlinear medium and $\Delta k$ 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 $\exp{(-\alpha x^2)}$ in order to derive analytical expressions for the SPDC process. Different values have been chosen in the literature for the optimization factor $\alpha$, for instance by comparing the widths of \textit{sinc} and Gaussian functions or the momentum of down-converted photons. As a consequence, different values for $\alpha$ provide different theoretical predictions for the same setup. Therefore, an informed and unique choice of this parameter is necessary. In this work, we present a choice of $\alpha$ which maximizes the validity of the Gaussian approximation. Moreover, we also discuss the so-called \textit{super}-Gaussian and \textit{cosine}-Gaussian approximations as practical alternatives with improved predictive power for experiments.

Realistic and general model for quantum key distribution with entangled-photon sources

Entanglement-based quantum key distribution (EB-QKD) has several advantages over prepare-and-measure protocols, such as eliminating the need for decoy states and active modulators. At present, entanglement sources based on the spontaneous parametric down-conversion process have been widely used in EB-QKD experiments. Most of the existing models regard the photon-number distribution of pulse-pumped entanglement sources as thermal. However, doing so ignores any effects of spectral modes, which will lead to the overestimation of the secure key rate. In this paper, we analyze the correlation between the photon-number distribution and the joint spectral distribution and rewrite the quantum state of the photon pairs. Then we apply the results to EB-QKD and present a general model which can be used to calculate the secure key rate not only for any pulse-pumped systems but even for cw-pumped systems.

Exact Solutions for Vector Phase-Matching Conditions in Nonlinear Uniaxial Crystals

The transcendental equations of vector phase matching are transformed into a fourth-order polynomial equation that admits an analytical solution. The real roots of this equation provide the optical axis orientations that are useful for efficient down-conversion in nonlinear uniaxial crystals. The production of entangled photon pairs is discussed in both collinear and non-collinear configurations of the spontaneous parametric down-conversion (SPDC) process. Degenerate and non-degenerate cases are also distinguished. As a practical example, SPDC processes of type-I and type-II are studied for beta-barium borate (BBO) crystals. The predictions are in very good agreement with experimental measurements already reported in the literature and include theoretical results of other authors as particular cases. Some properties that seem to be exclusive to BBO crystals are reported; the experimental verification of the latter would allow a better characterization of these crystals.

Experimental quantum state discrimination using the optimal fixed rate of inconclusive outcomes strategy

The problem of non-orthogonal state discrimination underlies crucial quantum information tasks, such as cryptography and computing protocols. Therefore, it is decisive to find optimal scenarios for discrimination among quantum states. We experimentally investigate the strategy for the optimal discrimination of two non-orthogonal states considering a fixed rate of inconclusive outcomes (FRIO). The main advantage of the FRIO strategy is to interpolate between unambiguous and minimum error discrimination by solely adjusting the rate of inconclusive outcomes. We present a versatile experimental scheme that performs the optimal FRIO measurement for any pair of generated non-orthogonal states with arbitrary a priori probabilities and any fixed rate of inconclusive outcomes. Considering different values of the free parameters in the FRIO protocol, we implement it upon qubit states encoded in the polarization mode of single photons generated in the spontaneous parametric down-conversion process. Moreover, we resort to a newfangled double-path Sagnac interferometer to perform a three-outcome non-projective measurement required for the discrimination task, showing excellent agreement with the theoretical prediction. This experiment provides a practical toolbox for a wide range of quantum state discrimination strategies using the FRIO scheme, which can significantly benefit quantum information applications and fundamental studies in quantum theory.

Entanglement distribution using a biphoton frequency comb compatible with DWDM technology.

We demonstrate a distribution of frequency-multiplexed polarization-entangled photon pairs over 16 frequency channels using demultiplexers for the signal and idler photons with a frequency spacing of 25 GHz, which is compatible with dense wavelength division multiplexing (DWDM) technology. Unlike conventional frequency-multiplexed photon-pair distribution by a broadband spontaneous parametric down-conversion (SPDC) process, we use photon pairs produced as a biphoton frequency comb by SPDC inside a cavity where one of the paired photons is confined. Owing to the free spectral range of 12.5 GHz and the finesse of over 10 of the cavity, the generated photons having a narrow linewidth in one channel are separated well from those in the other channels, which minimizes channel cross-talk in advance. The observed fidelities of the photon pairs range from 81 % to 96 % in the 16 channels. The results show the usefulness of the polarization-entangled biphoton frequency comb for frequency-multiplexed entanglement distribution via a DWDM system.

Quantum diagnosis of cancer with heralded single photons

The unique properties of single quantum photons have more potential for many applications in quantum metrology. Here, by using state-of-the-art techniques, the precision of the attenuation measurement of light by propagating in the tissue is enhanced and a method to diagnose cancer in the tissue is proposed. The measurement of light with precision beyond the shot-noise limit and near the ultimate quantum limit can be attained using the heralded single photons (HSPs) generated by the spontaneous parametric down-conversion process. The interaction of HSP with normal and malignant breast tissues announces the presence of its partner. Theoretically and experimentally, a quantum approach to diagnosing cancer by comparing the measured attenuation coefficient of the normal and malignant tissues is demonstrated using the HSPs. We experimentally show that it is possible to improve the attenuation uncertainty due to the scattering of HSPs from the bio-sample to distinguish the malignant tissue from the normal tissue. Here, we use a narrow-band filter to remove the Raman scattering effect and consequently increase the attenuation uncertainty. This method is one of the applications of quantum metrology for precision enhancement which can be used in the histology of unstained tissues and tumor margin detection.

Noise-tolerant object detection and ranging using quantum correlations

Imaging, detection and ranging of objects in the presence of significant background noise is a fundamental challenge in optical sensing. Overcoming the limitations imposed in conventional methods, quantum light sources show higher resistance against noise in a time-correlation-based quantum illumination. Here, we introduce the advantage of using not only time correlations but also polarization correlations in photon pairs in the detection of an object that is embedded in a noisy background. In this direction, a time- and polarization-correlated photon pair source using the spontaneous parametric down-conversion process is exploited. We found that the joint measurement of correlated pairs allows distinguishing the signal from the noise photons and that leads to an improved signal-to-noise ratio. Our comparative study revealed that using polarization correlations in addition to time correlations provides improved noise rejection. Furthermore, we show that polarization correlation allows undoing the detector limitation where high background often leads to detector saturation.

Spontaneous parametric down-conversion in bottom-up grown lithium niobate microcubes

Nonclassical light sources are highly sought-after as they are an integral part of quantum communication and quantum computation devices. Typical sources use bulk nonlinear crystals that rely on stringent phase-matching conditions, limiting the operating wavelength and bandwidth. In this work, we demonstrate the generation of photon pairs from a free-standing lithium niobate microcube at the telecommunication wavelength of 1.56 µm through the spontaneous parametric down-conversion process. The maximum photon pair generation rate obtained from a single microcube with the size of 3.6 µm is 490 Hz, resulting in an efficiency of 20.6 GHz/Wm, which is three orders of magnitude larger than the efficiency of biphoton generation in bulk nonlinear crystals. The microcubes are synthesized through a solvothermal method, offering the possibility for scalable devices via bottom-up assembly on any substrates. Our work constitutes an important step forward in the realization of compact nonclassical light sources with a wide bandwidth for various quantum applications.

Advantages of the frequency-conversion technique in quantum interference

Hong-Ou-Mandel (HOM) interference is a key phenomenon for understanding quantum interference and a basic tool for quantum information and metrological applications. By introducing the nonlinear frequency-conversion (NFC) technique into HOM interferometers, more phenomena could be found and more functions could be developed. Here, tunable quantum spatial beating is observed in a HOM interferometer based on the postfilter scheme, where two NFC modules function as tunable band-pass filters. Degenerate IR photon pairs at 1079.00 nm are generated based on the noncritical phase-matching spontaneous parametric down-conversion process and are up-converted to the visible band around 633.40 nm by the NFC modules before the detectors. We show that in addition to the filtering effect, the NFC can also improve the photon detection efficiency based on silicon avalanched detector, increasing the coherence length, and therefore improving the heralding efficiency and visibility. Our results demonstrate the advantages of the NFC technique in HOM interference, which could also be generalized to other quantum interference.

Inverse design of spontaneous parametric downconversion for generation of high-dimensional qudits

Spontaneous parametric downconversion (SPDC) in quantum optics is an invaluable resource for the realization of high-dimensional qudits with spatial modes of light. One of the main open challenges is how to directly generate a desirable qudit state in the SPDC process. This problem can be addressed through advanced computational learning methods; however, due to difficulties in modeling the SPDC process by a fully differentiable algorithm, progress has been limited. Here, we overcome these limitations and introduce a physically constrained and differentiable model, validated against experimental results for shaped pump beams and structured crystals, capable of learning the relevant interaction parameters in the process. We avoid any restrictions induced by the stochastic nature of our physical model and integrate the dynamic equations governing the evolution under the SPDC Hamiltonian. We solve the inverse problem of designing a nonlinear quantum optical system that achieves the desired quantum state of downconverted photon pairs. The desired states are defined using either the second-order correlations between different spatial modes or by specifying the required density matrix. By learning nonlinear photonic crystal structures as well as different pump shapes, we successfully show how to generate maximally entangled states. Furthermore, we simulate all-optical coherent control over the generated quantum state by actively changing the profile of the pump beam. Our work can be useful for applications such as novel designs of high-dimensional quantum key distribution and quantum information processing protocols. In addition, our method can be readily applied for controlling other degrees of freedom of light in the SPDC process, such as spectral and temporal properties, and may even be used in condensed-matter systems having a similar interaction Hamiltonian.

Direct generation of two-pair frequency entanglement via dual periodic poling in lithium niobate waveguides

In this paper, we address the generation of a two-pair frequency entangled state using type-0 spontaneous parametric down-conversion process in a dual periodically poled lithium niobate waveguide. We show that, by suitable domain engineering with two periods of quasi-phase matching grating, it is possible to achieve a frequency entangled state with two different pairs of frequencies. Numerical simulations show that the output state can be maximally entangled. We also perform numerical simulations to address other interesting and useful entangled states which can be generated with the help of our scheme. The proposed scheme can help create efficient photonic setups required for quantum communication systems and can have various applications considering the increasing interests of energy-time entanglement in quantum information regime.

Interferometric signature of different spectral symmetries of biphoton states

In this paper, we investigate the influence of the symmetry of the biphoton wave function on the coincidence measurement of the generalized Mach-Zehnder (MZ) interferometer, where there are a temporal and frequency shift operations between the two beam splitters. We show that the generalized MZ interferometer allows the measurement of the short-time Fourier transform of the function modeling the energy conservation of a spontaneous parametric down-conversion process if the full biphoton state is symmetric, and of the symmetric characteristic distribution of the phase-matching function if the state is antisymmetric. Thus, this technique is phase sensitive to the spectral distribution of the photon pairs. Finally, we investigate in detail the signature of a pair of anyons whose peculiar statistics can be simulated by engineering the spectrum of photon pairs.

Room-temperature biphoton source with a spectral brightness near the ultimate limit

Biphotons, generated from a hot atomic vapor via the process of spontaneous four-wave mixing (SFWM), have the following merits: Stable and tunable frequencies as well as linewidth. Such merits are very useful in the application of long-distance quantum communication. However, the hot-atom SFWM biphoton sources previously had far lower values of generation rate per linewidth, i.e., spectral brightness, as compared with the sources of biphotons generated by the spontaneous parametric down-conversion process. Here we report a hot-atom SFWM source of biphotons with a linewidth of 960 kHz and a generation rate of $3.7\ifmmode\times\else\texttimes\fi{}{10}^{5}$ pairs/s. The high generation rate, together with the narrow linewidth, results in a spectral brightness of $3.8\ifmmode\times\else\texttimes\fi{}{10}^{5}$ pairs/s/MHz, which is 17 times the previous best result with atomic vapors and also better than all known results with all kinds of media. The all-co-propagating scheme together with a large optical depth (OD) of the atomic vapor is the key improvement, enabling the achieved spectral brightness to be about one quarter of the ultimate limit. Furthermore, this biphoton source had a signal-to-background ratio (SBR) of 2.7, which violated the Cauchy-Schwartz inequality for classical light by about 3.6-fold. Although an increasing spectral brightness usually leads to a decreasing SBR, our systematic study indicates that both of the present spectral brightness and SBR can be enhanced by further increasing the OD. This work demonstrates a significant advancement and provides useful knowledge in quantum technology using photons.

Waveguide-based swappable hyperentangled photon states in a multi-period, postselection-free device

We explore the generation of four postselection-free, photonic hyperentangled states with the help of a multi-period waveguide device based on potassium titanyl phosphate. The output photons are emitted in the much-in-demand telecommunication wavelengths of 1550-nm and 1310-nm. The device geometry and design enables hyperentanglement in the spatial mode and polarization bases, through multi-period quasi-phase-matching involved in different spontaneous parametric downconversion processes. The spatially entangled part of these hyperentangled states are rendered swappable with the help of two embedded electro-optic phase modulators. A two-path design provides the flexibility of such a device in the choice of polarization-entangled states which is important in relevant experiments. Through the biphoton joint spectral amplitude, we decipher the parameters that make frequency correlation and further entanglement of the photon pairs feasible. Such maximally-hyperentangled biphoton states are useful in quantum information applications.

High-Performance Hyperentanglement Generation and Manipulation Based on Lithium Niobate Waveguides

Here, we demonstrate the generation and manipulation of hyperentanglement in polarization and time-energy degrees of freedom. The hyperentangled photon pairs are generated by cascaded second-harmonic generation and spontaneous parametric down-conversion processes in a high-efficiency periodically poled lithium niobate (PPLN) waveguide in a fiber Sagnac loop. The states achieve the maximum value of Clauser-Horne-Shimony-Holt Bell inequality of $S=2.76\ifmmode\pm\else\textpm\fi{}0.03$ with two-photon interference visibility of higher than 99% for polarization entanglement and the Franson-type two-photon interference visibility of 98.5% for time-energy entanglement. In addition, the polarization maximally entangled states can be fast switched to each other by using a PPLN on insulator chip through the electro-optic effect. After the entanglement manipulation, the two-photon interference visibility for polarization entanglement is still higher than 97% while keeping the quantum characteristics of time-energy degrees of freedom maintained. Our system paves a way toward reducing the complexity of quantum systems and has potential applications in many quantum-information tasks like fast superdense coding and teleportation.

Experimental demonstration of free-space two-photon interference.

Quantum interference plays an essential role in understanding the concepts of quantum physics. Moreover, the interference of photons is indispensable for large-scale quantum information processing. With the development of quantum networks, interference of photons transmitted through long-distance fiber channels has been widely implemented. However, quantum interference of photons using free-space channels is still scarce, mainly due to atmospheric turbulence. Here, we report an experimental demonstration of Hong-Ou-Mandel interference with photons transmitted by free-space channels. Two typical photon sources, i.e., correlated photon pairs generated in spontaneous parametric down conversion (SPDC) process and weak coherent states, are employed. A visibility of 0.744 ± 0.013 is observed by interfering with two photons generated in the SPDC process, exceeding the classical limit of 0.5. Our results demonstrate that the quantum property of photons remains even after transmission through unstable free-space channels, indicating the feasibility and potential application of free-space-based quantum interference in quantum information processing.

Frequency-to-Time Mapping Technique for Direct Spectral Characterization of Biphoton States From Pulsed Spontaneous Parametric Processes

The well-established frequency-to-time mapping technique is employed as a convenient and time-efficient method to directly characterize the spectral correlations of biphoton states from a pulsed-excited spontaneous parametric down-conversion process. We were enabled by this technique to implement for the first time, the spectral Hanbury-Brown and Twiss measurement, revealing directly the single frequency-mode bandwidth of the biphoton state.

Low-Temperature Bonding of Nanolayered InGaP/SiO2 Waveguides for Spontaneous-Parametric Down Conversion

The integration of III–V materials on photonic integrated circuits has enjoyed a lot of attention because of the necessity of merging photon sources with silicon electronics. Nevertheless, III–V source integration technologies are not sufficiently mature, inhibiting the employment of such platforms to a broader range of applications. Here, we present a novel approach that enables the transfer of III–V nanolayers (≈250 nm) to silicates via oxide bonding. Through use of a thick photoresist scaffold (≈30 μm), complete removal of the substrate can be performed while preserving the relative structure morphology. The use of the III–V native oxide without depositing interfacial oxide layers greatly reduces the processing time and cost. The transfer of an array composed of 1 mm long InGaP waveguides with 250 nm thickness and widths spanning from 0.7 to 11.2 μm to a SiO2 substrate has been experimentally demonstrated, evidencing the feasibility of the technique for wafer-scale processing. The application of the nanolayered waveguides in the spontaneous-parametric down-conversion process has been tested by photon-correlation measurement, showing good agreement with the theoretical model.

Measuring the tuning curve of spontaneous parameter downconversion using a comet-tail-like pattern.

Comet-tail-like interference patterns are observed using photons from the spontaneous parametric downconversion (SPDC) process. The patterns are caused by the angular-spectrum-dependent interference and the diffraction of a blazed grating. We present a theoretical explanation and simulation results for these patterns, which are in good agreement with the experimental results. The most significant feature of the patterns is the bright parabolic contour profile, from which one can deduce the parameter of the parabolic tuning curve of the SPDC process. This method could be helpful when designing experiments based on SPDC.

Cryogenic integrated spontaneous parametric down-conversion

Scalable quantum photonics relies on interfacing many optical components under mutually compatible operating conditions. To that end, we demonstrate that spontaneous parametric down-conversion (SPDC) in nonlinear waveguides, a standard technology for generating entangled photon pairs, squeezed states, and heralded single photons, is fully compatible with cryogenic operating conditions required for superconducting detectors. This is necessary for the proliferation of integrated quantum photonics in integration platforms exploiting quasi-phase-matched second-order nonlinear interactions. We investigate how cryogenic operation at 4 K affects the SPDC process by comparing the heralding efficiency, second-order correlation function, and spectral properties with operation at room temperature.