Spontaneous Parametric Down-conversion Process Research Articles

Electromagnetically Induced Quantum Holographic Imaging

We study the quantum holographic imaging of one-dimensional electromagnetically induced grating created by a strong standing wave in an atomic medium. Entangled photon pairs, generated in a spontaneous parametric down-conversion process, are employed as the imaging light to realize coincidence recording. By theoretical analysis and numerical simulation, we find that both the amplitude and phase information of the object can be imaged with the characteristic of imaging nonlocally and of arbitrarily controllable image variation in size.

Three-photon generation by means of third-order spontaneous parametric down-conversion in bulk crystals

We investigate the third-order spontaneous parametric down-conversion process in a nonlinear media with inversion centers. Specifically, we analyze in details the three-photon differential count rate in unit frequency and angular regions, total count rate and measurement time for rutile and calcite crystals which have comparatively large cubic susceptibilities. Special attention is given to consideration of limited frequency and angular detection ranges in order to calculate experimentally available detection rate values.

Experimental realization of positively momentum-correlated photon pairs from a long periodically poled lithium tantalate crystal

We experimentally realized the two-photon entangled state with correlated momentum and anticorrelated position, namely, the momentum positively correlated Einstein–Podolsky–Rosen (MPC-EPR) state from the spontaneous parametric downconversion process in a long periodically poled lithium tantalate (PPLT) crystal with a tightly focused pump beam. The MPC-EPR state is identified by measuring the momentum and position correlations at the Fourier plane and imaging plane of the PPLT crystal end face, respectively, showing a variance product (Δx+)2(Δp−)2=0.14±0.02ℏ2, which fulfills the entanglement criterion. The engineering of such an entangled state will bring interest to not only fundamental quantum physics but also the applied quantum technologies, such as quantum imaging, etc.

Two polarization-entangled sources from the same semiconductor chip

Generating nonclassical states of photons such as polarization entangled states on a monolithic chip is a crucial step towards practical applications of optical quantum information processing such as quantum computing and quantum key distribution. Here we demonstrate two polarization entangled photon sources in a single monolithic semiconductor waveguide. The first source is achieved through the concurrent utilization of two spontaneous parametric down-conversion (SPDC) processes, namely type-0 and type-I SPDC processes. The chip can also generate polarization entangled photons via the type-II SPDC process, enabling the generation of both co-polarized and cross-polarized entangled photons in the same device. In both cases, polarization entanglement is generated directly on the chip without the use of any off-chip compensation, interferometry or bandpass filtering. This enables direct, chip-based generation of both Bell states $(|H,H\rangle+|V,V\rangle)/\sqrt{2}$ and $(|H,V\rangle+|V,H\rangle)/\sqrt{2}$ simultaneously utilizing the same pump source. In addition, based on compound semiconductors, this chip can be directly integrated with it own pump laser. This technique ushers an era of self-contained, integrated, electrically pumped, room-temperature polarization entangled photon sources.

Hybrid-cascaded generation of tripartite telecom photons using an atomic ensemble and a nonlinear waveguide

Nonclassical multi-photon and number states are attractive because of their wide applicability, and experimental generation of these states is a longstanding aim. We prepare photon triplets using a spontaneous Raman scattering process in a hot atomic ensemble cascaded by a spontaneous parametric downconversion process in a periodically poled nonlinear waveguide; strong temporal correlations are observed between the photons. This represents the first combination of nonlinear processes of different orders with different physical systems, and demonstrates the scheme’s feasibility. The triplets exist in the telecommunications band, which is promising for testing of quantum mechanical laws for multi-photon entanglement over large distances.

An effective method for calculating phase-matching conditions in biaxial crystals

We present an effective method for calculating phase-matching conditions in biaxial crystals, especially for nonlinear orthorhombic crystals. Exploiting the angle definition introduced by Japanese mathematician Kodaira Kunihiko, we deduce the angular relations in geometry and obtain the expressions of refractive indices depending on angular orientation of wave vector k and optical axis angle. Then, we directly calculate the phase-matching conditions with BIBO crystal in spontaneous parametric down-conversion (SPDC) process and gain the optimum phase matching schemes for the type I and type II. On its basis, we discuss the angular gradients of the pump and emission wave refractive index near the exact phase matching direction and compare the SPDC with double-frequency process in geometrical relations of the refractive index ellipsoids. This method based on angle-dependent refractive index can be applied to three-wave interactions. It is convenient to calculate the phase matching parameters without solving the quadratic Fresnel equations.

Enhancing Heralding Efficiency and Biphoton Rate in Type-I Spontaneous Parametric Down-Conversion

The nonlinear optical process of spontaneous parametric down-conversion (SPDC) is widely studied for applications in quantum information science due to its ability to produce two photons that can be entangled in many degrees of freedom. For applications in quantum communication, two metrics of this process are particularly important: heralding efficiency and total joint rate. Here, we derive expressions for both quantities for a variety of different beam geometries and frequencies. We pay specific attention to the spectrum of both biphotons and individual photons. We reveal the underlying mechanisms responsible for the spectral shape and show they differ for different geometries and frequencies. We then use these spectra to calculate heralding efficiency and joint count rate and examine how each of these metrics changes with different geometries, frequencies, spectral filtering, and beam parameters. Interestingly, we find very high heralding efficiencies are achievable for collinear geometries without spectral filtering, while noncollinear geometries require spectral filtering to achieve the same values. We also find that the spectrum is narrower for nondegenerate SPDC than for degenerate SPDC, leading to lower joint count rates and higher heralding efficiency in the former. In addition to the theory, we verify selected predictions with experimental results.

Simulating single-photon sources based on backward-wave spontaneous parametric down-conversion in a periodically poled KTP waveguide

The properties of the backward-wave spontaneous parametric down-conversion (SPDC) in a periodically poled potassium titanyl phosphate (KTP) waveguide are studied in the context of creating narrowband heralded sources of single-photon states. The effective index of refraction and spatial profile of different waveguide modes, efficiency of different SPDC processes and purity of heralded photons are calculated numerically for a given waveguide. Compared to the usual co-propagating SPDC, spectral narrowing of the backward- wave SPDC was observed as should be expected.

Generation of higher-dimensional modal entanglement using a three-waveguide directional coupler

In this paper, we propose a method for the generation of higher-dimensional modal entanglement through a type II spontaneous parametric down-conversion process using a three-waveguide directional coupler in a periodically poled lithium niobate substrate. We show that by a proper design, it is possible to achieve an output state of two photons occupying three different spatial modes. The advantage of using such waveguide structure is its flexibility and the design space availability to achieve desired characteristics of the photon pairs generated in the down-conversion process.

Engineering of near-IR photon pairs to be factorable in space-time and entangled in polarization.

We present a source of near-infrared photon pairs based on the process of spontaneous parametric downconversion (SPDC), for which the joint signal-idler quantum state is designed to be factorable in the frequency-time and in the transverse position-momentum degrees of freedom. Our technique is based on the use of a broadband pump and vector group velocity matching between the pump, signal, and idler waves. We show experimentally that a source based on this technique can be configured for the generation of: i) pure heralded single photons, and ii) polarization-entangled photon pairs which are free from spectral correlations, in both cases without resorting to spectral filtering. While critical for many applications in optical quantum information processing, such a source has not previously been demonstrated.

Characterization of frequency entanglement under extended phase-matching conditions

Frequency-entangled photon pairs generated by spontaneous parametric down-conversion process under extended phase-matching conditions are found to be prospective resources for quantum information technology. The spectral indistinguishability and the degree of frequency entanglement of the down-converted photon pairs are two key features determining their potential applications. In this paper, both figures of merits are investigated. It is shown that the broadening of the pulsed pump bandwidth, the chirping of the pulse duration, and the lengthening of the nonlinear crystal all degrade the spectral indistinguishability. Furthermore, by changing the above conditions, it is possible to transfer the entanglement type from frequency-correlated to frequency-anticorrelated. For frequency-correlated entanglement, the degree of entanglement grows linearly with the pump bandwidth and the nonlinear crystal length, and quadratically with the chirp parameter of the pulse, while for anticorrelated frequency entanglement, the degree of frequency entanglement turns to behave with an inverse dependence on the above parameters. Guided by such investigations, the generation of desired frequency-entangled source for various quantum information applications can be optimized.

Generation of six-photon hyperentangled states

Nowadays, the nonlinear optical process of spontaneous parametric down-conversion is considered as the canonical approach for creating entangled-photon pairs. We consider three pairs of entangled photons emitted by the parametric down-conversion source, and introduce a setup for evolving these photons based on linear optics, which is composed of several polarizing beam splitters, beam splitters, and half wave plates. By using the parametric down-conversion source and the setup, we carefully design an efficient scheme for preparing six-photon hyperentangled states in both the polarization and the spatial degrees of freedom. Because we use almost all possible behaviors of the three pairs of entangled photons, the present scheme is efficient for creating six-photon hyperentangled states. Next, in the regime of weak nonlinearity we design a quantum nondemolition detection to distinguish the two cases of photons in two special spatial modes. It is worth pointing out that our scheme is much easier to realize, since the strength of the nonlinearities in the process of quantum nondemolition detection can be restricted to the scalable orders of magnitude in practicality.

Research of the impact of group velocity dispersion on the second-order correlation of entangled light field

In the experiment presented in the paper, HBT (Hanbury-Brown and Twiss) interferometer is used to measure the second-order correlation function (G2) for two entangled photons, denoted as signal and idle ones, generated by the spontaneous parametric down-conversion process. When an extra optical fiber is inserted in the signal's path, the arrival times of these two photons are different, so that the length of the fiber can be estimated by measuring the time offset in the G2 function.#br#As the laser light we used is not monochromatic, the experimental result is affected by the group velocity dispersion (GVD). Light of different wavelength has different velocity and leads to different travelling time in the fiber. Through calculation, we find that the G2 function of each wavelength has the same shape but different center time offset. Thus, the final G2 function, as a superimposition of the functions with different wavelengths, is broadened in a long-distance measurement, which seriously reduces the estimation accuracy. We analyze this phenomenon in both theory and experiment, and the experimental results fit our theoretical simulations quite well.#br#In the theoretical analysis, we find that the group velocity dispersion introduces an additional time offset to the final G2 function which is proportional to the total time offset. In our experiment, this additional time offset is about 1% of the total time offset. In particular, this effect results in a 63600 ps extra time offset, which can be compensated in post process, with a time accuracy of about 1 ps.#br#This paper focuses on the G2 function affected by the group velocity dispersion, and also calculates the additional time offset produced by group velocity dispersion, and thus gives a method to compensate the additional time offset through calculation.

Simulating Single-Photon Sources Based on Backward-Wave Spontaneous Parametric Down-Conversion in a Periodically Poled KTP Waveguide

The properties of the backward-wave spontaneous parametric down-conversion (SPDC) in a periodically poled potassium titanyl phosphate (KTP) waveguide are studied in the context of creating narrowband heralded sources of single-photon states. The effective index of refraction and spatial profile of different waveguide modes, efficiency of different SPDC processes and purity of heralded photons are calculated numerically for a given waveguide. Compared to the usual co-propagating SPDC, spectral narrowing of the backward-wave SPDC was observed as should be expected. Generation biphoton states in backward-wave regime is experimentally observed in two-photon detection scheme.

Effect of loss on photon-pair generation in nonlinear waveguide arrays

We describe theoretically the process of spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays in the presence of linear loss. We derive a set of discrete Schrodinger-type equations for the biphoton wave function, and the wave function of one photon when the other photon in a pair is lost. We demonstrate effects arising from loss-affected interference between the generated photon pairs and show that nonlinear waveguide arrays can serve as a robust loss-tolerant integrated platform for the generation of entangled photon states with non-classical spatial correlations.

Luminescence-induced noise in single photon sources based on BBO crystals

Single-photon sources based on the process of spontaneous parametric down-conversion play a key role in various applied disciplines of quantum optics. We characterize the intrinsic luminescence of BBO crystals as a source of non-removable noise in quantum-optics experiments. By analysing its spectral and temporal properties together with its intensity, we evaluate the impact of luminescence on single-photon state preparation using spontaneous parametric down-conversion.

Spontaneous parametric down-conversion using a pulse train

The process of spontaneous parametric down-conversion (SPDC) is studied for the case in which the pump is a train of pulses. Effects of such a train of pulses (equivalent to a frequency comb) on degenerate collinear type-II SPDC and degenerate collinear type-I SPDC are analyzed using the probability of photon coincidence counts and compared with the case when the medium is pumped by a single pulse.

Classical to quantum transfer of optical vortices.

We show that an optical vortex beam, implemented classically, can be transferred to the transverse amplitude of a heralded single photon. For this purpose we have relied on the process of spontaneous parametric downconversion (SPDC) for the generation of signal and idler photon pairs, using a pump in the form of a Bessel-Gauss (BG) beam with orbital angular momentum (specifically, with topological charge l = 1 and l = 2). We have designed our source so that it operates within the short SPDC crystal regime for which, the amplitude and phase of the pump may be transferred to a heralded single photon. In order to verify the vortex nature of our heralded single photon, we have shown that the conditional angular spectrum and the transverse intensity at the single-photon level match similar measurements carried out for the pump. In addition, we have shown that when our heralded single photon is diffracted through a triangular aperture, the far-field single-photon transverse intensity exhibits the expected triangular arrangement of intensity lobes associated with the presence of orbital angular momentum.

Two-photon quantum state engineering in nonlinear photonic nanowires

We propose and analyze a generic technique to engineer the two-photon quantum state generated by spontaneous parametric downconversion (SPDC) in nonlinear photonic nanowires using any suitable material system. Through dispersion engineering in nanowires, the group velocity of each photon involved in the SPDC process can be tuned such that pure heralded single photons or maximally polarization entangled photons can be directly generated on a chip. Implementations in III–V semiconductor and ferroelectric waveguides demonstrate minimal frequency correlations with Schmidt numbers of ∼1 for heralded single photons, and maximal entanglement with concurrences of ∼1 for polarization entangled photons.

Concurrent optical parametric down-conversion in χ(2) nonlinear photonic crystals.

We experimentally investigated concurrent parametric downconversion processes in a two-dimensional hexagonally poled lithium tantalate crystal. The substantial enhancement of parametric gain was observed when concurrent processes shared a common parametric beam. Both degenerate and nondegenerate concurrent parametric downconversion processes were studied. Analyses of the spatial forms and output angles showed a strong dependence on the working temperature, during which a well-defined beamlike parametric output was observed. Our results will stimulate the design for coherent high-gain generation of multiple parametric beams and also shed light on the compact engineering of path-entanglement with specific spatial forms based on concurrent spontaneous parametric downconversion processes.