Spontaneous Four-wave Mixing Research Articles

Electrically driven source of time-energy entangled photons based on a self-pumped silicon microring resonator.

Time-energy entangled photon pairs are fundamental resources for quantum communication protocols since they are robust against environmental fluctuations in optical fiber networks. Pair sources based on spontaneous four-wave mixing in silicon microring resonators usually employ expensive external tunable lasers to compensate for ambient fluctuations; adopting self-pumped configurations, instead, lifts the need for such external source. Here we demonstrate the emission of time-energy entangled photon pairs at telecom wavelengths from a silicon self-pumped ring, obtaining a Franson interference fringe with 93.9%±0.9% visibility.

Degenerate squeezing in waveguides: a unified theoretical approach

We consider pulsed-pump spontaneous parametric downconversion (SPDC) as well as pulsed single- and dual-pump spontaneous four-wave mixing processes in waveguides within a unified Hamiltonian theoretical framework. Working with linear operator equations in k-space, our approach allows inclusion of linear losses, self- and cross-phase modulation, and dispersion to any order. We describe state evolution in terms of second-order moments, for which we develop explicit expressions. We use our approach to calculate the joint spectral amplitude of degenerate squeezing using SPDC analytically in the perturbative limit, benchmark our theory against well-known results in the limit of negligible group velocity dispersion, and study the suitability of recently proposed sources for quantum sampling experiments.

Theory of four-wave mixing of cylindrical vector beams in optical fibers

Cylindrical vector (CV) beams are a set of transverse spatial modes that exhibit a cylindrically symmetric intensity profile and a variable polarization about the beam axis. They are composed of a non-separable superposition of orbital and spin angular momenta. Critically, CV beams are also the eigenmodes of optical fiber and, as such, are of widespread practical importance in photonics and have the potential to increase communications bandwidth through spatial multiplexing. Here, we derive the coupled amplitude equations that describe the four-wave mixing (FWM) of CV beams in optical fibers. These equations allow us to determine the selection rules that govern the interconversion of CV modes in FWM processes. With these selection rules, we show that FWM conserves the total angular momentum, the sum of orbital and spin angular momenta, in the conversion of two input photons to two output photons. When applied to spontaneous FWM, the selection rules show that photon pairs can be generated in CV modes directly and can be entangled in those modes. Such quantum states of light in CV modes could benefit technologies such as quantum key distribution with satellites.

Heralded single-photon and correlated-photon-pair generation via spontaneous four-wave mixing in tapered optical fibers

We study the generation of correlated photon pairs and heralded single photons via strongly non-degenerate spontaneous four-wave mixing (SFWM) in a series of identical micro-/nano fibers (MNF). Joint spectral intensity of the biphoton field generated at the wavelength of about 880 nm and 1310 nm has been measured under excitation by 100 ps laser pulses demonstrating good agreement with the theoretical prediction. The measured zero-time second-order autocorrelation function was about 0.2 when the emission rate of the heralded photons was of 4 Hz. The MNF-based source perfectly matches standard single-mode fibers, which makes it compatible with the existing fiber communication networks. In addition, SFWM observation in a series of identical MNFs allows increasing generation rate of single photons via spatial multiplexing.

Entanglement swapping with autonomous polarization-entangled photon pairs from a warm atomic ensemble.

Entanglement swapping forms a key concept in the realization of scalable quantum networks and large-scale quantum communication. For the practical implementation of entanglement swapping, completely autonomous entanglement sources and a joint Bell-state measurement (BSM) between two independent photons are essential. Here, we experimentally demonstrate entanglement swapping between two independent polarization-entangled photon-pair sources obtained via spontaneous four-wave mixing (SFWM) in a Doppler-broadened atomic ensemble of ${^{87}}{\rm Rb}$87Rb atoms. From the joint BSM, we estimate the ${\rm S}$S parameter in the Clauser-Horne-Shimony-Holt (CHSH) form of Bell's inequality and confirm the violation of the Bell-CHSH inequality by ${\rm S}={2.32} \pm {0.07}$S=2.32±0.07 with 4.5 standard deviations. We believe that this work is an important step toward realizing practical scalable quantum networks.

Generation of hyper-entangled photons in a hot atomic vapor.

A source of hyper-entangled photons plays a vital role in quantum information processing, owing to its high information capacity. In this Letter, we demonstrate a convenient method to generate polarization and orbital angular momentum (OAM) hyper-entangled photon pairs via spontaneous four-wave mixing (SFWM) in a hot $ ^{87}{\rm Rb} $87Rb atomic vapor. The polarization entanglement is achieved by coherently combining two SFWM paths with the aid of two beam displacers that constitute a phase self-stabilized interferometer, and OAM entanglement is realized by taking advantage of the OAM conservation condition during the SFWM process. Our hyper-entangled biphoton source possesses high brightness and high nonclassicality and may have broad applications in atom-photon-interaction-based quantum networks.

Temporal modes in quantum optics: then and now

We review the concepts of temporal modes (TMs) in quantum optics, highlighting Roy Glauber’s crucial and historic contributions to their development, and their growing importance in quantum information science. TMs are orthogonal sets of wave packets that can be used to represent a multimode light field. They are temporal counterparts to transverse spatial modes of light and play analogous roles—decomposing multimode light into the most natural basis for isolating statistically independent degrees of freedom. We discuss how TMs were developed to describe compactly various processes: superfluorescence, stimulated Raman scattering, spontaneous parametric down conversion, and spontaneous four-wave mixing. TMs can be manipulated, converted, demultiplexed, and detected using nonlinear optical processes such as three-wave mixing and quantum optical memories. As such, they play an increasingly important role in constructing quantum information networks.

Compact high-extinction tunable CROW filters for integrated quantum photonic circuits.

We describe the use of cascaded second-order coupled-resonator optical waveguide (CROW) tunable filters to achieve one of the highest reported measured extinction ratios of $ {\gt} {110}\;{\rm dB}$>110dB. The CROW filters were used to remove the pump photons in spontaneous four-wave mixing (SFWM) in a silicon waveguide. The SFWM generated quantum-correlated photons that could be measured after the cascaded CROW filters. The CROW filters offer a compact footprint for use in monolithic quantum photonic circuits.

Hybrid waveguide scheme for silicon-based quantum photonic circuits with quantum light sources

We propose a hybrid silicon waveguide scheme to avoid the impact of noise photons induced by pump lights in application scenarios of quantum photonic circuits with quantum light sources. The scheme is composed of strip waveguide and shallow-ridge waveguide structures. It utilizes the difference of biphoton spectra generated by spontaneous four-wave mixing (SFWM) in these two waveguides. By proper pumping setting and signal/idler wavelength selection, the generation of desired photon pairs is confined in the strip waveguide. The impact of noise photons generated by SFWM in the shallow-ridge waveguide can be avoided. Hence, the shallow-ridge waveguide could be used to realize various linear operation devices for pump light and quantum state manipulations. The feasibility of this scheme is verified by theoretical analysis and a primary experiment. Two applications are proposed and analyzed, showing its great potential in silicon-based quantum photonic circuits.

Correlated photon pair generation in ultra-silicon-rich nitride waveguide

Correlated photon pair generation is demonstrated using ultra-silicon-rich nitride waveguides. Waveguides with a length of 10 mm, nonlinear parameter of 530 W−1/m and anomalous dispersion are used to achieve spontaneous four-wave mixing. A generated coincidence rate of 2.40×105 counts per second is achieved, and derived from a measured coincidence rate of ∼1 counts per second at the maximum coupled power of 5 mW, in line with the expected quadratic dependence of spontaneous four-wave mixing efficiency on power. Utilizing picosecond pulses as the pump, we achieve a measured coincidence rate of up to 1.8 counts per second, resulting in a generated coincidence rate of 2.20×10−2 counts per pulse at the maximum peak power of 8.33 W. 2.3 times larger coincidence-to-accidental ratio is also obtained using a pulsed pump compared to that achieved with a continuous-wave pump. Further enhancements via the use of ring resonators may be adopted.

Optical Wave Guiding and Spectral Properties of Micro/Nanofibers Used for Quantum Sensing and Quantum Light Generation

Subwavelength optical micro/nanofibers have been widely used as basic building blocks in the field of quantum sensing and quantum light source by virtue of their properties which include pronounced evanescent field, large surface area, and small optical mode area. This paper presents theoretical studies on the propagation properties of the guided optical wave and the spectral properties of entangled photons from spontaneous four-wave mixing in micro/nanofibers. We first analyze numerically single-mode propagation, field distribution, fraction of power, and group-velocity-dispersions by solving Maxwell’s equations with boundary conditions in cylindrical coordinates. Then, optical wave guiding properties of micro/nanofibers are applied to estimate the spectral properties such as central wavelengths and bandwidths of the created photons via spontaneous four-wave mixing that can be tailored by controlling diameter and length of micro/nanofibers. This theoretical work provides useful guidelines to design micro/nanofiber-based quantum sensing and quantum light sources for quantum technologies.

Einstein-Podolsky-Rosen Energy-Time Entanglement of Narrow-Band Biphotons.

We report the direct characterization of energy-time entanglement of narrow-band biphotons produced from spontaneous four-wave mixing in cold atoms. The Stokes and anti-Stokes two-photon temporal correlation is measured by single-photon counters with nanosecond temporal resolution, and their joint spectrum is determined by using a narrow linewidth optical cavity. The energy-time entanglement is verified by the joint frequency-time uncertainty product of 0.063±0.0044, which does not only violate the separability criterion but also satisfies the continuous variable Einstein-Podolsky-Rosen steering inequality.

Complete evolution equation for the joint amplitude in photon-pair generation through spontaneous four-wave mixing

As four-wave-mixing-based photon-pair sources mature, accurate modelling of the photon-pair properties becomes important. Unlike spontaneous parametric down-conversion, four-wave mixing is accompanied by a number of parasitic effects such as nonlinear phase modulation. Currently, most modelling of photon-pair states are analytic in nature, which limits the number and type of effects that can be taken into account. In this work, we derive a complete, dual-pump evolution equation for the joint amplitude of photon pairs, wherein any desired effects can be included. We describe how to efficiently obtain numerical solution to this equation using a split-step approach. Lastly, we cover a few analytical solutions and compare two schemes for pure-photon generation under three different parasitic effects. We show how one scheme is highly sensitive to parasitic effects, while the other is very robust.

Correlated photon-pair generation in a liquid-filled microcavity

We report on the realization of a liquid-filled optical microcavity and demonstrate photon-pair generation by spontaneous four-wave mixing. Our source has a spectral brightness of 45 ± 7 mW−2 s−1 MHz−1 and the bandwidth of the emitted photons is ∼300 MHz. We demonstrate tuning of the emission wavelength between 770 and 800 nm. Moreover, by employing a liquid as the nonlinear optical medium completely filling the microcavity, we observe more than a factor 103 increase of the pair correlation rate per unit pump power and a factor of 1.7 improvement in the coincidence/accidental ratio as compared to our previous measurements.

Tunable Quantum Beat of Single Photons Enabled by Nonlinear Nanophotonics

We demonstrate the tunable quantum beat of single photons through the co-development of core nonlinear nanophotonic technologies for frequency-domain manipulation of quantum states in a common physical platform. Spontaneous four-wave mixing in a nonlinear resonator is used to produce non-degenerate, quantum-correlated photon pairs. One photon from each pair is then frequency shifted, without degradation of photon statistics, using four-wave mixing Bragg scattering in a second nonlinear resonator. Fine tuning of the applied frequency shift enables tunable quantum interference of the two photons as they are impinged on a beamsplitter, with an oscillating signature that depends on their frequency difference. Our work showcases the potential of nonlinear nanophotonic devices as a valuable resource for photonic quantum information science.

Generation and characterization of position-momentum entangled photon pairs in a hot atomic gas cell.

Continuous-variable position-momentum entanglement (or Einstein-Podolsky-Rosen entanglement) of two particles has played important roles in the fundamental study of quantum physics as well as in the progress of quantum information. In this paper, we propose a scheme to generate Einstein-Podolsky-Rosen (EPR) position-momentum entangled photon pairs efficiently via spontaneous four-wave mixing (SFWM) process in a hot rubidium gas cell. The EPR entanglement between the photon pair is measured and characterized by using the ghost interference and the ghost imaging method. Due to the simplicity of the experimental setup and the high photon pair generation rate, our EPR entangled photon source may has potential applications in quantum imaging, hyperentanglement preparation and atomic ensemble based quantum information processing and quantum communication protocols.

Nonlocal two-photon interference of energy-time entangled photon pairs generated in Doppler-broadened ladder-type Rb87 atoms

We experimentally demonstrate nonlocal two-photon interference of energy-time entangled photon pairs via spontaneous four-wave mixing (SFWM) process in Doppler-broadened ladder-type $^{87}\mathrm{Rb}$ atoms. The Doppler-broadened ladder-type atomic system offers collective two-photon coherence which results in strong temporal correlation between the entangled photons. The spacelike separated photon pairs clearly show nonlocal two-photon interference with high visibility of $97.1\ifmmode\pm\else\textpm\fi{}2.5%$, which violates the Bell-CHSH (Clauser-Horne-Shimony-Holt) inequality by 10.5 standard deviations, in which the travel time of a single-photon towards the interferometer is much longer than the coincidence window. Our work will provide an atom-based entangled photon source which is applicable for long distance atom-memory-based quantum communication.

Generating frequency-bin qubits via spontaneous four-wave mixing in a photonic molecule

A scheme for heralded generation of frequency-bin photonic qubits via spontaneous four-wave mixing in a system of coupled microring resonators (photonic molecule) is developed so that the qubit state is fully controlled by the frequency amplitude of the pump field. It is shown that coupling parameters of the photonic molecule can be optimized to provide generation of nearly pure heralded photons. The heralded qubit state does not depend on the microring resonator mode frequency, thereby allowing to take advantage of frequency multiplexing for improving efficiency of quantum information processing.

Quantum random numbers from a fiber-optic photon-pair source

We demonstrate a fiber-optic source of random numbers in which random-number generation (RNG) is implemented via an inherently quantum process—detection of correlated photon pairs produced by spontaneous four-wave mixing (FWM) inside an optical fiber. The detection times of individual photon pairs, generated in our RNG scheme via phase-matched FWM in a highly nonlinear photonic-crystal fiber with a suitable dispersion profile, are converted into megabit-size binary sequences, serving as strings of random numbers. The randomness of these bit strings is verified by the National Institute of Standards and Technology Statistical Test Suite. We identify FWM regimes in which mode-locked short-pulse laser sources can provide a high peak power needed to drive photon-pair generation in optical fibers without an excessive loss of randomness due to unwanted patterns in the RNG photon-pair output.

InP membrane micro-ring resonator for generating heralded single photons

In this paper, we experimentally verify the antibunching properties of multiple single photons located at distinct optical modes in a quantum frequency comb generated by cavity-enhanced spontaneous four-wave mixing in an InP membrane micro-ring resonator. The experimentally measured single photon conditional self-correlation parameter well below the classical regime (0.5) with the corresponding detector corrected Klyshko efficiency ηk of 3%–4.2%.