Spontaneous Four-wave Mixing Process Research Articles

Progress on Chip-Based Spontaneous Four-Wave Mixing Quantum Light Sources

Quantum light generated through spontaneous four-wave mixing (SFWM) process in nonlinear materials, such as entangled photon pairs and single photons, is an important resource for various emerging quantum applications. Integrated quantum photonics has enabled the generation, manipulation, and detection of quantum states of light with steadily increasing scale and complexity levels. Importantly, the exploration of on-chip integration has accumulated substantial progresses in recent years toward the realization of low-cost, large-scale quantum photonic circuits. Here, we review the underlying mechanism and discuss state-of-the-art SFWM on-chip quantum light sources fabricated with various structures and materials on chip. Furthermore, we enumerate the most appealing applications of on-chip SFWM such as heralding single-photon source, entangled photon source, and system-level integration.

Interpretable inverse-designed cavity for on-chip nonlinear photon pair generation

Inverse design is a powerful tool in wave physics for compact, high-performance devices. To date, applications in photonics have mostly been limited to linear systems and it has rarely been investigated or demonstrated in the nonlinear regime. In addition, the “black box” nature of inverse design techniques has hindered the understanding of optimized inverse-designed structures. We propose an inverse design method with interpretable results to enhance the efficiency of on-chip photon generation rate through nonlinear processes by controlling the effective phase-matching conditions. We fabricate and characterize a compact, inverse-designed device using a silicon-on-insulator platform that allows a spontaneous four-wave mixing process to generate photon pairs at a rate of 1.1 MHz with a coincidence to accidental ratio of 162. Our design method accounts for fabrication constraints and can be used for scalable quantum light sources in large-scale communication and computing applications.

Shaping the spectral correlation of bi-photon quantum frequency combs by multi-frequency excitation of an SOI integrated nonlinear resonator.

We reveal the generation of a broadband (> 1.9 THz) bi-photon quantum frequency comb (QFC) in a silicon-on-insulator (SOI) Fabry-Pérot micro-cavity and the control of its spectral correlation properties. Correlated photon pairs are generated through three spontaneous four-wave mixing (SFWM) processes by using a co-polarized bi-chromatic coherent input with power P1 and P2 on adjacent resonances of the nonlinear cavity. Adjusting the spectral power ratio r = P1/(P1 + P2) allows control over the influence of each process leading to an enhancement of the overall photon pair generation rate (PGR) μ(r) by a maximal factor of μ(r = 0.5)/μ(r = 0) ≈ 1.5, compared to the overall PGR provided by a single-pump configuration with the same power budget. We demonstrate that the efficiency aND of the non-degenerate excitation SFWM process (NDP) doubles the efficiency a1 ≈ a2 of the degenerate excitation SFWM processes (DP), showing a good agreement with the provided model.

Free-Space Quantum Teleportation with Orbital Angular Momentum Multiplexed Continuous Variable Entanglement

Quantum teleportation is one of the fundamental primitives of quantum cryptography. In order to achieve a wider range of high-capacity information transfer, we propose a free-space quantum teleportation (QT) protocol with orbital angular momentum (OAM) multiplexed continuous variable (CV) entangled states. The preparation of the entangled states is accomplished by the spontaneous four-wave mixing (SFWM) process occurring in a hot 85Rb vapor cell, and the mode selection for the Bell-state measurement is achieved by employing the balanced homodyne detection technique. The fidelity of teleporting EPR entangled states carrying different topological charges via a Kolmogorov-type atmospheric turbulence channel is derived, and the superiority of enhancing the system channel capacity via OAM multiplexing is demonstrated. Our work provides a feasible scheme to implement high-capacity quantum communication in atmospheric environments.

Temporally ultralong biphotons with a linewidth of 50 kHz

We report the generation of biphotons, with a temporal full width at the half maximum (FWHM) of 13.4 ± 0.3 µs and a spectral FWHM of 50 ± 1 kHz, via the process of spontaneous four-wave mixing with laser-cooled atoms. The temporal width is the longest, and the spectral linewidth is the narrowest to date. This is also the first biphoton result that obtains a linewidth below 100 kHz, reaching a new milestone. The very long biphoton wave packet has a signal-to-background ratio of 3.4, which violates the Cauchy–Schwarz inequality for classical light by 4.8 folds. Furthermore, we demonstrated a highly tunable-linewidth biphoton source and showed that while the biphoton source’s temporal and spectral width were controllably varied by about 24 folds, its generation rate only changed by less than 15%. A spectral brightness or generation rate per pump power per linewidth of 1.2× 106 pairs/(s mW MHz) was achieved at the temporal width of 13.4 µs. The above results were made possible by the low decoherence rate and high optical depth of the experimental system, as well as a novel scheme of classical fields’ and biphotons’ propagation directions in the experiment. This work has demonstrated a high-efficiency ultranarrow-linewidth biphoton source and has made substantial advancements in quantum technology utilizing heralded single photons.

Single-mode quantum non-Gaussian light from warm atoms

The distributed quantum information processing and hybridization of quantum platforms raises increasing demands on the quality of light-matter interaction and realization of efficient quantum interfaces. This becomes particularly challenging for needed states possessing fundamental quantum non-Gaussian (QNG) aspects. They correspond to paramount resources in most potent applications of quantum technologies. We demonstrate the generation of light with provably QNG features from a warm atomic ensemble in a single-mode regime. The light is generated in a spontaneous four-wave mixing process in the presence of decoherence effects caused by a large atomic thermal motion. Despite its high sensitivity to any excess noise, direct observability of heralded QNG light could be achieved due to a combination of a fast resonant excitation, large spectral bandwidth, and a low absorption loss of resonant photons guaranteed by the source geometry.

Generation of counterpropagating and spectrally uncorrelated photon-pair states by spontaneous four-wave mixing in photonic crystal waveguides

In this work, we propose and theoretically analyze a new scheme for generation of counterpropagating photon pairs in photonic crystal waveguides through the process of spontaneous four-wave mixing. Using the fundamental properties of periodic Bloch modes in a standard photonic crystal waveguide, we demonstrate how modal phase-matching can be reached between forward-propagating pump modes and counterpropagating signal and idler modes, for generation of degenerate and non-degenerate photon pairs. We then show how this scheme can be used for generation of photon pairs that are nearly uncorrelated in the spectral degree of freedom. Such a source will be highly interesting as a heralded source of single photons, especially as the spectrally separable signal and idler photons are also spatially separated directly at the source. We conduct our investigation based on a design in silicon, yet our design concept is general and can in principle be applied to any nanostructured material platform.

Photon-pair generation on resonance via a dark state

We present a scheme to generate photon-pair states through resonant spontaneous four-wave mixing (SFWM) in a five-level double-bowtie $(\ensuremath{\bowtie})$ configuration subject to two pumping fields and one coupling field when a quasidark state is created between two of three ground levels. The quasidark state is used here to largely suppress linear resonant absorption (gain) of the generated photon pairs while supporting strong SFWM nonlinearities and nonclassical cross-correlation. Numerical results for cold atomic samples show that the generation efficiency may be comparable to or even larger than that obtained in the off-resonance four-level single-bowtie configuration with only one pumping field. This scheme is robust to fluctuations of atomic populations and enables one to easily control the ratio of two rates with which distinct SFWM processes generate photon-pair states.

Temporal profile of biphotons generated from a hot atomic vapor and the spectrum of electromagnetically induced transparency

We systematically studied the temporal profile of biphotons, i.e., pairs of time-correlated single photons, generated from a hot atomic vapor via the spontaneous four-wave mixing process. The measured temporal width of biphoton wave packet or two-photon correlation function against the coupling power was varied from about 70 to 580 ns. We derived an analytical expression of the biphoton's spectral profile in the Doppler-broadened medium. The analytical expression reveals that the spectral profile is mainly determined by the effect of electromagnetically induced transparency (EIT), and behaves like a Lorentzian function with a linewidth approximately equal to the EIT linewidth. Consequently, the biphoton's temporal profile influenced by the Doppler broadening is an exponential-decay function, which was consistent with the experimental data. Employing a weak input probe field of classical light, we further measured the EIT spectra under the same experimental conditions as those in the biphoton measurements. The theoretical predictions of the biphoton wave packets calculated with the parameters determined by the classical-light EIT spectra are consistent with the experimental data. The consistency demonstrates that in the Doppler-broadened medium, the classical-light EIT spectrum is a good indicator for the biphoton's temporal profile. Besides, the measured biphoton's temporal widths well approximated to the predictions of the analytical formula based on the biphoton's EIT effect. This study provides an analytical way to quantitatively understand the biphoton's spectral and temporal profiles in the Doppler-broadened medium.

Photon-pair generation from a chip-scale Cs atomic vapor cell.

The realization of a narrowband photonic quantum source based on an atomic device is considered essential in the practical development of photonic quantum information science and technology. In this study, we present the first step toward the development of a photon-pair source based on a microfabricated Cs atomic vapor cell. Time-correlated photon pairs from the millimeter-scale Cs vapor cell are emitted via the spontaneous four-wave mixing process of the cascade-type 6S1/2-6P3/2-8S1/2 transition of 133Cs. The maximum normalized cross-correlation value between the signal and idler photons is measured as 622(8) under a weak pump power of 10 µ;W. Our photon source violates the Cauchy-Schwartz inequality by a factor of >105. We believe that our approach has very important applications in the context of realizing practical scalable quantum networks based on atom-photon interactions.

Path–orbital-angular-momentum high-dimensional hyperentangled photons from a warm atomic ensemble

We experimentally demonstrate a scheme for the preparation of high-dimensional hyperentangled photon pairs with path degree of freedom (DOF) and orbital-angular-momentum (OAM) DOF using beam displacer (BD) interferometers from a warm atomic ensemble. A strong Gaussian pump beam of fixed frequency passes through the BD to produce a superposition state of two paths. The biphoton state is generated from two parallel spontaneous four-wave mixing processes in the $^{85}\mathrm{Rb}$ vapor cell. We successfully detect the path entanglement, two-dimensional OAM entanglement, and three-dimensional OAM entanglement by selecting the appropriate measurement. Due to the advantages of the simplicity of our interaction system and high dimensionality of the narrowband hyperentangled photons we generated, such hyperentangled source from an atomic ensemble can be utilized to realize high-dimensional multiple-DOF quantum memory and quantum communication in the future.

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.

Correlation interference demultiplexer controlled by phase transition for Pr3+/Eu3+: YPO4

We propose a model of optical demultiplexer based on second- and third-order temporal interference of intensity-noise correlation, which is based on the superposition principle in Feynman's path integral theory. The switch from two-mode bunching to anti-bunching is controlled by gate position for pure hexagonal-phase of Pr3+/Eu3+: YPO4 crystal. We report, robust side correlation peaks caused by the destructive interference between two spontaneous parametric four-wave mixing processes from mixed (hexagonal and tetragonal)-phase of Pr3+/Eu3+: YPO4. By adjusting power of laser beam, the transition from asymmetric correlation side peaks to symmetric correlation side peaks are investigated. The robust center peak comes from the interference between two-mode and three-mode bunching. The switching from single correlation peak to multi-peaks is controlled by laser power. The multi-sharp peaks are translated into multi-dips through gate position. Such results may be used for the design of the optical multiplexer and demultiplexer. Our experimental results provide a technique to achieve larger linewidth change rate about 93% and higher channel equalization ratio about 70%.

Observation of Nonclassical Correlations in Biphotons Generated from an Ensemble of Pure Two-Level Atoms.

We report the experimental verification of nonclassical correlations for an unfiltered spontaneous four-wave mixing process in an ensemble of cold two-level atoms, confirming theoretical predictions by Du etal. in 2007 for the violation of a Cauchy-Schwarz inequality in the system, and obtaining R=(1.98±0.03)≰1. Quantum correlations are observed in a nanoseconds timescale in the interference between the central exciting frequency and sidebands dislocated by the detuning to the atomic resonance. They prevail over the noise background coming from Rayleigh scattering from the same optical transition. These correlations are fragile with respect to processes that disturb the phase of the atomic excitation, but are robust to variations in number of atoms and to increasing light intensities.

Violation of high-dimensional Bell inequality using narrowband orbital-angular-momentum entanglement from warm atomic vapor

Narrowband biphotons from an atomic ensemble are an extraordinary source for quantum information science. The generation of biphotons in the warm atomic system has many applicable prospects for its simplicity, stability, and compactness. In this article we experimentally demonstrate the generation of biphotons from the spontaneous four-wave mixing (SFWM) process in a warm rubidium vapor cell. By performing high-dimensional Bell-type measurements and mutually unbiased measurements, we maximally obtain a three-dimensional orbital-angular-momentum discrete-variable (DV) entangled state. The violation of high-dimensional Bell inequalities shows the great potential of warm atomic systems in generating DV high-dimensional entanglement. Such narrowband photon pairs may find applications in quantum-memory-based quantum communication networks. Through integration with the continuous-variable (CV) entanglement already existing in the same SFWM platform, our results here pave the way to construct atomic-ensemble-based DV-CV hybrid quantum information protocols.

Generation of a bright four-photon entangled state from a warm atomic ensemble via inherent polarization entanglement

We report the stable generation of a bright four-photon polarization-entangled Greenberger–Horne–Zeilinger (GHZ) state obtained by the spatial multiplexing of inherently polarization-entangled photons from a warm atomic ensemble of 87Rb. Owing to the total angular momentum conservation of the atomic state in the spontaneous four-wave mixing process of a cascade-type atomic system, the polarizations of the signal and idler photons in the two-photon decay are entangled. With a Rb vapor cell, we realize the generation of robust and bright four-photon GHZ states using two symmetrical spatial modes of inherently polarization-entangled photon pairs without applying an interferometric configuration. The four-photon average coincidence rate of the GHZ state with a fidelity of 0.88(2) is measured as 1.69(7) Hz under a weak pump power of 10 μW. The minimum Allan variance for the stability of the four-photon GHZ state is estimated as 0.92° for an average time of 10 h.

Cooperative Spontaneous Four-wave Mixing in Single-channel and Dualchannel Sequences of Side-coupled Ring Resonators

Cooperative photon pair generation by Spontaneous Four-Wave Mixing (SFWM) process in singlechannel and dual-channel side-coupled ring resonator sequences is investigated. Our analysis shows that superlinear growth of generation rate with respect to the number of rings is possible even in presence of loss. Experimental evidence of super-SFWM is provided by comparing individual and collective generation rates obtained from a dual-channel ring resonator sequence. The results are in good agreement with theory and suggest that high photon pair generation rates can be achieved from integrated silicon ring resonator sequences without initiating nonlinear absorption processes.

Submegahertz spectral width photon pair source based on fused silica microspheres

High-efficiency submegahertz bandwidth photon pair generators will enable the field of quantum technology to transition from laboratory demonstrations to transformational applications involving information transfer from photons to atoms. While spontaneous parametric processes are able to achieve high-efficiency photon pair generation, the spectral bandwidth tends to be relatively large, as defined by phase-matching constraints. To solve this fundamental limitation, we use an ultrahigh quality factor ( Q ) fused silica microsphere resonant cavity to form a photon pair generator. We present the full theory for the spontaneous four-wave mixing (SFWM) process in these devices, fully taking into account all relevant source characteristics in our experiments. The exceptionally narrow (down to kilohertz-scale) linewidths of these devices result in a reduction in the bandwidth of the photon pair generation, allowing submegahertz spectral bandwidth to be achieved. Specifically, using a pump source centered around 1550 nm, photon pairs with the signal and idler modes at wavelengths close to 1540 and 1560 nm, respectively, are demonstrated. We herald a single idler-mode photon by detecting the corresponding signal photon, filtered via transmission through a wavelength division multiplexing channel of choice. We demonstrate the extraction of the spectral profile of a single peak in the single-photon frequency comb from a measurement of the signal–idler time of emission distribution. These improvements in device design and experimental methods enabled the narrowest spectral width ( Δ ν = 366 kHz ) to date in a heralded single-photon source based on SFWM.

Roles of fiber birefringence and Raman scattering in the spontaneous four-wave mixing process through birefringent fibers.

We investigate the impact of fiber birefringence and spontaneous Raman scattering on the properties of photon pairs that are generated by the spontaneous four-wave mixing process in birefringent fibers. Starting from the formulation of the theory of four-wave mixing, we show a theoretical model for a generated optical field with the consideration of the Raman scattering and a Gaussian-distributed pump. The theoretical model is then applied for deriving the closed expressions of the photon-pair spectral properties as a function of the fiber birefringence. Also, with the modeled Raman gain, we evaluate the reduction of the pair production rate due to the presence of the Raman effect as well as the contributions of the Raman-scattered photons over a broad wavelength range. The predictions are experimentally verified with a commercial polarization-maintaining fiber.

Frequency and polarization emission properties of a photon-pair source based on a photonic crystal fiber

In this work, we experimentally demonstrate a photon-pair source with correlations in the frequency and polarization degrees of freedom. We base our source on the spontaneous four-wave mixing (SFWM) process in a photonic crystal fiber. We show theoretically that the two-photon state is the coherent superposition of up to six distinct SFWM processes, each corresponding to a distinct combination of polarizations for the four waves involved and giving rise to an energy-conserving pair of peaks. Our experimental measurements, both in terms of single and coincidence counts, confirm the presence of these pairs of peaks, while we also present related numerical simulations with excellent experiment-theory agreement. We explicitly show how the pump frequency and polarization may be used to effectively control the signal-idler photon-pair properties, defining which of the six processes can participate in the overall two-photon state and at which optical frequencies. We analyze the signal-idler correlations in frequency and polarization, and in terms of fiber characterization, we input the SFWM-peak experimental data into a genetic algorithm which successfully predicts the values of the parameters that characterize the fiber cross section, as well as predict the particular SFWM process associated with a given pair of peaks. We believe our work will help advance the exploitation of photon-pair correlations in the frequency and polarization degrees of freedom.