Parametric Four-wave Mixing Research Articles

Raman parametric four-wave mixing mechanism of the first-order Stokes generated in CO2 and H2.

Without the axial component, an annular spatial profile of the first-order Stokes (S1) was observed during the SRS process in low-energy pumped CO2 gas, which is supposed to be generated by a parametric four-wave mixing process (PFWM), i.e., 2ωP = ωAS1 + ωS1. In order to verify such a mechanism, similar experiments were conducted in H2, and the annular S1 intensity distribution was also noticed. Furthermore, simulations of S1 radial intensity distributions were carried out based on the proposed PFWM phase matching geometry. The PFWM has been verified to be a process that directly annihilates two pump photons and simultaneously produces one AS1 photon and one S1 photon.

Frequency characteristics of collimated blue light generated by four-wave mixing in cesium vapor.

The frequency evaluation of collimated blue light (CBL) generated by parametric four-wave mixing (FWM) in hot atomic vapor is presented. The cesium (133Cs) atoms are excited from the 6S1/2 ground state to 8S1/2 excited state with the 852 and 795 nm pump lasers, producing an optical field at 4.2 µm through an amplified spontaneous emission via population inversion on the 8S1/2 → 7P3/2 transition and the 456 nm CBL via FWM on the 7P3/2 → 6S1/2 transition. The frequency shift of 456 nm CBL has been measured by velocity-selective optical pumping spectral technique when the frequency of any one of two pumping lasers is tuned. The ratio of the frequency shift of 456 nm CBL to the two-photon frequency detuning of two pumping lasers is 0.8912, implying that the generated 4.2 µm light frequency is also correspondingly shifted.

Spectral and temporal atomic coherence interaction in Eu3+ : NaYF4 and Eu3+ : BiPO4.

We investigate the spectral and temporal atomic coherence interaction based on out-of-phase fluorescence (FL) and spontaneous parametric four-wave mixing (SFWM) from the hexagonal phase of Eu3+ : NaYF4 and different phases of Eu3+ : BiPO4. Spectral and temporal interactions are interrelated and reduced by about 2 times due to two-photon nested dressing in contrast to the sum of each laser excitation. As the lifetime of photons increases, off-resonance profile cross-interaction decreases because cross-interaction reverses the signal at the near time gate position and keeps it consistent at the far time gate position. Moreover, the thermal phonon dressing at 300 K exhibits 6 times more eminent and obvious temporal interaction than that at 77 K. In a different phase of Eu3+ : BiPO4, there are three dark dips having stronger self-interaction; however, Eu3+ : NaYF4 has two dark dips as Eu3+ : BiPO4 has two phonon dressing. Further, the pure hexagonal phase of Eu3+ : BiPO4 demonstrates the strongest cross-interaction and longest coherent time under the dressing effect due to the smallest dressing phonon detuning and off-resonance profile cross-interaction at PMT2 because the angle quantization is the strongest. Such results can be used for designing novel quantum devices and have potential applications in quantum memory devices.

Enhanced stimulated Raman scattering during intense laser propagation.

Stimulated Raman scattering is ubiquitous in many high-intensity laser environments. Parametric four-wave mixing between the pump and Raman sidebands can affect the Raman gain, but stringent phase matching requirements and strongly nonlinear dynamics obscure clear understanding of its effects at high laser powers. Here we investigate four-wave mixing in the presence of strong self-focusing and weak ionization at laser powers above the Kerr critical power. Theoretical analysis shows that the plasma generated at focus naturally leads to phase matching conditions suitable for enhanced Raman gain, almost without regard to the initial phase mismatch. Multidimensional nonlinear optical simulations with multiphoton and collisional ionization confirm the enhancement and suggest that it may lead to significantly higher Raman losses in some high-intensity laser environments.

Competition of collimated ultraviolet lights generated by four-wave mixing process in Cs vapor

Using the two-color two-photon scheme, caesium (Cs) atoms were excited to (or around) the 112D5/2 level, generating terahertz (THz) and infrared (IR) radiations. then, a series of collimated ultraviolet (UV) lights were obtained through the four-wave mixing process. There was a competition among the collimated UV lights. The pump intensity directly affects the refractive index of Cs vapor at the pump laser wavelength, affecting the phase matching. Under the good phase-matching condition, 334.7 nm (UV1) and 339.8 nm (UV2) collimated lights were used to study the competition between ∼1.1 THz (THz1) and ∼20.9μm (IR2) radiations. After tuning the wavelength combination of the pump lasers, the intensities of THz and IR radiations were affected by the competition among parametric four-wave mixing, stimulated Raman scattering, and amplified spontaneous emission.

Resonant metasurfaces for generating complex quantum states.

Quantum state engineering, the cornerstone of quantum photonic technologies, mainly relies on spontaneous parametric downconversion and four-wave mixing, where one or two pump photons spontaneously decay into a photon pair. Both of these nonlinear effects require momentum conservation for the participating photons, which strongly limits the versatility of the resulting quantum states. Nonlinear metasurfaces have subwavelength thickness and allow the relaxation of this constraint; when combined with resonances, they greatly expand the possibilities of quantum state engineering. Here, we generated entangled photons via spontaneous parametric downconversion in semiconductor metasurfaces with high-quality factor, quasi-bound state in the continuum resonances. By enhancing the quantum vacuum field, our metasurfaces boost the emission of nondegenerate entangled photons within multiple narrow resonance bands and over a wide spectral range. A single resonance or several resonances in the same sample, pumped at multiple wavelengths, can generate multifrequency quantum states, including cluster states. These features reveal metasurfaces as versatile sources of complex states for quantum information.

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%.

Higher-order photon antibunching of phase-variable squeezed coherent state

<sec>Squeezed state has important applications in quantum communication, quantum computing, and precision measurement. It has been used to improve the sensitivity and measurement accuracy of gravitational wave detectors. Currently, squeezed state can be prepared by optical parametric oscillators, four-wave mixing, and atom–optomechanical coupling. As a typical non-classical light, the photon statistics of squeezed state usually shows obvious bunching effect, but it can also present photon antibunching effect through interference or photon subtraction operation. More importantly, squeezed coherent state is prepared by performing displacement operation on the squeezed state. In the case of certain displacement and squeezing operations, squeezed coherent state with obvious antibunching effect can be produced. The squeezed coherent state with photon antibunching effect can be employed to achieve super-resolution imaging beyond the diffraction limit, and the state exhibits good particle features which can suppress the multiphoton emission. Then it has become a focus for studying the antibunching effect and quantum statistical properties of squeezed coherent state at a single-photon level.</sec><sec>The photon antibunching effect can be characterized by the second-order photon correlation <i>g</i><sup>(2)</sup>(τ), which is introduced by Glauber to determine the non-classical properties of the light field. Namely, the second-order photon correlation <i>g</i><sup>(2)</sup> can be used as a metric to distinguish different lights. Hanbury Brown-Twiss (HBT) scheme is used to measure the second-order photon correlation experimentally. However, the second-order photon correlation <i>g</i><sup>(2)</sup> can reflect only the variance of the photon-number statistical distribution. In order to obtain more information about the photon statistical distribution and non-classical features, it is necessary to measure higher-order photon correlations. Then the higher-order photon correlations for different light fields are studied by extending the traditional HBT scheme and combining with multiplex single-photon detection technology. This method can be applied to ghost imaging, characterization of single-photon detectors, research of exciton dynamics, and analysis of NV center fluorescence emission. However, the research on photon statistics of the squeezed state focuses mainly on the second-order photon correlation and the effect of displacement amplitude on the statistical properties. The effect of squeezed phase on photon antibunching and higher-order photon correlation of squeezed coherent states, with background noise and detection efficiency taken into consideration, have not been investigated.</sec><sec>In this paper, we study high-order photon correlations and antibunching effect of phase-variable squeezed coherent state based on an extended HBT scheme. The photon statistics of the squeezed coherent state manifests prominent antibunching effect by adjusting the squeezing parameter r, displacement amplitude <i>α</i> and squeezing phase <i>θ</i>. The antibunching effect of the state can be obtained in a wide range of <i>α</i>-<i>r</i> parameter space when squeezing phase <i>θ</i>∈[0,π/2]. In an ideal case, the minimum antibunching values of the squeezed coherent state are <i>g</i><sup>(2)</sup> = 4.006 × 10<sup>–4</sup>, <i>g</i><sup>(3)</sup> = 1.3594 × 10<sup>–4</sup> and <i>g</i><sup>(4)</sup> = 6.6352 × 10<sup>–5</sup>. When the detection efficiency <i>η</i> = 0.1 and background noise <i>γ</i> = 10<sup>–6</sup>, the strong antibunching effect can still be observed, specifically, <i>g</i><sup>(2)</sup> = 0.1740, <i>g</i><sup>(3)</sup> = 0.0432, <i>g</i><sup>(4)</sup> = 0.0149. The results indicate that the antibunching effect of higher-order photon correlation has strong robustness against the experimental environment. In addition, the antibunching effect of the phase-variable squeezed coherent state is studied as a function of the measured mean photon number <<i>n</i>> and the squeezing degree S. When the measured mean photon number is much less than 1 and the squeezing parameter is less than 10<sup>–4</sup>, a prominent photon anti-bunching effect of <i>g</i><sup>(<i>n</i>)</sup> <inline-formula><tex-math id="Z-20220921173504">\begin{document}$\ll $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20220574_Z-20220921173504.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20220574_Z-20220921173504.png"/></alternatives></inline-formula> 0.5 can still be obtained. The results show that the control of the squeezing phase <i>θ</i> can be used to prepare the squeezed coherent state with obvious antibunching effect, which has potentially important applications in quantum metrology and secure communication.</sec>

Coherent blue light enhancement via repumping laser in cesium vapor

We demonstrate the generation of coherent and collimated blue light (CBL) based on cesium (Cs) 6S<sub>1/2</sub>(<i>F</i> = 4)→6P<sub>3/2</sub>(<i>F'</i> = 5)→6D<sub>5/2</sub>(<i>F''</i> = 6)→7P<sub>3/2</sub>(<i>F'</i> = 5)→6S<sub>1/2</sub>(<i>F</i> = 4) diamond-type atomic system in a heated vapor cell. Two infrared pumping lasers with wavelengths at 852 nm (6S<sub>1/2</sub>→6P<sub>3/2</sub>) and 917 nm (6P<sub>3/2</sub>→6D<sub>5/2</sub>), provide step-wise excitation to the 6D<sub>5/2</sub> excited state, and induce strong two-photon coherence between the 6S<sub>1/2</sub> state and 6D<sub>5/2</sub> state. The atoms undergo a double cascade accompanied with the amplified spontaneous emission at 15.1 μm via the 7P<sub>3/2</sub> intermediate excited state, and produce a beam of 455 nm (7P<sub>3/2</sub>→6S<sub>1/2</sub>) CBL with highly spatiotemporal coherence through a parametric four-wave mixing process. We investigate the influence of experimental parameters such as polarization combination of the two pumping lasers, and their power, and the temperature of Cs vapor cell on the CBL. Especially, we add a beam of 894 nm laser operating at the 6S<sub>1/2</sub>(<i>F</i> = 3) →6P<sub>1/2</sub> transition as repumping laser, which can pump atoms back to the 6S<sub>1/2</sub>(<i>F</i> = 4) state from the 6S<sub>1/2</sub>(<i>F</i> = 3) state, thus significantly improving the power of CBL. This technique of the CBL enhancement via optical pumping is also useful for the other alkali metal atoms.

Poissonian twin-beam states and the effect of symmetrical photon subtraction in loss estimations

We have devised an experimentally realizable model generating twin beam states whose individual beam photon statistics are varied from thermal to Poissonian keeping the non-classical mode correlation intact. We have studied the usefulness of these states for loss measurement by considering three different estimators, comparing with the correlated thermal twin beam states generated from spontaneous parametric down conversion or four-wave mixing. We then incorporated the photon subtraction operation into the model and demonstrate their advantage in loss estimations with respect to un-subtracted states at both fixed squeezing and per photon exposure of the absorbing sample. For instance, at fixed squeezing, for two photon subtraction, up to three times advantage is found. In the latter case, albeit the advantage due to photon subtraction mostly subsides in standard regime, an unexpected result is that in some operating regimes the photon subtraction scheme can also give up to 20% advantage over the correlated Poisson beam result. We have also made a comparative study of these estimators for finding the best measurement for loss estimations. We present results for all the values of the model parameters changing the statistics of twin beam states from thermal to Poissonian.

Trans-spectral vector beam nonlinear conversion via parametric four-wave mixing in alkali vapor.

Coherent frequency conversion of vector beams (VBs) without distorting their intensity profile or spatial polarization distribution is important for novel applications in quantum and classical regimes. Here, we experimentally and theoretically investigate VB transfer from near-infrared to blue light using a Sagnac interferometer, combining the parametric four-wave mixing process in atomic vapor. The vector probe beam is converted into a completely different wavelength, and the vector mode of the generated blue beam is highly similar to the incident probe beam. These results may provide a feasible solution for communication interfaces in classical and quantum science fields based on atomic ensembles.

Multimodal Tip-Enhanced Nonlinear Optical Nanoimaging of Plasmonic Silver Nanocubes.

Optical field localization at plasmonic tip-sample nanojunctions has enabled high-spatial-resolution chemical analysis through tip-enhanced linear optical spectroscopies, including Raman scattering and photoluminescence. Here, we illustrate that nonlinear optical processes, including parametric four-wave mixing (4WM), second-harmonic/sum-frequency generation (SHG and SFG), and two-photon photoluminescence (TPPL), can be enhanced at plasmonic junctions and spatiospectrally resolved simultaneously with few-nm spatial resolution under ambient conditions. Through a detailed analysis of our spectral nanoimages, we find that the efficiencies of the local nonlinear signals are determined by sharp tip-sample junction resonances that vary over the few-nanometer length scale. Namely, plasmon resonances centered at or around the different nonlinear signals are tracked through TPPL, and they are found to selectively enhance nonlinear signals with closely matched optical resonances.

Phase transition filter from controllable hybrid line shape of correlation and squeezing of Pr3+: YPO4 and Eu3+: YPO4

We report the symmetry-dependent intensity–noise correlation and the intensity-difference squeezing of spontaneous parametric four-wave mixing (SP-FWM) and fluorescence (FL) hybrid signals from the different phases [hexagonal (H) + tetragonal (T), T + H] of Pr3+: YPO4 and Eu3+: YPO4 crystals. The competition between FL and SP-FWM in hybrid signals determines the amplitude and hybrid line shape of the two-mode and three-mode correlation. The correlation amplitude switches from positive to negative due to strong double dressing caused by a high transition probability and a dipole moment of the (more H + less T)-phase of Pr3+: YPO4. This switching phenomenon is used to realize a metal–oxide semiconductor field-effect transistor-based logic inverter. Furthermore, the line shape of correlation changes from broad to sharp due to weak dressing, transition probability, and a low dipole moment of the (more T + less H)-phase of Pr3+: YPO4. Based on these results, we proposed the model of a tunable correlation filter. Gate position, frequency detuning, and laser power control the amplitude and hybrid line shape. Our experimental results provide an advanced technique of bandwidth contrast of about 0.9%. Such notch filters have potential applications in quantum communications.

Narrowband and broadband single-photon sources using custom-tapered waveguides

In this paper, we present a thorough investigation for a spontaneous parametric four-wave mixing process in third-order nonlinear waveguides with various continuous tapering patterns. It has been previously shown that these devices can quasi-phase-match the four-wave mixing process and enhance its conversion efficiency by orders of magnitude. By altering the tapering profile curve we found that these devices can enable single-photon sources with either narrow or broadband spectral widths at on-demand frequencies. Using our model, we were also able to identify the waveguide length at which the single-photon spectral purity is maximized.

Interference between atomic Rb (5d 5/2–5p 3/2) and (5p 3/2–5s 1/2) coherences: observation of an exceptional point by quantum beating at ∼2.1 THz

Coupled oscillators are prevalent in nature and fundamental to fields as disparate as astrophysics, photonics, the mechanical sciences, and geophysics. Theory has identified singularities in the response of coupled oscillators, known as exceptional points (EPs), that are associated with non-Hermitian operators and lie at the transition between weak and strong coupling of the oscillator. Although several EPs have been reported or predicted to exist in nanophotonic resonators and Feshbach resonances, for example, tuning the phase of two interfering atomic or molecular coherences near an EP has not been demonstrated previously. We report the observation of an EP associated with a pair of interfering atomic coherences in Rb, oscillating at 386.3 and 384.2 THz, and confirm the theoretical prediction of an abrupt phase shift of ∼π/4 as the EP is traversed by independently varying two experimental parameters. Pairs (and trios) of coupled coherences in thermal Rb atoms are established among the 7s 1/2, 5d 5/2, 5p 3/2, and 5s 1/2 states in pump–probe experiments with <200 fs laser pulses, and observed directly in the temporal and spectral domains through the ensuing quantum beating in the ∼2–36 THz interval. Interference between the (5d 5/2–5p 3/2) and (5p 3/2–5s 1/2) coherences is mediated by the 5p 3/2 state and detected through quantum beating in the vicinity of the (5d 5/2–5p 3/2)–(5p 3/2–5s 1/2) difference frequency of 2.11 THz which is monitored by a parametric four-wave mixing process. Phase of this composite atomic oscillator is first controlled by varying the mean Rb–Rb nearest neighbor distance (⟨R⟩) in a thermalized vapor. A discontinuous transition of (0.8 ± 0.2) ∼ π/4 radians in the phase of the coupled oscillator occurs when ⟨R⟩ is varied over the ∼80–90 nm interval, a phase shift associated with the transformation of a broadband, dissipative oscillator (characterized by a Fano interference window) into a strongly-coupled system resonant at 2.1 THz.

Hybrid communication assisted by coherent oscillator using resonant excitation of Nitrogen–vacancy center in diamond

We propose the multi-channel hybrid communication assisted by a coherent oscillator, by configuring the diamond Nitrogen–vacancy center using spontaneous parametric four-wave mixing. For one-channel hybrid communication, composite signal of fluorescence (information) and Stokes (carrier) is sent to the receiver; information is recovered by subtracting intensities of composite signal and reference coherent signal (from coherent oscillator) at demodulator. Further, we achieved two-channel and three-channel hybrid communication through two-mode and three-mode intensity–noise correlation, respectively. Two-mode correlation of hybrid signal (produced through photon subtraction) and anti-Stokes demonstrates the nonclassical behavior by violating Cauchy–Schwarz inequality, verified through corresponding squeezing (−5 dB). Such phenomenon of non-classical behavior was also verified by non-Gaussian negativity of Wigner function. Our hybrid communication model is based on temporal width- and coherence time-contrast, which can be controlled by wavelength (power) of input beams. The coherence time-contrast is about 90%.

Temporal and spectral hybrid interference from phase transition of Eu3+/Pr3+: YPO4 and evolution of amplifier and multiplexer

We study the temporal and spectral oscillation originated from the interference between the fluorescence (FL) and spontaneous parametric four-wave mixing (SP-FWM) signals. The FL and SP-FWM are generated from different phases of Eu3+ or Pr3+ doped YPO4 under the nonlinear SP-FWM process. We discuss and compare the spectral interfering oscillations and self-Rabi oscillations controlled via multiple phase transitions (hexagonal-phase and mixed-phase) of Eu3+: YPO4 and Pr3+: YPO4. The coexistence mechanism of interference and self-oscillations in time domain is also investigated. Further, we discuss the cross-Rabi oscillation in correlated light beams, which evolves from FL signal (having Sinc profile) to SP-FWM (having Cosine profile) in the hybrid signal regime. Based on these results, we have realized wavelength division multiplexing, and temporal amplifier with the temporal interference being controlled by the gate position, and frequency detuning. Our experimental results provide a technique to achieve higher channel equalization ratio about 85%.

Coherent near-infrared light generation based on self-seeded parametric four-wave mixing in Rb vapor

We demonstrate 1.37 µm coherent near-infrared light generation via self-seeded parametric four-wave mixing (FWM) process in Rb atomic vapor. Two lasers (780 nm and 776 nm) in the co-propagating configuration, drive the Rb atoms from the 5S1/2 ground state to the 5D5/2 excited state. The parametric FWM around the 5P3/2–5D5/2–6P3/2–6S1/2–5P3/2 transition loop is effectively established under phase matching conditions. The generated coherent light wavelength is confirmed using an optical spectrum analyzer, and the output power is investigated with the input laser frequency, power and atomic density. Consequently, a 1.37 µm coherent light with the power of 27 µW and the beam quality of = 1.22 and = 1.25 is obtained. An additional 795 nm laser is introduced to enhance the output power by 1.5 times through velocity-selective optical hyperfine repumping.

Wideband tuning of four-wave mixing in liquid-filled photonic crystal fiber

A wideband tuning of parametric four-wave mixing generation in a liquid-filled photonic crystal fiber is theoretically demonstrated, and influence of its temperature is investigated. The broadband spectrum is generated via a supercontinuum generation process induced by degenerate four-wave mixing (DFWM), for which the thermo-optic coefficient of the oil (the refractive index matching fluid) is considered. The signal band tuning from 734 nm to 923 nm, and the idler band from 1931 nm to 1255 nm, are observed when the temperature increases from 30°C to 90°C. The findings can be applied in many fields, such as CARS.

Broadband phononic frequency comb generation in a parametrically excited capacitive micromachined ultrasonic transducer

Optical frequency combs consisting of evenly spaced discrete frequencies have been used for a number of applications such as frequency metrology, range finding and molecular fingerprinting. Recently, the acoustic equivalent of these frequency combs, known as phononic frequency combs (PFCs), have been demonstrated in micro and nanoscale resonators. However, such demonstrations are restricted to PFC generation in high-Q mechanical resonators under carefully controlled operating conditions with limited practical applications. In this work, we demonstrate a novel method of generating PFCs with a parametrically driven capacitive micromachined ultrasonic transducer (CMUT) operating in a fluid medium. The proposed system consists of an electrically driven CMUT array that forms part of a resonant RLC circuit of frequency w0. By applying two drive tones of frequency w0 and w0+Δ, we are able to generate broadband acoustic frequency combs via a parametric four-wave mixing process. The intensity and number of combs generated is strongly dependent on the relative strength of the two driving tones whereas the comb spacing is determined by the frequency difference Δ between the drive signals. We also briefly discuss a potential application of PFCs in extended non-ambiguous range (NAR) distance metrology with interferometric resolution.