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DOE OSTI2025

Probing coherent electronic superpositions of singly and doubly excited states of krypton with extreme-ultraviolet four-wave-mixing spectroscopy

Radiative nonlinear four-wave mixing can monitor the evolution of electronic wave packets, providing access to lifetimes and quantifying the light-induced couplings between excited states. In this article, we report the observation of quantum beats in an autoionizing electronic wave packet in krypton, probed using this technique. Analysis of the signal reveals that these beats originate from the contribution of previously unassigned, doubly excited states interacting with singly excited ones. We introduce a minimal theoretical model, based on multichannel quantum-defect theory, which quantitatively reproduces both the wave-packet dynamics and the static spectrum. This work combines a versatile, noncommensurate XUV-IR-based experimental scheme with a tractable model, establishing a powerful approach for the metrology and control of complex, correlated electronic states.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Optimizing spectral phase transfer in four-wave mixing with gas-filled capillaries

Four-wave mixing (FWM) in gas-filled hollow-core capillaries, a nonlinear optical process that mixes signal and pump photon frequencies to generate idler frequency photons, offers a method for precise spectral phase transfer from signal to idler at ultrashort timescales and extreme powers. However, this regime is challenged by competing linear and nonlinear dynamics, leading to significant trade-offs between spectral phase transfer and conversion efficiency. Our computational investigation focuses on the upconversion of femtosecond pulses from the infrared (IR) to the ultraviolet (UV), a range notoriously difficult to manipulate. We explore an intermediate energy regime that strikes an optimal balance between FWM-mediated phase-transfer fidelity and nonlinear conversion efficiency. By adjusting the energy ratios and spectral phase profiles of the input signal, we achieve conversion efficiencies of approximately 5-15% while maintaining an effective quasi-linear spectral phase transfer. These findings will contribute to establishing first-principles and scaling laws essential for applications such as high-precision imaging, spectroscopy, quantum transduction, and distributed entangled interconnects, facilitating advanced control of ultrafast photonic and electronic wavepackets in quantum materials with unprecedented spatial and temporal precision.

Zhang, Hao↗

DOE OSTI2025

Bi-chromatic intensity squeezing using four-wave mixing in 85 Rb vapor

We experimentally investigate four-wave mixing (FWM) in a diamond interaction scheme using 85 Rb vapor, and identify the optimal conditions for joint amplification and relative intensity squeezing of two optical fields: one near the 85 Rb D1 optical transition (λ = 794.6 nm) and the other in the telecom O-band (λ = 1324 nm). We achieved a reduction of relative intensity noise by up to 2.6 ± 0.4 dB compared with the shot noise level, signifying the non-classical quantum correlations. The observed level of intensity squeezing is primarily limited by the available pump laser power, which constrains the achievable FWM gain. Numerical simulations show good agreement with the experimental results.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1989

The influence of velocity-changing collisions on resonant degenerate four-wave mixing

The phase-conjugate signal observed in resonant degenerate four-wave mixing on the 6 3P2 to 7 3S1 transition of atomic Hg in an Hg-Ar discharge is investigated. At a fixed Ar pressure the variation of the signal with pump powers is explained by a model that includes the effects of velocity-changing collisions (VCCs). As the Ar pressure was varied from 0 to 1 torr, an increase in the phase-conjugate signal was observed and is ascribed to a change in the discharge dynamics with Ar pressure and to the influence of VCCs. To further clarify the role of collisions and optical pumping, degenerate four-wave mixing spectra are examined as a function of pump power. Line shapes are briefly discussed.

Richardson, W. H.↗

NASA NTRS2008

Kinetic Temperature and Electron Density Measurement in an Inductively Coupled Plasma Torch using Degenerate Four-Wave Mixing

Laser wave mixing is presented as an effective technique for spatially resolved kinetic temperature measurements in an atmospheric-pressure radio-frequency inductively-coupled plasma. Measurements are performed in a 1 kW, 27 MHz RF plasma using a continuous-wave, tunable 811.5-nm diode laser to excite the 4s(sup 3)P2 approaches 4p(sup 3)D3 argon transition. Kinetic temperature measurements are made at five radial steps from the center of the torch and at four different torch heights. The kinetic temperature is determined by measuring simultaneously the line shape of the sub-Doppler backward phase-conjugate degenerate four-wave mixing and the Doppler-broadened forward-scattering degenerate four-wave mixing. The temperature measurements result in a range of 3,500 to 14,000 K+/-150 K. Electron densities measured range from 6.1 (+/-0.3) x 10(exp 15)/cu cm to 10.1 (+/-0.3) x 10(exp 15)/cu cm. The experimental spectra are analyzed using a perturbative treatment of the backward phase-conjugate and forward-geometry wave-mixing theory. Stark width is determined from the collisional broadening measured in the phase-conjugate geometry. Electron density measurements are made based on the Stark width. The kinetic temperature of the plasma was found to be more than halved by adding deionized water through the nebulizer.

Schafer, Julia↗

DOE OSTI2024

Four-wave mixing with anti-parity-time symmetry in hot 85 Rb vapor

Here, we report an experimental demonstration of anti-parity-time symmetric optical four-wave mixing in thermal rubidium vapor, where the propagation of probe and stokes fields in a double-Λ scheme is governed by a non-Hermitian Hamiltonian. We are particularly interested in studying quantum intensity correlations between the two fields near the exceptional point, taking into account loss and accompanied Langevin noise. Our experimental measurements of classical four-wave mixing gain and the associated two-mode relative-intensity squeezing are in reasonable agreement with the theoretical predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Progress towards subsurface spectroscopy inside heterogeneous materials using four wave mixing phase conjugation

Herein, we report preliminary results on subsurface spectroscopy inside heterogeneous materials using four wave mixing phase conjugation. For our test material we use an inert plastic bonded explosive simulant that contains fluorescent guidestar particles. Using phase conjugation, we are able to obtain spectral enhancements approximately equal to the phase conjugate reflectivity. Additionally, we discuss future directions to improve this technique to obtain greater signal enhancements.

47 OTHER INSTRUMENTATION↗

NASA NTRS1993

Self-pumped phase conjugation and four-wave mixing in 0- and 45-deg-cut n-type BaTiO3:Co

Relatively fast self-pumped phase-conjugate and four-wave-mixing rise times are reported in n-type cobalt-doped barium titanate. With the crystal oriented in a 45-deg cut as compared with the same crystal in a 0-deg cut we find a factor of 3 decrease in the 0-90-percent rise time to 800 ms with 25-mW input power at 514.5 nm. Also, the self-pumped phase-conjugate reflectivity increases from 20 to 40 percent. We deduce that the phase conjugation is from internally seeded stimulated photorefractive backscattering. The four-wave-mixing rise time of the 45-deg-cut crystal is 4 ms with a reflectivity of 48 percent when the pumping beams are derived from self-pumped phase conjugation that has an input power of 25 mW.

Garrett, M. H.↗

DOE OSTI2025

Femtosecond two-photon-resonant parametric four-wave mixing detection of atomic hydrogen

Here, we demonstrate an ultrafast parametric four-wave mixing method for the collisional-quenching-free detection of atomic hydrogen. Two photons of 243 nm light resonantly excite the n = 1 to n = 2 transition of atomic hydrogen, and a third probe photon scatters from the electronic coherence to generate the parametric emission of a degenerate signal photon. Laser-induced photofragmentation fluorescence from water, also excited with the same 243 nm pulses, is used as a convenient method to visualize beam overlap in space and time. The femtosecond time resolution enables the suppression of unwanted nonresonant contributions to the signal and separation from resonant mixing in water molecules because of the significantly different coherence lifetimes. A folded BOXCARS phase-matching configuration yields a spatially isolated, laser-like, signal beam, amenable to measurements in highly luminous backgrounds. Measurements in an H 2 /CH 4 /air flame demonstrate quantitative agreement with simulated H-atom concentration profiles. A coherence decay time constant of 42 ps is recorded in the atmospheric pressure flame.

Kliewer, Christopher Jesse [Sandia National Labora↗

NASA NTRS1987

Image processing by four-wave mixing in photorefractive GaAs

Three image processing experiments were performed by degenerate four-wave mixing in photorefractive GaAs. The experiments were imaging by phase conjugation, edge enhancement, and autocorrelation. The results show that undoped, semiinsulating, liquid-encapsulated Czochralski-grown GaAs crystals can be used as effective optical processing media despite their small electrooptic coefficient.

Gheen, Gregory↗

NASA NTRS1989

Phase conjugation by four-wave mixing in inhomogeneous plasmas

The effects of density, temperature, and velocity gradients on four-wave mixing (FWM) in a plasma are investigated. A fluid model is used in which the stimulated Brillouin terms are included, but pump depletion is neglected. The steady state phase conjugate reflectivity and signal transmission coefficients are calculated and discussed for both degenerate and resonant FWM. The substantial effects of inhomogeneity on the use of FWM as a plasma diagnostic are discussed.

Williams, Edward A.↗

DOE OSTI2026

Long-term stabilization of intensity-difference squeezing from four-wave mixing in rubidium vapor

Generation of quantum states of light through off-resonance four-wave mixing in rubidium vapor is a straightforward and well-established technique. However, achieving a sufficiently high and consistent level of intensity difference squeezing (IDS) and intrinsic quantum correlations between photon pairs over an extended timescale, necessary for quantum-light-based nonlinear optical spectroscopy and microscopy, remains challenging and largely unexplored. Here, we report a simple stabilization method combining an active periodic laser frequency retuning with an automatic control algorithm based on quantitatively assessing the factors affecting the IDS level and squeezed light intensity. Validation of our method was performed by acquiring data over a 5-hour period, and the results demonstrate a remarkably stable squeezing level of -7.8 dB in combination with a > 4× reduction of the standard deviation of IDS level from 0.46 dB to 0.10 dB. The achieved stabilization further enables us to quantitatively assess the IDS reduction due to the scattering in a polystyrene bead suspension as a function of sample transmission. Our approach should enable a variety of applications requiring an extended squeezing stability over multiple hours, especially for those following biological processes and chemical reactions in real time.

Allen, Christian Harry [Oak Ridge National Laborat↗

DOE OSTI2026

Interplay between Ultrafast Electronic and Librational Dynamics in Liquid Nitrobenzene Probed with Two-Color Four-Wave Mixing

Here, we present an experimental and theoretical study of the interplay between ultrafast electron dynamics and librational dynamics in liquid nitrobenzene. A femtosecond ultraviolet pulse and two femtosecond near-infrared pulses interact with nitrobenzene molecules, generating a four-wave mixing nonlinear signal measured in the Optical Kerr Effect geometry. The signal is measured to be nonzero only at negative time delays, corresponding to the near-infrared pulses arriving before the ultraviolet pulse. We perform time-dependent Quantum Master Equation calculations with classical libration to simulate the experiment. The simulations support the conclusion that the near-infrared pulses launch librational motion while creating electronic coherences resulting in a libration-modulated electronic nonlinear response. The analysis of the phase-matched four-wave mixing signals suggests a nonparametric process leaving the molecules in an excited electronic state, providing new insight into ultrafast nonlinear optical interactions in liquids and advancing toward probing ultrafast electronic coherences in complex molecular liquids.

Shivaram, Niranjan [Lawrence Berkeley National Lab↗

NASA NTRS1989

Polarization properties of degenerate four-wave mixing in GaAs

The effect of an applied dc electric field on beam-polarization properties of degenerate four-wave mixing in GaAs is investigated. The results can be interpreted in terms of the phase retardation arising from the applied electric field and the light-induced periodic space-charge field. The conditions for attaining a cross-polarized diffracted beam and read beam are discussed. The experimental results agree reasonably well with the theoretical calculations for an applied voltage of 6 kV.

Liu, Duncan T.↗

DOE OSTI2025

Giant Enhancement of Four-Wave Mixing by Doubly Zone-Folded Nonlocal Metasurfaces

Resonant optical metasurfaces hold promise for enhancing nonlinear optical signals and manipulating their fundamental properties. However, they rarely excel at amplifying signals from nonlinear processes with two incident pump beams, such as four-wave mixing (FWM) or sum-frequency generation. Frequency-mixing experiments impose challenging requirements for metasurface design due to the need to support multiple optical resonances with compatible field profiles at specified resonant wavelengths, often across a substantial spectral separation. Here, in this work, we introduce nonlocal ‘quadromer’ metasurfaces containing four nanostructures per unit cell as the key to unlocking configurable, multiresonant metasurfaces that enhance frequency-mixing processes. As a proof of concept, we experimentally demonstrate enhanced FWM using quadromer metasurfaces made of silicon and silicon-rich silicon nitride. The results are relevant for applications such as imaging of infrared light upconverted into the visible spectrum and the generation of quantum light via spontaneous FWM.

four-wave mixing↗

NASA NTRS1989

Optical Stark effect in the four-wave mixing and stimulated Raman spectra of N2

The influence of the optical Stark effect on spectral line shapes in four-wave-mixing Raman spectroscopy (FWMRS) and stimulated Raman spectroscopy (SRS) is investigated experimentally and theoretically. Using an experimental setup capable of rapid alternation between the simultaneous measurement of coherent Stokes Raman spectroscopy and inverse Raman spectroscopy at low and high intensities, together with a sophisticated frequency reference scheme, it was possible to perform a rather direct comparison between Stark-broadened and non-Stark-broadened spectra of both classes of Raman spectroscopies. The results demonstrate that SRS spectra show more Stark shift and broadening than their FWMRS counterparts. A discrepancy with theoretical results is pointed out, and an attempt is made to explain it.

Moosmuller, H.↗

DOE OSTI2024

Non-resonant Bragg scattering four-wave mixing at near-visible wavelengths in low-confinement silicon nitride waveguides

Quantum state coherent frequency conversion processes—such as Bragg-scattering four-wave mixing (BSFWM)—hold promise as a flexible technique for networking heterogeneous and distant quantum systems. In this Letter, we demonstrate BSFWM within an extended (1.2-m) low-confinement silicon nitride waveguide and show that this system has the potential for near-unity frequency conversion in visible and near-visible wavelength ranges. Using sensitive classical heterodyne laser spectroscopy at low optical powers, we characterize the Kerr coefficient (∼1.55 W −1 m −1 ) and linear propagation loss (∼0.0175 dB/cm) of this non-resonant waveguide system, revealing a record-high nonlinear figure of merit (NFM = γ / α ≈ 3.85 W −1 ) for BSFWM of near-visible light in non-resonant silicon nitride waveguides. We predict how, at high yet achievable on-chip optical powers, this NFM would yield a comparatively large frequency conversion efficiency, opening the door to near-unity flexible frequency conversion without cavity enhancement and resulting bandwidth constraints.

Jaber, Nicholas (ORCID:000900070106809X)↗

DOE OSTI2024

In situ characterization of two unknown ultrashort laser pulses using four-wave mixing in gas

Accurate characterization of two ultrashort laser pulses is of great interest in many ultrafast pump-probe experiments. We demonstrate a method based on four-wave mixing (FWM) in a gas which could be easily implemented into many existing pump-probe setups with minimal modifications for accurate, in situ characterization of both unknown pulses. This technique is tested on pairs of unknown pulses at wavelengths of 400/800 nm, and 266/400 nm. We measured the spectrogram of the pulse generated through FWM of the two unknown pulses by scanning the delay between two unknown pulses. The retrieval algorithm converges to accurately predict the intensity and the phase profiles of both unknown pulses with a trace error of < 1% and the accuracy is verified using an independent pulse characterization device.

Nambu, Noa (ORCID:0000000197303400)↗