Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Down-conversion of electronic frequencies and their dephasing dynamics: Interferometric four-wave-mixing spectroscopy with broadband light

Jason C. Kirkwood, A. C. Albrecht

Published Feb 10, 2000• 22 citations
Publisher

Abstract

The theory for temporally multidimensional, electronically resonant four-wave-mixing (FWM) spectroscopy based on broadband light interferometry is developed. Both homodyne and heterodyne detection are considered. Upon spectrally resolving the signal, the electronic Bohr frequency is seen to be extremely down-converted, even to zero frequency, but only with homodyne detection. These very low frequency fringes, referred to as radiation difference oscillations, are well known in the interferometric coherent Raman broadband light spectroscopies. Such low frequency fringes permit interferometry in the optical region using Nyquist criteria corresponding to far infrared sampling rates. Possible applications are illustrated by simulations of the two-dimensional third order signals from an electronic two-level system in a variety of ``baths.'' It is seen how homogeneous and inhomogeneous line-shaping mechanisms manifest themselves differently and revealingly in the free induction decay, the photon echo decay and their cross term components of the FWM signal.

DOI
10.1103/physreva.61.033802

Related papers

Interferometric six-wave mixing spectroscopy with broadband light: Isomorphism and factorized time correlator diagrams

Jason C. Kirkwood, A. C. Albrecht

The theory of an interferometric six-wave mixing quasiecho signal from a modeled molecular liquid using broadband (``noisy'') light is reported. The line-shaping function is treated by a standard mixture of a dynamic (homogeneous) dephasing process and a static (inhomogeneous) Bohr frequency distribution. Simulations are presented in either limit of the overall process to demonstrate the rephasing aspects of this nonlinear spectroscopy. The general aspects of the two-dimensional signal are inferred from factorized time correlator (FTC) diagrams. These diagrams pictorially represent the correlation functions of the random noise (associated with the broadband light) that arise upon stochastic averaging at the signal level. The entire set of FTC diagrams is seen to be isomorphic with those that describe a nonecho interferometric noisy light spectroscopy at fifth order, and the third-order electronically resonant four-wave mixing. Similarities between these three very different processes are discussed in terms of this one-to-one correspondence.

Physical Review A•Mar 7, 2000•6 citations

Ultrafast modulation spectroscopy in cascading three-level and four-level systems

Panming Fu, Yanbang Wang, Qian Jiang +2 more

We study theoretically ultrafast modulation spectroscopy in Doppler-broadened cascading three-level and four-level systems. The pump beams consist of two frequency components that drive two-pathway excitation. The four-wave mixing (FWM) signal exhibits damping oscillation as the relative time delay τ between the two pump beams is varied, from which the resonant frequencies between energy levels can be deduced. Furthermore, Doppler-free precision in the measurement of the resonant frequencies can be achieved when the pump beams have either narrow-band or broadband linewidths. We study two-photon resonant FWM induced by time-delayed correlated fluctuating fields in a Doppler-broadened cascading three-level system. It is related intrinsically to the sum-frequency trilevel echo when the pump beams have broadband linewidths. However, unlike the corresponding incoherent-light stimulated photon echo, the maximum of the FWM signal is shifted from τ≃0. If we consider the fluctuations of the pump beams, the FWM signal exhibits damping oscillation when the laser frequency is off resonant from the two-photon transition.

Journal of the Optical Society of America B•Mar 1, 2001•14 citations

Fundamentals of heterodyne wave mixing spectroscopy: a tutorial

Daniel Groll, Thilo Hahn, Paweł Machnikowski +3 more

Abstract This tutorial provides a joint theoretical and experimental overview of heterodyne wave mixing spectroscopy, focusing mainly on four-wave mixing (FWM). This powerful and versatile time-resolved nonlinear optical spectroscopy technique enables the investigation of individual localized single photon emitters, as well as microscopy of extended samples, e.g. two-dimensional transition metal dichalcogenides. Starting with the fundamental theory of optically driven two-level systems, we motivate the utility of wave mixing spectroscopy via a discussion on homogeneous and inhomogeneous linewidths which can be independently measured using FWM. We then provide a detailed overview of the heterodyne wave mixing setup operated by one of the authors (JK) at Institut Néel in Grenoble, supported by theoretical modeling of the signal detection process. Throughout the paper we elaborate on important benefits of heterodyne wave mixing spectroscopy, e.g. background-free detection, measurement of the full signal field including amplitude and phase, and investigation of coupling mechanisms in few-level systems. Within the context of the latter point we discuss the significance of two-dimensional FWM spectra. This tutorial is dedicated to students, young researchers, as well as experts in the field of nonlinear spectroscopy in general and FWM in particular. It explains the fundamental concepts and building blocks required to operate a heterodyne wave mixing experiment both from the experimental and theoretical side. This joint approach is helpful for theoreticians who want to accurately and quantitatively model wave mixing signals, as well as for experimentalists who aim to interpret their recorded data.

arXiv:2503.19750•Nano Futures•Oct 7, 2025•5 citations

Radiation-matter oscillations and spectral line narrowing in field-correlated four-wave mixing. I. Theory

Mark A. Dugan, A. C. Albrecht

The theoretical basis for new signal transients and spectral features generated in field-correlated four-wave mixing spectroscopies is developed. Special attention is given to those signal responses that are sensitive to phase or amplitude correlation among the input driving fields, and not simply their intensity correlation. Thus the cases of incoherent broadband excitation and of coherent short-pulsed excitation will be discussed and compared. Applications to the coherent Raman spectroscopies, both electronically nonresonant and full resonant, are analyzed. Novel interferometric oscillatory behavior is exposed in terms of radiation-matter detuning beats and matter-matter bilevel and trilevel quantum beats. In addition, new resonances are found that have submaterial linewidths and detuning parameters that lock onto the mode frequency of the driven chromophore. These spectral features are members of a class of bichromophore resonant line shapes arising from nonlinear mixing with correlated driving fields. Analytic results are presented and modeled to anticipate experimental results presented in the following paper [Phys. Rev. A 43, 3922 (1991)].

Physical Review A•Apr 1, 1991•81 citations

Radiation-matter oscillations and spectral line narrowing in field-correlated four-wave mixing. II. Experiment

Mark A. Dugan, A. C. Albrecht

New radiation-matter phenomena in four-wave mixing spectroscopies, given a theoretical basis in the preceding paper [Dugan and Albrecht, Phys. Rev. A 43, 3877 (1991)], are examined experimentally here. A new class of Rabi detuning oscillations is recorded in interferometric coherent Stokes Raman scattering (CSRS). Two identical nanosecond incoherent light fields are mutually delayed, while simultaneously mixing in a nonlinear medium with a narrow-band field of a different color. Spectral filtering of the CSRS signal is essential. From such signals the frequencies and the dephasing rate constants can be a measure of the Raman-active vibrations in both the electronic ground state and the electronic excited state of the scattering chromophore. In principle, analogous probing of vibronic transitions is possible. Detuning oscillations for multimode systems are presented. It is shown how they are transformed into quantum beats, exactly those seen with femtosecond CSRS, when the narrow-band field is made broad and/or the detection is ``white.'' Finally, an example of the sub-Raman linewidth spectral feature, predicted in the preceding paper, is presented. It determines a Raman frequency, but does not carry its linewidth.

Physical Review A•Apr 1, 1991•48 citations

Theory of degenerate four-wave mixing in resonant Doppler-broadened media. - II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems

M. Ducloy, Daniel Bloch

In this article, we analyse a new sensitive spectroscopic technique in which a sample cell is irradiated by a two-frequency pump beam (ω + Δ ± δ/2) and a counter-propagating probe beam (ω). The phase-conjugate fields re-emitted at frequencies ω ± δ, via four-wave mixing processes, are detected through their heterodyne beating with the probe field. The properties of the heterodyne beat signal are studied by means of a perturbation calculation of the nonlinear response of the medium, carried out to the third order in the incident fields. In resonant gas media, the emission lineshape exhibits a Doppler-free doublet structure [frequency splitting 3 δ/2 for single-photon resonances, and δ/2 for two-photon transitions]. By using a phase-sensitive detection of the beat signal, one can separately analyse real (dispersion) or imaginary parts (absorption) of the nonlinear susceptibility. For single-photon transitions, the signal phase shift is related to the atomic levels lifetime and allows one to study the relaxation dynamics in gas phase (like quenching collisions, velocity diffusion, etc...). This is particularly interesting for cross-over resonances, in which only the common level contributes. In three-level systems, one also predicts a selective resonant enhancement of the phase-conjugate emission through Raman-type two-photon processes. Most of these predictions have been experimentally verified.

Journal de physique•Jan 1, 1982•48 citations
The theory for temporally multidimensional, electronically resonant four-wave-mixing (FWM) spectroscopy based on broadband light interferometry is developed. Both homodyne and heterodyne detection are considered. Upon spectrally resolving the signal, the electronic Bohr frequency is seen to be extremely down-converted, even to zero frequency, but only with homodyne detection. These very low frequency fringes, referred to as radiation difference oscillations, are well known in the interferometric coherent Raman broadband light spectroscopies. Such low frequency fringes permit interferometry in the optical region using Nyquist criteria corresponding to far infrared sampling rates. Possible applications are illustrated by simulations of the two-dimensional third order signals from an electronic two-level system in a variety of ``baths.'' It is seen how homogeneous and inhomogeneous line-shaping mechanisms manifest themselves differently and revealingly in the free induction decay, the photon echo decay and their cross term components of the FWM signal.
The theory of an interferometric six-wave mixing quasiecho signal from a modeled molecular liquid using broadband (``noisy'') light is reported. The line-shaping function is treated by a standard mixture of a dynamic (homogeneous) dephasing process and a static (inhomogeneous) Bohr frequency distribution. Simulations are presented in either limit of the overall process to demonstrate the rephasing aspects of this nonlinear spectroscopy. The general aspects of the two-dimensional signal are inferred from factorized time correlator (FTC) diagrams. These diagrams pictorially represent the correlation functions of the random noise (associated with the broadband light) that arise upon stochastic averaging at the signal level. The entire set of FTC diagrams is seen to be isomorphic with those that describe a nonecho interferometric noisy light spectroscopy at fifth order, and the third-order electronically resonant four-wave mixing. Similarities between these three very different processes are discussed in terms of this one-to-one correspondence.
We study theoretically ultrafast modulation spectroscopy in Doppler-broadened cascading three-level and four-level systems. The pump beams consist of two frequency components that drive two-pathway excitation. The four-wave mixing (FWM) signal exhibits damping oscillation as the relative time delay τ between the two pump beams is varied, from which the resonant frequencies between energy levels can be deduced. Furthermore, Doppler-free precision in the measurement of the resonant frequencies can be achieved when the pump beams have either narrow-band or broadband linewidths. We study two-photon resonant FWM induced by time-delayed correlated fluctuating fields in a Doppler-broadened cascading three-level system. It is related intrinsically to the sum-frequency trilevel echo when the pump beams have broadband linewidths. However, unlike the corresponding incoherent-light stimulated photon echo, the maximum of the FWM signal is shifted from τ≃0. If we consider the fluctuations of the pump beams, the FWM signal exhibits damping oscillation when the laser frequency is off resonant from the two-photon transition.
Abstract This tutorial provides a joint theoretical and experimental overview of heterodyne wave mixing spectroscopy, focusing mainly on four-wave mixing (FWM). This powerful and versatile time-resolved nonlinear optical spectroscopy technique enables the investigation of individual localized single photon emitters, as well as microscopy of extended samples, e.g. two-dimensional transition metal dichalcogenides. Starting with the fundamental theory of optically driven two-level systems, we motivate the utility of wave mixing spectroscopy via a discussion on homogeneous and inhomogeneous linewidths which can be independently measured using FWM. We then provide a detailed overview of the heterodyne wave mixing setup operated by one of the authors (JK) at Institut Néel in Grenoble, supported by theoretical modeling of the signal detection process. Throughout the paper we elaborate on important benefits of heterodyne wave mixing spectroscopy, e.g. background-free detection, measurement of the full signal field including amplitude and phase, and investigation of coupling mechanisms in few-level systems. Within the context of the latter point we discuss the significance of two-dimensional FWM spectra. This tutorial is dedicated to students, young researchers, as well as experts in the field of nonlinear spectroscopy in general and FWM in particular. It explains the fundamental concepts and building blocks required to operate a heterodyne wave mixing experiment both from the experimental and theoretical side. This joint approach is helpful for theoreticians who want to accurately and quantitatively model wave mixing signals, as well as for experimentalists who aim to interpret their recorded data.
The theoretical basis for new signal transients and spectral features generated in field-correlated four-wave mixing spectroscopies is developed. Special attention is given to those signal responses that are sensitive to phase or amplitude correlation among the input driving fields, and not simply their intensity correlation. Thus the cases of incoherent broadband excitation and of coherent short-pulsed excitation will be discussed and compared. Applications to the coherent Raman spectroscopies, both electronically nonresonant and full resonant, are analyzed. Novel interferometric oscillatory behavior is exposed in terms of radiation-matter detuning beats and matter-matter bilevel and trilevel quantum beats. In addition, new resonances are found that have submaterial linewidths and detuning parameters that lock onto the mode frequency of the driven chromophore. These spectral features are members of a class of bichromophore resonant line shapes arising from nonlinear mixing with correlated driving fields. Analytic results are presented and modeled to anticipate experimental results presented in the following paper [Phys. Rev. A 43, 3922 (1991)].
New radiation-matter phenomena in four-wave mixing spectroscopies, given a theoretical basis in the preceding paper [Dugan and Albrecht, Phys. Rev. A 43, 3877 (1991)], are examined experimentally here. A new class of Rabi detuning oscillations is recorded in interferometric coherent Stokes Raman scattering (CSRS). Two identical nanosecond incoherent light fields are mutually delayed, while simultaneously mixing in a nonlinear medium with a narrow-band field of a different color. Spectral filtering of the CSRS signal is essential. From such signals the frequencies and the dephasing rate constants can be a measure of the Raman-active vibrations in both the electronic ground state and the electronic excited state of the scattering chromophore. In principle, analogous probing of vibronic transitions is possible. Detuning oscillations for multimode systems are presented. It is shown how they are transformed into quantum beats, exactly those seen with femtosecond CSRS, when the narrow-band field is made broad and/or the detection is ``white.'' Finally, an example of the sub-Raman linewidth spectral feature, predicted in the preceding paper, is presented. It determines a Raman frequency, but does not carry its linewidth.
In this article, we analyse a new sensitive spectroscopic technique in which a sample cell is irradiated by a two-frequency pump beam (ω + Δ ± δ/2) and a counter-propagating probe beam (ω). The phase-conjugate fields re-emitted at frequencies ω ± δ, via four-wave mixing processes, are detected through their heterodyne beating with the probe field. The properties of the heterodyne beat signal are studied by means of a perturbation calculation of the nonlinear response of the medium, carried out to the third order in the incident fields. In resonant gas media, the emission lineshape exhibits a Doppler-free doublet structure [frequency splitting 3 δ/2 for single-photon resonances, and δ/2 for two-photon transitions]. By using a phase-sensitive detection of the beat signal, one can separately analyse real (dispersion) or imaginary parts (absorption) of the nonlinear susceptibility. For single-photon transitions, the signal phase shift is related to the atomic levels lifetime and allows one to study the relaxation dynamics in gas phase (like quenching collisions, velocity diffusion, etc...). This is particularly interesting for cross-over resonances, in which only the common level contributes. In three-level systems, one also predicts a selective resonant enhancement of the phase-conjugate emission through Raman-type two-photon processes. Most of these predictions have been experimentally verified.