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

Anharmonicity and mode-mode coupling effects analyzed by four-wave-mixing photon-echo spectroscopy

Kuo Kan Liang, A. A. Villaeys

Published Jul 30, 2010• 4 citations
Publisher

Abstract

The present work is devoted to the description of a nonperturbative treatment of anharmonic effect and mode-mode coupling taking place in molecular vibrational systems. The information is obtained from the four-wave-mixing signal detected in the usual photon-echo phase-matched direction, termed 4WM photon-echo, using heterodyne detection to test separately the real and the imaginary parts of the third-order polarization. This approach allows a complete redistribution of the relaxation, dephasing, and transition constants on account of the magnitude of the coupling strength. In addition, our analytical approach accounts for the contributions provided by the various possible chronological orderings of the field interactions. The high sensitivity of the signal with both the energy shifts induced by the internal couplings and off-resonant energy parameter of the laser excitation is properly analyzed in the framework of our analytical description.

DOI
10.1103/physreva.82.013423

Related papers

Photon echoes and related four-wave-mixing spectroscopies using phase-locked pulses

Minhaeng Cho, Norbert F. Scherer, Graham R. Fleming +1 more

The use of phase-locked pulses in various spectroscopic techniques related to the third-order polarization P(3) is analyzed. Using correlation function expressions for the nonlinear response function, we clarify the interrelationship among several photon echo, pump–probe, and spontaneous light emission techniques, without alluding to any specific model for the material system. By combining phase-locked pulses and heterodyne detection it becomes possible to probe separately the real and imaginary parts of the nonlinear response function. Combining two phase-locked pulse excitation with time-resolved detection of the spontaneous light emission allows direct separation of the Raman and fluorescence contributions.

The Journal of Chemical Physics•Apr 15, 1992•150 citations

Nonperturbative response functions: A tool for the interpretation of four-wave-mixing signals beyond third order

Lipeng Chen, Elisa Palacino‐González, Maxim F. Gelin +1 more

Considering an electronic two-level system coupled to vibrational degrees of freedom and driven by short and intense non-overlapping laser pulses, we introduce the concept of nonperturbative response functions. These response functions are expressed in terms of effective electronic transition dipole moments which depend on the strength of the field-matter coupling and on the pulse durations. It is shown that the nonlinear polarization representing four-wave-mixing signals can elegantly be expressed in terms of these nonperturbative response functions to all orders in the field-matter coupling. The nonperturbative response functions generalize the interpretative power of the familiar third-order response functions to four-wave-mixing experiments with intense laser pulses.

The Journal of Chemical Physics•Dec 18, 2017•19 citations

Two-dimensional optical three-pulse photon echo spectroscopy. I. Nonperturbative approach to the calculation of spectra

Tomáš Mančal, Andrei V. Pisliakov, Graham R. Fleming

The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].

The Journal of Chemical Physics•Jun 16, 2006•74 citations

Effects of permanent dipole moments in transient four-wave mixing experiments

J. P. Lavoine

A two-pulse degenerate four-wave mixing experiment is analyzed in the case where the medium under investigation can be modeled by two-level systems having unequal permanent dipole moments. By modeling the light pulses by double exponentials [exp(-Gamma/t/)], we give an analytical expression of the third-order nonlinear polarization of the medium. We apply this result to simulate the measured signal in such experiment. We show that in the case of a two-photon transition, a signal can be detected if the pump pulse interacts with the medium before the probe pulse contrary to what is observed for excitations in the resonance region. An attempt to explain this behavior is made and the detected signal is analyzed in terms of pure coherent processes. This effect appears as a signature of the presence of permanent dipole moments. To test this property on a more realistic system, we then have considered a one-dimensional frequency-selected infrared degenerate four-wave mixing experiment on a molecular anharmonic vibrational mode modeled by a Morse potential and coupled to a dissipative bath of harmonic oscillators. We show that the two-photon transitions allowed by the presence of permanent dipole moments enable to analyze the multilevel system dynamics as if they were the one of a two-level system. Our results can also be extended to the case of inhomogeneous broadening and are of interest to study the infrared photon-echo response of anharmonic vibrational modes.

The Journal of Chemical Physics•Sep 7, 2007•11 citations

Nonperturbative approach to the nonlinear photon echo of V-type system

Xue Zhang, Dong, Hui

The analysis of nonlinear spectroscopy, widely used to study the dynamics and structures of condensed-phase matter, typically employs a perturbative approach noticing the weak interaction between the laser and the matter of interest. However, such perturbative approach is no longer applicable once the interaction between the laser and the matter is strong. We adapt the method of quantum dynamical evolution into the calculation of signal and present the response formalism of the nonlinear spectroscopy in a nonperturbative approach. In this new approach, we demonstrate that in addition to the third-order term in the perturbative method, the higher-order terms have essential contributions to the nonlinear signal of the two-pulse and three-pulse photon echo (2PPE and 3PPE). The detailed calculations are demonstrated with the example of a three-level V-type system, which is widely used in the studies of quantum optics. We consider the effect of the environment via a pure dephasing mechanism with both the localized modes of each molecule and the shared modes between molecules.

arXiv:2206.10857•Jun 22, 2022•0 citations

Nonperturbative approach to the nonlinear photon echo of a V-type system

Xue Zhang, Hui Dong

The analysis of nonlinear spectroscopy, widely used to study the dynamics and structures of condensed-phase matter, typically employs a perturbative approach noticing the weak interaction between the laser and the matter of interest. However, such a perturbative approach is no longer applicable once the interaction between the laser and the matter is strong. We adapt the method of quantum dynamical evolution into the calculation of signal and present the response formalism of the nonlinear spectroscopy in a nonperturbative approach. In this approach, we demonstrate that, in addition to the third-order term in the perturbative method, the higher-order terms have essential contributions to the nonlinear signal of the two-pulse and three-pulse photon echo (2PPE and 3PPE). The detailed calculations are demonstrated with the example of a three-level V-type system, which is widely used in the studies of quantum optics. We consider the effect of the environment via a pure dephasing mechanism with both the localized modes of each molecule and the shared modes between molecules.

Physical Review A•Oct 24, 2022•2 citations
The present work is devoted to the description of a nonperturbative treatment of anharmonic effect and mode-mode coupling taking place in molecular vibrational systems. The information is obtained from the four-wave-mixing signal detected in the usual photon-echo phase-matched direction, termed 4WM photon-echo, using heterodyne detection to test separately the real and the imaginary parts of the third-order polarization. This approach allows a complete redistribution of the relaxation, dephasing, and transition constants on account of the magnitude of the coupling strength. In addition, our analytical approach accounts for the contributions provided by the various possible chronological orderings of the field interactions. The high sensitivity of the signal with both the energy shifts induced by the internal couplings and off-resonant energy parameter of the laser excitation is properly analyzed in the framework of our analytical description.
The use of phase-locked pulses in various spectroscopic techniques related to the third-order polarization P(3) is analyzed. Using correlation function expressions for the nonlinear response function, we clarify the interrelationship among several photon echo, pump–probe, and spontaneous light emission techniques, without alluding to any specific model for the material system. By combining phase-locked pulses and heterodyne detection it becomes possible to probe separately the real and imaginary parts of the nonlinear response function. Combining two phase-locked pulse excitation with time-resolved detection of the spontaneous light emission allows direct separation of the Raman and fluorescence contributions.
Considering an electronic two-level system coupled to vibrational degrees of freedom and driven by short and intense non-overlapping laser pulses, we introduce the concept of nonperturbative response functions. These response functions are expressed in terms of effective electronic transition dipole moments which depend on the strength of the field-matter coupling and on the pulse durations. It is shown that the nonlinear polarization representing four-wave-mixing signals can elegantly be expressed in terms of these nonperturbative response functions to all orders in the field-matter coupling. The nonperturbative response functions generalize the interpretative power of the familiar third-order response functions to four-wave-mixing experiments with intense laser pulses.
The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].
A two-pulse degenerate four-wave mixing experiment is analyzed in the case where the medium under investigation can be modeled by two-level systems having unequal permanent dipole moments. By modeling the light pulses by double exponentials [exp(-Gamma/t/)], we give an analytical expression of the third-order nonlinear polarization of the medium. We apply this result to simulate the measured signal in such experiment. We show that in the case of a two-photon transition, a signal can be detected if the pump pulse interacts with the medium before the probe pulse contrary to what is observed for excitations in the resonance region. An attempt to explain this behavior is made and the detected signal is analyzed in terms of pure coherent processes. This effect appears as a signature of the presence of permanent dipole moments. To test this property on a more realistic system, we then have considered a one-dimensional frequency-selected infrared degenerate four-wave mixing experiment on a molecular anharmonic vibrational mode modeled by a Morse potential and coupled to a dissipative bath of harmonic oscillators. We show that the two-photon transitions allowed by the presence of permanent dipole moments enable to analyze the multilevel system dynamics as if they were the one of a two-level system. Our results can also be extended to the case of inhomogeneous broadening and are of interest to study the infrared photon-echo response of anharmonic vibrational modes.
The analysis of nonlinear spectroscopy, widely used to study the dynamics and structures of condensed-phase matter, typically employs a perturbative approach noticing the weak interaction between the laser and the matter of interest. However, such perturbative approach is no longer applicable once the interaction between the laser and the matter is strong. We adapt the method of quantum dynamical evolution into the calculation of signal and present the response formalism of the nonlinear spectroscopy in a nonperturbative approach. In this new approach, we demonstrate that in addition to the third-order term in the perturbative method, the higher-order terms have essential contributions to the nonlinear signal of the two-pulse and three-pulse photon echo (2PPE and 3PPE). The detailed calculations are demonstrated with the example of a three-level V-type system, which is widely used in the studies of quantum optics. We consider the effect of the environment via a pure dephasing mechanism with both the localized modes of each molecule and the shared modes between molecules.
The analysis of nonlinear spectroscopy, widely used to study the dynamics and structures of condensed-phase matter, typically employs a perturbative approach noticing the weak interaction between the laser and the matter of interest. However, such a perturbative approach is no longer applicable once the interaction between the laser and the matter is strong. We adapt the method of quantum dynamical evolution into the calculation of signal and present the response formalism of the nonlinear spectroscopy in a nonperturbative approach. In this approach, we demonstrate that, in addition to the third-order term in the perturbative method, the higher-order terms have essential contributions to the nonlinear signal of the two-pulse and three-pulse photon echo (2PPE and 3PPE). The detailed calculations are demonstrated with the example of a three-level V-type system, which is widely used in the studies of quantum optics. We consider the effect of the environment via a pure dephasing mechanism with both the localized modes of each molecule and the shared modes between molecules.