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

Journal of the Optical Society of America B

Nonperturbative transient four-wave-mixing line shapes due to excitation-induced shift and excitation-induced dephasing

Justin M. Shacklette, Steven T. Cundiff

Published Apr 1, 2003• 48 citations
Publisher

Abstract

We numerically calculate the transient-four-wave-mixing (TFWM) response in systems that exhibit either a resonance frequency or a dephasing rate that depends on the level of excitation, which can occur in semiconductors or a dense atomic vapor. These effects change the intensity dependence of the TFWM signal, causing it to display noncubic behavior for significantly lower pulse areas and even a reduction in signal intensity for increasing pulse area. They also qualitatively change both the temporal behavior and spectrum of the TFWM signal in ways that cannot adequately be described in perturbation theory. For time-integrated TFWM, the saturation behavior is also found to depend on the delay between pulses. For comparison, the effects of local fields are also calculated as they produce similar effects. These results can help provide discrimination among the various phenomena.

DOI
10.1364/josab.20.000764

Related papers

Transient four-wave-mixing lineshapes due to excitation induced shift and excitation induced dephasing

Justin M. Shacklette, Steven T. Cundiff

Summary form only given. In an optically dense material, such as a semiconductor or a dense vapor, many-body interactions can dramatically modify the results of coherent experiments as compared to the dilute limit. The optical Bloch equations (OBE), which are appropriate in the dilute limit, must be modified to include many-body interactions. Such modified OBE (MOBE) are correct for a dense vapor and a phenomenological approximation for semiconductors, where a full treatment is based on the interacting electron-hole Hamiltonian. Previously, terms describing the local field correction (LFC) and excitation-induced dephasing (EID) have been added to the OBE to describe interactions. We show that an excitation-induced shift (EIS) is equally important. Perturbation calculations demonstrate that EIS gives rise to an additional signal in transient four-wave-mixing (TFWM), a common experiment for probing coherence. Comparison to numerical calculations shows that perturbation theory does not adequately describe either EIS or EID.

Quantum Electronics and Laser Science Conference•Jun 25, 2003•0 citations

Transient four-wave-mixing line shapes: Effects of excitation-induced dephasing

H. Wang, Kyle B. Ferrio, Duncan G. Steel +4 more

We describe the transient four-wave-mixing (FWM) response in systems where decay of the optically induced coherence depends on the excitation level of the system. Using modified optical Bloch equations, we show that excitation-induced dephasing due to phase-interrupting excited-state interactions qualitatively modifies the temporal behavior and polarization dependence of the FWM signal.

Physical Review A•Mar 1, 1994•112 citations

Role of excitation-induced shift in the coherent optical response of semiconductors

Justin M. Shacklette, Steven T. Cundiff

A transient four-wave-mixing signal is shown to arise from an excitation induced shift. In semiconductors, this signal can be comparable to or stronger than signals arising from saturation, local fields, or excitation induced dephasing. Calculations using modified optical Bloch equations show that multiple peaks in the transient four-wave-mixing spectrum are a signature of an excitation induced shift contributing to the signal. We observe this experimentally from a semiconductor multiple quantum well and confirm the presence of a shift directly using spectrally resolved differential transmission.

Physical review. B, Condensed matter•Jul 17, 2002•106 citations

Coherent exciton-continuum coupling in semiconductors

Steven T. Cundiff, M. Koch, Wayne H. Knox +2 more

Summary form only given. Despite recent effort, there are aspects of the transient four-wave-mixing (TFWM) response of semiconductors that remain puzzling. By performing partially nondegenerate TFWM (PND-TFWM) we show that for broadband excitation, the signal emitted at the 1 s exciton is dominated by contributions that correspond to excitation of higher states by the first pulse. The interference of these contributions results in the rapid decay of the excitonic signal. Our results demonstrate that, because TFWM is inherently a many-particle phenomenon, the many-body interactions always couple the excitonic transitions.

Quantum Electronics and Laser Science Conference•Jun 7, 1996•0 citations

The influence of finite bandwidth excitation sources in degenerate four-wave mixing spectroscopy

Thierry A. W. Wasserman, Patrick H. Vaccaro, Bruce R. Johnson

The effects of finite-bandwidth excitation are incorporated into the theoretical treatment of degenerate four-wave mixing (DFWM) spectroscopy by employing a general description of applied electromagnetic fields, thereby permitting the transient nature of typical laser sources to be taken explicitly into account. A computationally efficient perturbative (weak-field) formalism is developed by exploiting exponentially-decaying wave forms as a flexible basis for expanding the temporal envelope functions of incident quasimonochromatic pulses. This approach has the distinct advantage of yielding time-domain response integrals that can be evaluated analytically since they are almost as simple in form as their monochromatic counterparts. The resulting frequency-domain expressions for the induced DFWM signal polarization reflect the pronounced influence of finite-bandwidth excitation without needing to cobble such behavior into phenomenological rates for population decay and coherence dissipation. Spectral line shapes are examined for both stationary and nonstationary ensembles of isolated (gas-phase) target molecules, with the latter analyses demonstrating the systematic degradation of spatial discrimination introduced by nonmonochromatic implementations of the sub-Doppler (phase-conjugate) four-wave mixing scheme. In keeping with recent experimental findings, the precipitous drop in signal intensity accompanying the action of collisional dephasing processes is predicted to be tempered greatly by the use of short-duration excitation pulses.

The Journal of Chemical Physics•May 30, 2002•10 citations

Line shape of time-resolved four-wave mixing

Martin Wegener, D. S. Chemla, Stefan Schmitt-Rink +1 more

Time-resolved four-wave-mixing experiments are usually interpreted in terms of noninteracting two-level systems in order to obtain information on the polarization dephasing time ${\mathit{T}}_{2}$. Recent experiments involving excitonic resonances in semiconductor quantum wells (including results presented in this paper) show striking qualitative deviations from this simple picture. In particular, an exponential tail is observed at low excitation for negative time delays. At high excitation, the four-wave-mixing signal is found to evolve into two distinct temporal maxima. We demonstrate that the microscopic origin of this time dependence can be understood in terms of coherent exciton-exciton interactions. We show in fact that this behavior is more general and should be seen in numerous dense media where strong nonlinear interactions of polarizations occur. In addition to presenting rigorous numerical results, we analyze two simple situations in which such interactions exist: dielectric media with local-field effects and the anharmonic oscillator. We derive analytical expressions for their time-dependent four-wave-mixing response and discuss the physical origin of these new nonlinear-optical effects.

Physical Review A•Nov 1, 1990•376 citations
We numerically calculate the transient-four-wave-mixing (TFWM) response in systems that exhibit either a resonance frequency or a dephasing rate that depends on the level of excitation, which can occur in semiconductors or a dense atomic vapor. These effects change the intensity dependence of the TFWM signal, causing it to display noncubic behavior for significantly lower pulse areas and even a reduction in signal intensity for increasing pulse area. They also qualitatively change both the temporal behavior and spectrum of the TFWM signal in ways that cannot adequately be described in perturbation theory. For time-integrated TFWM, the saturation behavior is also found to depend on the delay between pulses. For comparison, the effects of local fields are also calculated as they produce similar effects. These results can help provide discrimination among the various phenomena.
Summary form only given. In an optically dense material, such as a semiconductor or a dense vapor, many-body interactions can dramatically modify the results of coherent experiments as compared to the dilute limit. The optical Bloch equations (OBE), which are appropriate in the dilute limit, must be modified to include many-body interactions. Such modified OBE (MOBE) are correct for a dense vapor and a phenomenological approximation for semiconductors, where a full treatment is based on the interacting electron-hole Hamiltonian. Previously, terms describing the local field correction (LFC) and excitation-induced dephasing (EID) have been added to the OBE to describe interactions. We show that an excitation-induced shift (EIS) is equally important. Perturbation calculations demonstrate that EIS gives rise to an additional signal in transient four-wave-mixing (TFWM), a common experiment for probing coherence. Comparison to numerical calculations shows that perturbation theory does not adequately describe either EIS or EID.
A transient four-wave-mixing signal is shown to arise from an excitation induced shift. In semiconductors, this signal can be comparable to or stronger than signals arising from saturation, local fields, or excitation induced dephasing. Calculations using modified optical Bloch equations show that multiple peaks in the transient four-wave-mixing spectrum are a signature of an excitation induced shift contributing to the signal. We observe this experimentally from a semiconductor multiple quantum well and confirm the presence of a shift directly using spectrally resolved differential transmission.
Summary form only given. Despite recent effort, there are aspects of the transient four-wave-mixing (TFWM) response of semiconductors that remain puzzling. By performing partially nondegenerate TFWM (PND-TFWM) we show that for broadband excitation, the signal emitted at the 1 s exciton is dominated by contributions that correspond to excitation of higher states by the first pulse. The interference of these contributions results in the rapid decay of the excitonic signal. Our results demonstrate that, because TFWM is inherently a many-particle phenomenon, the many-body interactions always couple the excitonic transitions.
The effects of finite-bandwidth excitation are incorporated into the theoretical treatment of degenerate four-wave mixing (DFWM) spectroscopy by employing a general description of applied electromagnetic fields, thereby permitting the transient nature of typical laser sources to be taken explicitly into account. A computationally efficient perturbative (weak-field) formalism is developed by exploiting exponentially-decaying wave forms as a flexible basis for expanding the temporal envelope functions of incident quasimonochromatic pulses. This approach has the distinct advantage of yielding time-domain response integrals that can be evaluated analytically since they are almost as simple in form as their monochromatic counterparts. The resulting frequency-domain expressions for the induced DFWM signal polarization reflect the pronounced influence of finite-bandwidth excitation without needing to cobble such behavior into phenomenological rates for population decay and coherence dissipation. Spectral line shapes are examined for both stationary and nonstationary ensembles of isolated (gas-phase) target molecules, with the latter analyses demonstrating the systematic degradation of spatial discrimination introduced by nonmonochromatic implementations of the sub-Doppler (phase-conjugate) four-wave mixing scheme. In keeping with recent experimental findings, the precipitous drop in signal intensity accompanying the action of collisional dephasing processes is predicted to be tempered greatly by the use of short-duration excitation pulses.
Time-resolved four-wave-mixing experiments are usually interpreted in terms of noninteracting two-level systems in order to obtain information on the polarization dephasing time T2{\mathit{T}}_{2}T2​. Recent experiments involving excitonic resonances in semiconductor quantum wells (including results presented in this paper) show striking qualitative deviations from this simple picture. In particular, an exponential tail is observed at low excitation for negative time delays. At high excitation, the four-wave-mixing signal is found to evolve into two distinct temporal maxima. We demonstrate that the microscopic origin of this time dependence can be understood in terms of coherent exciton-exciton interactions. We show in fact that this behavior is more general and should be seen in numerous dense media where strong nonlinear interactions of polarizations occur. In addition to presenting rigorous numerical results, we analyze two simple situations in which such interactions exist: dielectric media with local-field effects and the anharmonic oscillator. We derive analytical expressions for their time-dependent four-wave-mixing response and discuss the physical origin of these new nonlinear-optical effects.