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

Transient polarization characteristics associated with resonant light scattering by a degenerate two-level system

Masaki Aihara

Published Aug 1, 1978• 20 citations
Publisher

Abstract

The time dependence of the polarized and unpolarized parts of the secondary-radiation intensity, ${I}_{\mathrm{p}}$ and ${I}_{\mathrm{up}}$, and the time-dependent degree of polarization $P(t)$ are calculated. A method is based upon the Feynman-diagram technique which is extended to enable the calculation of the reduced-density matrix element. It is found that, for the step excitation, $P(t)$ does not show a simple exponential decay. Especially in the off-resonance case, $P(t)$ shows oscillatory behavior. In the case of pulse excitation, ${I}_{\mathrm{up}}$ takes its maximum value after the excitation pulse has been turned off, and in the long-time limit it decays with the radiative-damping rate. In contrast to ${I}_{\mathrm{up}}$, ${I}_{\mathrm{p}}$ quickly responds to the excitation pulse and shows rapid exponential decay with the transverse-relaxation rate. It is also found that, contrary to the nondegenerate case, the total intensity of the secondary radiation does not exhibit simple exponential decay with the radiative-damping rate.

DOI
10.1103/physreva.18.606

Related papers

Nonlinear polarizations and excitations and their time dependence in discrete multilevel systems

H. B. Puell, C. R. Vidal

For the interaction of coherent radiation with a nondegenerate, homogeneously broadened multilevel system the nonlinear susceptibilities and excitations and their time dependence are evaluated using a perturbation approach to the density matrix up to fourth order. This is done for the "off-resonance" case, ${(\ensuremath{\Delta}{\ensuremath{\omega}}^{2}+{\ensuremath{\Gamma}}^{2})}^{\frac{1}{2}}\ensuremath{\gg}\frac{1}{\ensuremath{\tau}}$, as well as for the "on-resonance" case, ${(\ensuremath{\Delta}{\ensuremath{\omega}}^{2}+{\ensuremath{\Gamma}}^{2})}^{\frac{1}{2}}\ensuremath{\ll}\frac{1}{\ensuremath{\tau}}$, with $\ensuremath{\tau}$ being the pulse duration, by taking into account the temporal change of the electric field amplitude and the phase and energy relaxation times, ${T}_{2}$ and ${T}_{1}$. It is shown that the transient one-photon excitation known as adiabatic following, is not only important for a pulse duration $\ensuremath{\tau}<{T}_{2}$, but may also be important for ${T}_{2}\ensuremath{\lesssim}\ensuremath{\tau}<{T}_{1}$. In addition, expressions for the transient two-photon excitation in a multilevel system are derived. Finally, the two-level limit is evaluated to all orders of the perturbation including damping effects, which gives results valid also for large incident light intensities. For the "off-resonance" case an expression is obtained which describes not only the transient adiabatic following process, but also the usual one-photon absorption including saturation effects giving rise to power broadening.

Physical Review A•Dec 1, 1976•32 citations

Transients in media with near dipole-dipole interatomic interaction

Oleg Kh Khasanov, Русецкий Григорий Александрович, Самарцев Виталий Владимирович +2 more

The effect that may be exerted by an interatomic near dipole-dipole interaction upon optical transient processes in dense resonance media is analyzed. The behavior of the macroscopic polarization after a one-pulse excitation of a dense ensemble of two-level atoms is considered. It is shown that the free polarization signal is of oscillatory nature, with the oscillation frequency varying in time and being dependent on the dipole-dipole interaction constant, the intensity and duration of the exciting pulse, and the detuning of its carrier frequency from the resonance. The free polarization signal decay, which depends on the magnitude and sign of the sum of the detuning of the exciting pulse carrier frequency from the resonance and the Lorentz frequency, may obey either a power or an exponential law. The signal decay rate is determined not only by the inhomogeneous broadening, but also by the ratio of the above parameters. The peculiarities of echo-responses under one- or two-pulse excitation conditions are studied.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 20, 2004•1 citation

Relative intensities and time characteristics of Raman scattering and luminescence under nearly resonant light excitation

Takashi Kushida, Shuichi Kinoshita

Various characteristics of frequency-integrated intensities of secondary radiation components near the resonance excitation region have been calculated for a three-level system coupled with a reservoir using a stochastic model. It has been found that the spectral and temporal characteristics of the resonant second-order optical processes can be understood consistently by considering that Raman scattering results from the average value of the induced-dipole moment with respect to the energy fluctuation due to the system-reservoir interaction, while luminescence results from its deviation from the average value. A simple method to determine parameter values that characterize the excited-state dynamics in condensed phases from the secondary radiation data is also discussed.

Physical Review A•Jun 1, 1990•14 citations

Free polarization decay in media with a short-range dipole-dipole interatomic interaction

Oleg Kh Khasanov, Русецкий Григорий Александрович, Anatoly A. Afanas'ev +3 more

The effect that may be exerted by an interatomic dipole-dipole interaction upon optical transient processes in dense resonance media, in particular, free polarization decay, is analyzed. The behavior of the macroscopic polarization after a single-pulse excitation of a dense ensemble of two-level atoms is considered. It is shown that the free polarization signal is of oscillatory nature, with the oscillation frequency varying in time and being dependent on the dipole-dipole interaction constant, the intensity and duration of the exciting pulse, and the detuning of its carrier frequency from the resonance. The free polarization signal decay, which depends on the magnitude and sign of the sum of the detuning of the exciting pulse carrier frequency from the resonance and the Lorentz frequency, may obey either a power or an exponential law. The signal decay rate is determined not only by the inhomogeneous broadening, but also by the ratio of the above parameters.

Optics and Spectroscopy•Oct 1, 2003•1 citation

Optical Response of Materials

Tatsuo Yajima

General behavior of the transient response of materials excited by a stepwise optical field has been studied by means of numerical analysis based on a model of the inhomogeneously broadened two-level atomic system with relaxation obeylng the quantum mechanical equation of motion. The time dependences of the polarization and the excited state probability of atoms are investigated in detail under a wide variety of conditions including both the resonant and far off-resonant excitations. The behaviors are found to be quite different depending on the relative magnitudes of the light frequency, the center frequency and the bandwidth of transition, the Rabi frequency, the longitudinal and transverse relaxation rates. Two kinds of response times are defined to describe the rapidity of the response, and the physical parameters goveming them are detennined for a variety of cases. Another kind of response time originated from the statistical behavior of atoms is further considered and discussed. Based on these results, the range of the values of the response times are estimated in general. The results for both cases with and without the rotating wave approximation are also calculated and compared.

•Jan 1, 1992•0 citations

Transient scattering of resonance radiation in a two-level system

A. A. Panteleev, V. Roerich, A. N. Starostin

A new method is developed for the description of transfer and scattering of a time-dependent laser pulse, which is based on a hierarchy of Bogoliubov-Born-Green-Kirkwood-Yvone (BBGKY) equations for reduced density matrices. The systems of equations are obtained for the atomic and photon density matrices and the correlation operator in the second-order Born approximation. The system of equations describes stimulated and spontaneous scattering of laser radiation in an optically thin medium, where reabsorption of spontaneous radiation can be neglected. The method proposed in the paper yields for the first time the correct expressions for nonstationary resonance fluorescence spectra, which do not give the negative values for fluorescence intensity. The expressions obtained for the resonance emission spectra coincide in limiting cases with those obtained within the framework of the quantum regression theorem.

Journal of Experimental and Theoretical Physics•Feb 1, 2003•5 citations
The time dependence of the polarized and unpolarized parts of the secondary-radiation intensity, Ip{I}_{\mathrm{p}}Ip​ and Iup{I}_{\mathrm{up}}Iup​, and the time-dependent degree of polarization P(t)P(t)P(t) are calculated. A method is based upon the Feynman-diagram technique which is extended to enable the calculation of the reduced-density matrix element. It is found that, for the step excitation, P(t)P(t)P(t) does not show a simple exponential decay. Especially in the off-resonance case, P(t)P(t)P(t) shows oscillatory behavior. In the case of pulse excitation, Iup{I}_{\mathrm{up}}Iup​ takes its maximum value after the excitation pulse has been turned off, and in the long-time limit it decays with the radiative-damping rate. In contrast to Iup{I}_{\mathrm{up}}Iup​, Ip{I}_{\mathrm{p}}Ip​ quickly responds to the excitation pulse and shows rapid exponential decay with the transverse-relaxation rate. It is also found that, contrary to the nondegenerate case, the total intensity of the secondary radiation does not exhibit simple exponential decay with the radiative-damping rate.
For the interaction of coherent radiation with a nondegenerate, homogeneously broadened multilevel system the nonlinear susceptibilities and excitations and their time dependence are evaluated using a perturbation approach to the density matrix up to fourth order. This is done for the "off-resonance" case, ${(\ensuremath{\Delta}{\ensuremath{\omega}}^{2}+{\ensuremath{\Gamma}}^{2})}^{\frac{1}{2}}\ensuremath{\gg}\frac{1}{\ensuremath{\tau}}$, as well as for the "on-resonance" case, ${(\ensuremath{\Delta}{\ensuremath{\omega}}^{2}+{\ensuremath{\Gamma}}^{2})}^{\frac{1}{2}}\ensuremath{\ll}\frac{1}{\ensuremath{\tau}}$, with $\ensuremath{\tau}$ being the pulse duration, by taking into account the temporal change of the electric field amplitude and the phase and energy relaxation times, T2{T}_{2}T2​ and T1{T}_{1}T1​. It is shown that the transient one-photon excitation known as adiabatic following, is not only important for a pulse duration $\ensuremath{\tau}<{T}_{2}$, but may also be important for ${T}_{2}\ensuremath{\lesssim}\ensuremath{\tau}<{T}_{1}$. In addition, expressions for the transient two-photon excitation in a multilevel system are derived. Finally, the two-level limit is evaluated to all orders of the perturbation including damping effects, which gives results valid also for large incident light intensities. For the "off-resonance" case an expression is obtained which describes not only the transient adiabatic following process, but also the usual one-photon absorption including saturation effects giving rise to power broadening.
The effect that may be exerted by an interatomic near dipole-dipole interaction upon optical transient processes in dense resonance media is analyzed. The behavior of the macroscopic polarization after a one-pulse excitation of a dense ensemble of two-level atoms is considered. It is shown that the free polarization signal is of oscillatory nature, with the oscillation frequency varying in time and being dependent on the dipole-dipole interaction constant, the intensity and duration of the exciting pulse, and the detuning of its carrier frequency from the resonance. The free polarization signal decay, which depends on the magnitude and sign of the sum of the detuning of the exciting pulse carrier frequency from the resonance and the Lorentz frequency, may obey either a power or an exponential law. The signal decay rate is determined not only by the inhomogeneous broadening, but also by the ratio of the above parameters. The peculiarities of echo-responses under one- or two-pulse excitation conditions are studied.
Various characteristics of frequency-integrated intensities of secondary radiation components near the resonance excitation region have been calculated for a three-level system coupled with a reservoir using a stochastic model. It has been found that the spectral and temporal characteristics of the resonant second-order optical processes can be understood consistently by considering that Raman scattering results from the average value of the induced-dipole moment with respect to the energy fluctuation due to the system-reservoir interaction, while luminescence results from its deviation from the average value. A simple method to determine parameter values that characterize the excited-state dynamics in condensed phases from the secondary radiation data is also discussed.
The effect that may be exerted by an interatomic dipole-dipole interaction upon optical transient processes in dense resonance media, in particular, free polarization decay, is analyzed. The behavior of the macroscopic polarization after a single-pulse excitation of a dense ensemble of two-level atoms is considered. It is shown that the free polarization signal is of oscillatory nature, with the oscillation frequency varying in time and being dependent on the dipole-dipole interaction constant, the intensity and duration of the exciting pulse, and the detuning of its carrier frequency from the resonance. The free polarization signal decay, which depends on the magnitude and sign of the sum of the detuning of the exciting pulse carrier frequency from the resonance and the Lorentz frequency, may obey either a power or an exponential law. The signal decay rate is determined not only by the inhomogeneous broadening, but also by the ratio of the above parameters.
General behavior of the transient response of materials excited by a stepwise optical field has been studied by means of numerical analysis based on a model of the inhomogeneously broadened two-level atomic system with relaxation obeylng the quantum mechanical equation of motion. The time dependences of the polarization and the excited state probability of atoms are investigated in detail under a wide variety of conditions including both the resonant and far off-resonant excitations. The behaviors are found to be quite different depending on the relative magnitudes of the light frequency, the center frequency and the bandwidth of transition, the Rabi frequency, the longitudinal and transverse relaxation rates. Two kinds of response times are defined to describe the rapidity of the response, and the physical parameters goveming them are detennined for a variety of cases. Another kind of response time originated from the statistical behavior of atoms is further considered and discussed. Based on these results, the range of the values of the response times are estimated in general. The results for both cases with and without the rotating wave approximation are also calculated and compared.
A new method is developed for the description of transfer and scattering of a time-dependent laser pulse, which is based on a hierarchy of Bogoliubov-Born-Green-Kirkwood-Yvone (BBGKY) equations for reduced density matrices. The systems of equations are obtained for the atomic and photon density matrices and the correlation operator in the second-order Born approximation. The system of equations describes stimulated and spontaneous scattering of laser radiation in an optically thin medium, where reabsorption of spontaneous radiation can be neglected. The method proposed in the paper yields for the first time the correct expressions for nonstationary resonance fluorescence spectra, which do not give the negative values for fluorescence intensity. The expressions obtained for the resonance emission spectra coincide in limiting cases with those obtained within the framework of the quantum regression theorem.