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

Unknow

Velocity-changing collisional effects in nonlinear atomic spectroscopy and photon echo decay in gases

R. M. Herman

Published Jan 1, 1983• 0 citations
OpenAlex

Abstract

A general theory of atomic dipole coherence under the influence of collisional phase changes, inelastic effects and optically active atom velocity changes, including those due to anisotropic interactions is presented. Velocity change effects are obtained in closed form. Line shapes appear as convolutions of standard pressure broadening contours with velocity-change contours. Width and shift parameters for the He-broadened Na D lines at 2 m bar pressure, 380 K are calculated, as are He-induced photon echo decay rates for these lines. Overall agreement with xperiment is reasonably good.

Related papers

Comprehensive theory for line broadening in high-resolution and nonlinear spectroscopies: application to the Na D lines

R. M. Herman, E. W. Weber

A general method for analysing line broadening caused by Doppler, phaseshift, inelastic and velocity-changing collisional effects is proposed for transitions at optical wavelengths. In a unified approach Poisson statistics are used to describe collision probabilities randomly distributed in a time interval which can terminate the optical coherence in a combination of the above effects; markoffian independence is assumed for each collision. Then the dipole moment correlation function is obtained in a form which is virtually exact in accounting for all effects of isotropic forces, and which is correct to second-order terms in the anisotropic interaction potentials. Phenomena as diverse as standard optical pressure broadening, broadening due to velocity-changing collisions in nonlinear spectroscopies, and Dicke narrowing of the Doppler contour are described. The implications of the theory are discussed in detail and applied to the case of the NaD lines perturbed by He buffer gas. Numerical calculations reveal that the substantially different lineshift and broadening parameters in nonlinear and in standard optical spectroscopies can be reasonably well understood within the limitations posed by present uncertainties in the Na 3 2 P-He interaction potentials. However, the large differences in shift and width between the D 2 and D 1 lines in saturation spectroscopy cannot be explained within the present theory.

Journal of Physics B Atomic and Molecular Physics•Apr 28, 1983•8 citations

Collisional transfer of electronic state coherence

P. R. Berman

The role of collision-induced transfer of electronic state coherence on the spectral response of an atomic vapor is investigated. It is shown that such collisional effects can lead to the appearance of narrow resonances in the nonlinear spectroscopy of three-level systems. Collisional transfer between different multipoles of electronic state coherence is shown to lead to a breakdown of several percent in Becquerel's relation between the Faraday rotation and dispersion of a vapor. All calculations are carried out in the impact limit of pressure broadening theory. Particular emphasis is given to the order in which the various averages over the velocity distributions of both the active atoms and perturbers must be performed. In particular, for the effects described herein, the various collisional transfer rates vanish when averaged over the active atom velocity distribution. It is essential, therefore, to obtain the final line-shape formulas, including velocity-dependent collisional transfer rates, before carrying out the average over the active atom velocity distribution. The experimental observation of these spectral features would provide direct evidence for the existence of these collisional transfer processes.

Physical Review A•Jan 1, 1995•7 citations

Theory of optical coherent transients including collisional effects: Application to an extended-pulse photon echo

Ruwang Sung, P. R. Berman

The interaction between an intense radiation field and atoms that undergo collisions in an atomic vapor is studied. With the assumption that velocity-changing collisions are state independent and weak, we obtain an analytic expression for the time-dependent density-matrix elements by solving a quantum-mechanical transport equation using a dressed-state approach. Our analytical calculation is used to predict the form of the signal in an extended-pulse photon echo. The results show good agreement with an experiment carried out by Yodh et al. [Phys. Rev. Lett. 53, 659 (1984)]. It is found that the decay rate of the echo signal decreases rapidly with increasing duration of the second pulse in the pulse excitation sequence. A comparison between theory and experiment is presented and a physical interpretation of the results is given.

Physical Review A•Jun 1, 1989•2 citations

Theory of collision effects in Doppler-free spectroscopy

P. R. Berman

A theory of the influence of binary collisions on the line shapes associated with Doppler-free spectroscopy is presented. The specific calculation is for two-photon absorption through a real or virtual intermediate state, but the extension of the results to alternative level schemes is included. Collisions are treated quite generally at first, but, ultimately, a simple but reasonable collision model is adopted to properly account for both the "phase-interrupting" and "velocity-changing" aspects of collisions. It is shown that collisional processes can be used to distinguish between the "two-quantum" and "stepwise" contributions to the two-photon excitation rate. Moreover, it is demonstrated that systematic experimental line-shape investigations, in addition to providing tests of current collision theories, can lead to values for collision broadening and shift parameters, excitation transfer rates, magnetic substate relaxation rates, velocity-changing collision rates, and collision kernels. Consequently, Doppler-free spectroscopy can provide a new and important probe of collision effects in atomic and molecular systems.

Physical Review A•Jun 1, 1976•49 citations

Observation of Collisional Velocity Changes Associated with Atoms in a Superposition of Dissimilar Electronic States

THOMAS W. MOSSBERG, Ravinder Kachru, Sven R. Hartmann

Photon-echo measurements in atomic Na perturbed by He provide the first demonstration of the contribution of velocity-changing-like effects to the transverse relaxation of atoms in superposition of two states even when the states follow different post-collision trajectories. The apparent anomaly that broadening cross sections derived from either absorption line widths or photon-echo relaxation measurements are smaller than the total cross section for scattering of atoms in either pure state is explained.

Physical Review Letters•Jan 14, 1980•35 citations

Theory of velocity-dependent, collision-broadened, Doppler-free line shapes

M. J. O’Callaghan, J. Cooper

Line-shape expressions for two-step resonant excitation in the presence of low-pressure perturbers are derived. These expressions allow for velocity-dependent broadening rates and are well suited for studying the line-shape contributions due to coherent excitation, incoherent excitation (due to dephasing collisions), interference between coherent and incoherent excitation, and velocity-changing collisions. Using the sodium 3S-3P-4D system perturbed by noble-gas atoms as an example and assuming ${C}_{6}$ interaction potentials, line shapes at a variety of laser detunings (Doppler selected atomic velocities) are numerically calculated to study variation in the line shape due to competing excitation paths and speed-dependent collision rates. In order to deal with both the line core and the line wing a composite collision kernel consisting of a Lorentzian kernel for small \ensuremath{\Delta}${v}_{z}$ collisions and a Keilson-Storer kernel for large \ensuremath{\Delta}${v}_{z}$ collisions is used. It is also demonstrated how the inelastic (3${P}_{3/2}$-3${P}_{1/2}$) velocity-changing collision kernel may be obtained from experimental data at low pressures. Theoretical line shapes and broadening rates are compared with experiment.

Physical Review A•Jun 1, 1989•23 citations
A general theory of atomic dipole coherence under the influence of collisional phase changes, inelastic effects and optically active atom velocity changes, including those due to anisotropic interactions is presented. Velocity change effects are obtained in closed form. Line shapes appear as convolutions of standard pressure broadening contours with velocity-change contours. Width and shift parameters for the He-broadened Na D lines at 2 m bar pressure, 380 K are calculated, as are He-induced photon echo decay rates for these lines. Overall agreement with xperiment is reasonably good.
A general method for analysing line broadening caused by Doppler, phaseshift, inelastic and velocity-changing collisional effects is proposed for transitions at optical wavelengths. In a unified approach Poisson statistics are used to describe collision probabilities randomly distributed in a time interval which can terminate the optical coherence in a combination of the above effects; markoffian independence is assumed for each collision. Then the dipole moment correlation function is obtained in a form which is virtually exact in accounting for all effects of isotropic forces, and which is correct to second-order terms in the anisotropic interaction potentials. Phenomena as diverse as standard optical pressure broadening, broadening due to velocity-changing collisions in nonlinear spectroscopies, and Dicke narrowing of the Doppler contour are described. The implications of the theory are discussed in detail and applied to the case of the NaD lines perturbed by He buffer gas. Numerical calculations reveal that the substantially different lineshift and broadening parameters in nonlinear and in standard optical spectroscopies can be reasonably well understood within the limitations posed by present uncertainties in the Na 3 2 P-He interaction potentials. However, the large differences in shift and width between the D 2 and D 1 lines in saturation spectroscopy cannot be explained within the present theory.
The role of collision-induced transfer of electronic state coherence on the spectral response of an atomic vapor is investigated. It is shown that such collisional effects can lead to the appearance of narrow resonances in the nonlinear spectroscopy of three-level systems. Collisional transfer between different multipoles of electronic state coherence is shown to lead to a breakdown of several percent in Becquerel's relation between the Faraday rotation and dispersion of a vapor. All calculations are carried out in the impact limit of pressure broadening theory. Particular emphasis is given to the order in which the various averages over the velocity distributions of both the active atoms and perturbers must be performed. In particular, for the effects described herein, the various collisional transfer rates vanish when averaged over the active atom velocity distribution. It is essential, therefore, to obtain the final line-shape formulas, including velocity-dependent collisional transfer rates, before carrying out the average over the active atom velocity distribution. The experimental observation of these spectral features would provide direct evidence for the existence of these collisional transfer processes.
The interaction between an intense radiation field and atoms that undergo collisions in an atomic vapor is studied. With the assumption that velocity-changing collisions are state independent and weak, we obtain an analytic expression for the time-dependent density-matrix elements by solving a quantum-mechanical transport equation using a dressed-state approach. Our analytical calculation is used to predict the form of the signal in an extended-pulse photon echo. The results show good agreement with an experiment carried out by Yodh et al. [Phys. Rev. Lett. 53, 659 (1984)]. It is found that the decay rate of the echo signal decreases rapidly with increasing duration of the second pulse in the pulse excitation sequence. A comparison between theory and experiment is presented and a physical interpretation of the results is given.
A theory of the influence of binary collisions on the line shapes associated with Doppler-free spectroscopy is presented. The specific calculation is for two-photon absorption through a real or virtual intermediate state, but the extension of the results to alternative level schemes is included. Collisions are treated quite generally at first, but, ultimately, a simple but reasonable collision model is adopted to properly account for both the "phase-interrupting" and "velocity-changing" aspects of collisions. It is shown that collisional processes can be used to distinguish between the "two-quantum" and "stepwise" contributions to the two-photon excitation rate. Moreover, it is demonstrated that systematic experimental line-shape investigations, in addition to providing tests of current collision theories, can lead to values for collision broadening and shift parameters, excitation transfer rates, magnetic substate relaxation rates, velocity-changing collision rates, and collision kernels. Consequently, Doppler-free spectroscopy can provide a new and important probe of collision effects in atomic and molecular systems.
Photon-echo measurements in atomic Na perturbed by He provide the first demonstration of the contribution of velocity-changing-like effects to the transverse relaxation of atoms in superposition of two states even when the states follow different post-collision trajectories. The apparent anomaly that broadening cross sections derived from either absorption line widths or photon-echo relaxation measurements are smaller than the total cross section for scattering of atoms in either pure state is explained.
Line-shape expressions for two-step resonant excitation in the presence of low-pressure perturbers are derived. These expressions allow for velocity-dependent broadening rates and are well suited for studying the line-shape contributions due to coherent excitation, incoherent excitation (due to dephasing collisions), interference between coherent and incoherent excitation, and velocity-changing collisions. Using the sodium 3S-3P-4D system perturbed by noble-gas atoms as an example and assuming C6{C}_{6}C6​ interaction potentials, line shapes at a variety of laser detunings (Doppler selected atomic velocities) are numerically calculated to study variation in the line shape due to competing excitation paths and speed-dependent collision rates. In order to deal with both the line core and the line wing a composite collision kernel consisting of a Lorentzian kernel for small \ensuremath{\Delta}vz{v}_{z}vz​ collisions and a Keilson-Storer kernel for large \ensuremath{\Delta}vz{v}_{z}vz​ collisions is used. It is also demonstrated how the inelastic (3P3/2{P}_{3/2}P3/2​-3P1/2{P}_{1/2}P1/2​) velocity-changing collision kernel may be obtained from experimental data at low pressures. Theoretical line shapes and broadening rates are compared with experiment.