Annual Report

Interaction of Radiation with Matter: Atomic Collision Processes Occurring in the Presence of Radiation Fields

P. R. Berman

Published Sep 15, 1988• 0 citations

Abstract

Abstract : Work is summarized in areas of: Laser Assisted Collisions; Velocity Changing collisions in Atomic Vapors; Coherent Transients; Collision Induced Extra Resonances; Breakdown of the Optical Bloch Equations; Saturation Spectroscopy; Dynamics of Two-and Three-level Atoms Interacting with Radiation Fields; Pulse Propagation. Keywords: Laser spectroscopy, Optical collisions, Radiative collisions, Two-level atom, Atomic coherence, Degenerate four-wave mixing, Saturation spectroscopy, Laser propagation,, Dressed atom, Photon echo, Bloch equations, Collision kernal, Collisions, Optical noise.

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Theoretical Studies Relating to the Interaction of Radiation with Matter: Atomic Collision Processes Occurring in the Presence of Radiation Fields

P. R. Berman

Contents: Collisional studies using laser spectroscopy; The nature and validity of collision kernels; Strong field effects in laser spectroscopy; Optical collisions including a model potential calculation; Radiative collisions including model potential calculations; Laser assisted heating or cooling; and Collisional studies using photon echoes or Optical Ramsey Fringes.

Annual ReportSep 1, 19810 citations

Theoretical studies relating to the interaction of radiation with matter

P. R. Berman

During the past year, progress has been made in the areas of: (1) Coherent transients using counterpropagating fields; (2) New resonances in cold- atom spectroscopy; (3) Laser cooling in one dimension using linearly polarized fields; and, (4) Theory of four-wave mixing.... Laser spectroscopy, 4-wave mixing, Recoil-induced resonances, Laser cooling, Coherent transients, Grating echoes

Annual ReportJun 1, 19930 citations

Collision kernels and laser spectroscopy

P. R. Berman, THOMAS W. MOSSBERG, Sven R. Hartmann

Physical Review AMay 1, 198291 citations

Theory of electronic-state coherences produced in combined laser-field—collisional reactions

P. R. Berman, E. Giacobino

Physical Review ANov 1, 198313 citations

Principles of Laser Spectroscopy and Quantum Optics

P. R. Berman, Vladimir S. Malinovsky

Princeton University Press eBooksDec 31, 2011157 citations

Theory of High Intensity Multimode Gas Lasers - Inclusion of Collisional Effects.

P. R. Berman

May 31, 19770 citations

Annual Report

Interaction of Radiation with Matter: Atomic Collision Processes Occurring in the Presence of Radiation Fields

P. R. Berman

Published Sep 15, 1988• 0 citations

OpenAlex

Abstract

Related papers

Theoretical Studies Relating to the Interaction of Radiation with Matter: Atomic Collision Processes Occurring in the Presence of Radiation Fields

P. R. Berman

Annual ReportSep 1, 19810 citations

Theoretical studies relating to the interaction of radiation with matter

P. R. Berman

Annual ReportJun 1, 19930 citations

Collision kernels and laser spectroscopy

P. R. Berman, THOMAS W. MOSSBERG, Sven R. Hartmann

Collisional processes occurring within an atomic vapor can be conveniently described in terms of collision kernels. The population kernel ${W}_{\mathrm{ii}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}})$ gives the probability density per unit time that an "active" atom in state $i$ undergoes a collision with a perturber that changes the active atom's velocity from ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}$ to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$. For active atoms in a linear superposition of states $i$ and $j$ , there is an analogous coherence kernel ${W}_{\mathrm{ij}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}) (i\ensuremath{\ne}j)$ reflecting the effects of collisions on the off-diagonal density-matrix element ${\ensuremath{\rho}}_{\mathrm{ij}}$. In this work, we discuss the general properties of the collision kernels which characterize a two-level active atom which, owing to the action of a radiation field, is in a linear superposition of its two levels. Using arguments based on the uncertainty principle, we show that collisions can be divided roughly into the following two categories: (1) collisions having impact parameters less than some characteristic radius which may be described classically and (2) collisions having impact parameters larger than this characteristic radius which give rise to diffractive scattering and must be treated using a quantum-mechanical theory. For the population kernels, collisions of type (1) can lead to a large-angle scattering component, while those of type (2) lead to a small-angle (diffractive) scattering component. For the coherence kernel, however, assuming that the collisional interaction for states $i$ and $j$ differ appreciably, only collisions of type (2) contribute, and the coherence kernel contains a small-angle scattering component only. The absence of a large-angle scattering component in the coherence kernel is linked to a collision-induced spatial separation of the trajectories associated with states $i$ and $j$ . Interestingly enough, the width of the diffractive kernel, as measured in the laboratory frame, is found to be insensitive to the perturber to active-atom mass ratio. To illustrate these features, a specific calculation of the kernels is carried out using a hard-sphere model for the scattering. The relationship of the present description of collisions to that of traditional pressure-broadening theory in which trajectory separation effects are ignored is discussed. It is explained why traditional pressure-broadening theory correctly describes collision effects in linear spectroscopy, but fails to provide an adequate description of some saturation spectroscopy and photonecho experiments in which velocity-changing collisions associated with the coherence kernel play a significant role. An expression for the collisionally modified photon-echo amplitude is derived which clearly displays the role played by velocity-changing collisions associated with the coherence kernel.Collisional processes occurring within an atomic vapor can be conveniently described in terms of collision kernels. The population kernel ${W}_{\mathrm{ii}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}})$ gives the probability density per unit time that an "active" atom in state $i$ undergoes a collision with a perturber that changes the active atom's velocity from ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}$ to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$. For active atoms in a linear superposition of states $i$ and $j$, there is an analogous coherence kernel ${W}_{\mathrm{ij}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}) (i\ensuremath{\ne}j)$ reflecting the effects of collisions on the off-diagonal density-matrix element ${\ensuremath{\rho}}_{\mathrm{ij}}$. In this work, we discuss the general properties of the collision kernels which characterize a two-level active atom which, owing to the action of a radiation field, is in a linear superposition of its two levels. Using arguments based on the uncertainty principle, we show that collisions can be divided roughly into the following two categories: (1) collisions having impact parameters less than some characteristic radius which may be described classically and (2) collisions having impact parameters larger than this characteristic radius which give rise to diffractive scattering and must be treated using a quantum-mechanical theory. For the population kernels, collisions of type (1) can lead to a large-angle scattering component, while those of type (2) lead to a small-angle (diffractive) scattering component. For the coherence kernel, however, assuming that the collisional interaction for states $i$ and $j$ differ appreciably, only collisions of type (2) contribute, and the coherence kernel contains a small-angle scattering component only. The absence of a large-angle scattering component in the coherence kernel is linked to a collision-induced spatial separation of the trajectories associated with states $i$ and $j$. Interestingly enough, the width of the diffractive kernel, as measured in the laboratory frame, is found to be insensitive to the perturber to active-atom mass ratio. To illustrate these features, a specific calculation of the kernels is carried out using a hard-sphere model for the scattering. The relationship of the present description of collisions to that of traditional pressure-broadening theory in which trajectory separation effects are ignored is discussed. It is explained why traditional pressure-broadening theory correctly describes collision effects in linear spectroscopy, but fails to provide an adequate description of some saturation spectroscopy and photonecho experiments in which velocity-changing collisions associated with the coherence kernel play a significant role. An expression for the collisionally modified photon-echo amplitude is derived which clearly displays the role played by velocity-changing collisions associated with the coherence kernel.

Physical Review AMay 1, 198291 citations

Theory of electronic-state coherences produced in combined laser-field—collisional reactions

P. R. Berman, E. Giacobino

A method for producing electronic-state coherences using either collisionally-aided radiative excitation (or "optical collision") or laser-induced collisional energy transfer (or "radiative collision") is proposed. Two atoms, $A$ and ${A}^{\ensuremath{'}}$, collide in the presence of two pulsed-laser fields having frequencies $\ensuremath{\Omega}$ and ${\ensuremath{\Omega}}_{1}$. It is shown that by choosing ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ such that an energy-conserving transition can occur in the composite $A{A}^{\ensuremath{'}}$ system, one can create an electronic-state coherence in the $A$ or ${A}^{\ensuremath{'}}$ atoms. The coherence can be produced between states of the same or of opposite parity; if it is between states of opposite parity, coherent emission at frequency ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ may be generated. The relationship of this work to theories of "pressure-induced extra resonances" in four-wave mixing is discussed.A method for producing electronic-state coherences using either collisionally-aided radiative excitation (or "optical collision") or laser-induced collisional energy transfer (or "radiative collision") is proposed. Two atoms, $A$ and ${A}^{\ensuremath{'}}$, collide in the presence of two pulsed-laser fields having frequencies $\ensuremath{\Omega}$ and ${\ensuremath{\Omega}}_{1}$. It is shown that by choosing ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ such that an energy-conserving transition can occur in the composite $A{A}^{\ensuremath{'}}$ system, one can create an electronic-state coherence in the $A$ or ${A}^{\ensuremath{'}}$ atoms. The coherence can be produced between states of the same or of opposite parity; if it is between states of opposite parity, coherent emission at frequency ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ may be generated. The relationship of this work to theories of "pressure-induced extra resonances" in four-wave mixing is discussed.

Physical Review ANov 1, 198313 citations

Principles of Laser Spectroscopy and Quantum Optics

P. R. Berman, Vladimir S. Malinovsky

Principles of Laser Spectroscopy and Quantum Optics is an essential textbook for graduate students studying the interaction of optical fields with atoms. It also serves as an ideal reference text for researchers working in the fields of laser spectroscopy and quantum optics. The book provides a rigorous introduction to the prototypical problems of radiation fields interacting with two- and three-level atomic systems. It examines the interaction of radiation with both atomic vapors and condensed matter systems, the density matrix and the Bloch vector, and applications involving linear absorptioPrinciples of Laser Spectroscopy and Quantum Optics is an essential textbook for graduate students studying the interaction of optical fields with atoms. It also serves as an ideal reference text for researchers working in the fields of laser spectroscopy and quantum optics. The book provides a rigorous introduction to the prototypical problems of radiation fields interacting with two- and three-level atomic systems. It examines the interaction of radiation with both atomic vapors and condensed matter systems, the density matrix and the Bloch vector, and applications involving linear absorptio

Princeton University Press eBooksDec 31, 2011157 citations

Theory of High Intensity Multimode Gas Lasers - Inclusion of Collisional Effects.

P. R. Berman

Several topics in laser theory and the interaction of radiation with matter have been addressed. First, a mathematical theory of a high intensity single mode gas laser has been developed. New computational techniques have been applied which serve to unite several previous approaches to single mode laser theory. A generalized dressed atom approach was formulated to provide a new way of viewing the physical processes occurring when high intensity fields interact with matter. Second, a theoretical study of the manner in which laser sepctroscopy can be used to probe collision effects in atomic and molecular systems has been undertaken. Both two and three level systems were studied; steady state and coherent transient techniques were examined. It is now apparent that laser spectroscopy will be a useful tool for the determination of various excited state differential and total cross sections. (Author)Several topics in laser theory and the interaction of radiation with matter have been addressed. First, a mathematical theory of a high intensity single mode gas laser has been developed. New computational techniques have been applied which serve to unite several previous approaches to single mode laser theory. A generalized dressed atom approach was formulated to provide a new way of viewing the physical processes occurring when high intensity fields interact with matter. Second, a theoretical study of the manner in which laser sepctroscopy can be used to probe collision effects in atomic and molecular systems has been undertaken. Both two and three level systems were studied; steady state and coherent transient techniques were examined. It is now apparent that laser spectroscopy will be a useful tool for the determination of various excited state differential and total cross sections. (Author)

May 31, 19770 citations

i

undergoes a collision with a perturber that changes the active atom's velocity from ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}$ to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$. For active atoms in a linear superposition of states

i

and

j

, there is an analogous coherence kernel ${W}_{\mathrm{ij}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}) (i\ensuremath{\ne}j)$ reflecting the effects of collisions on the off-diagonal density-matrix element ${\ensuremath{\rho}}_{\mathrm{ij}}$. In this work, we discuss the general properties of the collision kernels which characterize a two-level active atom which, owing to the action of a radiation field, is in a linear superposition of its two levels. Using arguments based on the uncertainty principle, we show that collisions can be divided roughly into the following two categories: (1) collisions having impact parameters less than some characteristic radius which may be described classically and (2) collisions having impact parameters larger than this characteristic radius which give rise to diffractive scattering and must be treated using a quantum-mechanical theory. For the population kernels, collisions of type (1) can lead to a large-angle scattering component, while those of type (2) lead to a small-angle (diffractive) scattering component. For the coherence kernel, however, assuming that the collisional interaction for states

i

and

j

differ appreciably, only collisions of type (2) contribute, and the coherence kernel contains a small-angle scattering component only. The absence of a large-angle scattering component in the coherence kernel is linked to a collision-induced spatial separation of the trajectories associated with states

i

and

j

. Interestingly enough, the width of the diffractive kernel, as measured in the laboratory frame, is found to be insensitive to the perturber to active-atom mass ratio. To illustrate these features, a specific calculation of the kernels is carried out using a hard-sphere model for the scattering. The relationship of the present description of collisions to that of traditional pressure-broadening theory in which trajectory separation effects are ignored is discussed. It is explained why traditional pressure-broadening theory correctly describes collision effects in linear spectroscopy, but fails to provide an adequate description of some saturation spectroscopy and photonecho experiments in which velocity-changing collisions associated with the coherence kernel play a significant role. An expression for the collisionally modified photon-echo amplitude is derived which clearly displays the role played by velocity-changing collisions associated with the coherence kernel.

A

and ${A}^{\ensuremath{'}}$, collide in the presence of two pulsed-laser fields having frequencies $\ensuremath{\Omega}$ and ${\ensuremath{\Omega}}_{1}$. It is shown that by choosing ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ such that an energy-conserving transition can occur in the composite $A{A}^{\ensuremath{'}}$ system, one can create an electronic-state coherence in the

A

or ${A}^{\ensuremath{'}}$ atoms. The coherence can be produced between states of the same or of opposite parity; if it is between states of opposite parity, coherent emission at frequency ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ may be generated. The relationship of this work to theories of "pressure-induced extra resonances" in four-wave mixing is discussed.