The two-state model of laser-induced collisions introduced by Gudzenko and Yakovlenko is shown to lead to cross sections with a universal behavior in terms of the variables $z=|{C}_{3}|{E}_{0}{v}^{\ensuremath{-}\frac{3}{5}}{|{C}_{6}|}^{\ensuremath{-}\frac{2}{5}}$ and $d=\ensuremath{\delta}{|{C}_{6}|}^{\frac{1}{5}}{v}^{\ensuremath{-}\frac{6}{5}}\mathrm{sgn}({C}_{6})$. In terms of a physical description the dimensionless frequency-detuning variable is $d\ensuremath{\propto}$ (detuning of the laser from the large- $R$ resonance) (time of collision at the Weisskopf radius). The dimensionless variable $z$ is independent of laser frequency and measures the power dependence of the cross section. It is in fact proportional to $\ensuremath{\int}{\ensuremath{-}\ensuremath{\infty}}^{t}\frac{{C}_{3}{E}_{0}\mathrm{dt}}{R{(t)}^{3}}$ evaluated at an impact parameter given by the ${b}_{\ensuremath{\nu}}={(\frac{{C}_{6}}{v})}^{\frac{1}{5}}\ensuremath{\propto}$ Weisskopf radius = impact parameter where the phase shift due to the Van der Waals potential becomes $\ensuremath{\pi}$. Above, $\frac{{C}_{3}{E}_{0}}{{R}^{3}}$ is the coupling parameter at intranuclear separation $R$ and ${E}_{0}$ is the laser field amplitude. The cross section is of the form $\ensuremath{\sigma}={(\frac{|{C}_{6}|}{v})}^{\frac{2}{5}}H(d,z)$, where $H(d,z)$ is tabulated in detail. For large laser fields (i.e., $z>2$ ), the line shape for collisions at a particular relative velocity $v$ , laser field amplitude ${E}_{0}$ , and detuning (from the large- $R$ resonance frequency), $\ensuremath{\sigma}$ becomes symmetric about $\ensuremath{\delta}=0$ with the width decreasing with increasing laser power. The physical reason for the symmetric $H(d,z)$ at large $z$ is shown to be the decreased importance of curve-crossing effects for large positive $d$ corresponding to the onset of adiabatic behavior and the increased importance of contributions to $\ensuremath{\sigma}$ from such large impact parameters that the Van der Waals shifts can be neglected. Correspondingly, at large $z$ the linewidth is due entirely to time-of-collision effects. When $z\ensuremath{\ge}2$, both the long-range version of the atom-atom interaction and the assumption of straight-line orbits are excellent because of the dominant contribution to $\ensuremath{\delta}$ from impact parameters > 15 \AA{}.The two-state model of laser-induced collisions introduced by Gudzenko and Yakovlenko is shown to lead to cross sections with a universal behavior in terms of the variables $z=|{C}_{3}|{E}_{0}{v}^{\ensuremath{-}\frac{3}{5}}{|{C}_{6}|}^{\ensuremath{-}\frac{2}{5}}$ and $d=\ensuremath{\delta}{|{C}_{6}|}^{\frac{1}{5}}{v}^{\ensuremath{-}\frac{6}{5}}\mathrm{sgn}({C}_{6})$. In terms of a physical description the dimensionless frequency-detuning variable is $d\ensuremath{\propto}$ (detuning of the laser from the large-$R$ resonance) (time of collision at the Weisskopf radius). The dimensionless variable $z$ is independent of laser frequency and measures the power dependence of the cross section. It is in fact proportional to $\ensuremath{\int}{\ensuremath{-}\ensuremath{\infty}}^{t}\frac{{C}_{3}{E}_{0}\mathrm{dt}}{R{(t)}^{3}}$ evaluated at an impact parameter given by the ${b}_{\ensuremath{\nu}}={(\frac{{C}_{6}}{v})}^{\frac{1}{5}}\ensuremath{\propto}$ Weisskopf radius = impact parameter where the phase shift due to the Van der Waals potential becomes $\ensuremath{\pi}$. Above, $\frac{{C}_{3}{E}_{0}}{{R}^{3}}$ is the coupling parameter at intranuclear separation $R$ and ${E}_{0}$ is the laser field amplitude. The cross section is of the form $\ensuremath{\sigma}={(\frac{|{C}_{6}|}{v})}^{\frac{2}{5}}H(d,z)$, where $H(d,z)$ is tabulated in detail. For large laser fields (i.e., $z>2$), the line shape for collisions at a particular relative velocity $v$, laser field amplitude ${E}_{0}$, and detuning (from the large-$R$ resonance frequency), $\ensuremath{\sigma}$ becomes symmetric about $\ensuremath{\delta}=0$ with the width decreasing with increasing laser power. The physical reason for the symmetric $H(d,z)$ at large $z$ is shown to be the decreased importance of curve-crossing effects for large positive $d$ corresponding to the onset of adiabatic behavior and the increased importance of contributions to $\ensuremath{\sigma}$ from such large impact parameters that the Van der Waals shifts can be neglected. Correspondingly, at large $z$ the linewidth is due entirely to time-of-collision effects. When $z\ensuremath{\ge}2$, both the long-range version of the atom-atom interaction and the assumption of straight-line orbits are excellent because of the dominant contribution to $\ensuremath{\delta}$ from impact parameters > 15 \AA{}.

Physical Review ASep 1, 197941 citations

Excited states in stochastic electrodynamics

H. M. França, Trevor W. Marshall

We show that the set of Wigner functions associated with the excited states of the harmonic oscillator constitutes a complete set of functions over the phase space. An arbitrary probability distribution can be expanded in terms of these Wigner functions. By studying the time evolution, according to stochastic electrodynamics, of the expansion coefficients, we are able to separate explicitly the contributions of the radiative reaction and the vacuum field to the Einstein A coefficients for this system. We also supply a simple semiclassical explanation of the Weisskopf-Heitler phenomenon in resonance fluorescence.We show that the set of Wigner functions associated with the excited states of the harmonic oscillator constitutes a complete set of functions over the phase space. An arbitrary probability distribution can be expanded in terms of these Wigner functions. By studying the time evolution, according to stochastic electrodynamics, of the expansion coefficients, we are able to separate explicitly the contributions of the radiative reaction and the vacuum field to the Einstein A coefficients for this system. We also supply a simple semiclassical explanation of the Weisskopf-Heitler phenomenon in resonance fluorescence.

Physical Review AOct 1, 198825 citations

Laser linewidth effects in intense fields. Quantum theory (A)

K. Wódkiewicz

Journal of the Optical Society of America AJan 1, 19800 citations

Theory of a homogeneously broadened laser with arbitrary mirror outcoupling: Intrinsic linewidth and phase diffusion

Sudhakar Prasad

We present a theory of the homogeneously broadened laser that is based on the simple boundary conditions that govern the connection of intracavity traveling fields and the leaking vacuum field at the cavity mirrors. The approach is uniformly valid for arbitrary output-mirror transmissions. We compute the intrinsic linewidth of the laser both below and above threshold and for arbitrary mirror outcoupling. In the limit of complete output-mirror transmission, for which any semblance of the cavity to a lasing cavity is completely untenable and the laser is severely below threshold, we show that the laser linewidth reduces to the natural linewidth of spontaneous emission by atoms in free space. Above threshold, in contrast with most previously obtained results, the fundamental linewidth exhibits a power-independent contribution that arises from gain saturation that is spatially nonuniform.We present a theory of the homogeneously broadened laser that is based on the simple boundary conditions that govern the connection of intracavity traveling fields and the leaking vacuum field at the cavity mirrors. The approach is uniformly valid for arbitrary output-mirror transmissions. We compute the intrinsic linewidth of the laser both below and above threshold and for arbitrary mirror outcoupling. In the limit of complete output-mirror transmission, for which any semblance of the cavity to a lasing cavity is completely untenable and the laser is severely below threshold, we show that the laser linewidth reduces to the natural linewidth of spontaneous emission by atoms in free space. Above threshold, in contrast with most previously obtained results, the fundamental linewidth exhibits a power-independent contribution that arises from gain saturation that is spatially nonuniform.

Physical Review AAug 1, 199224 citations

Natural linewidth of a two-level two-photon laser

Imrana Ashraf, Muhammad Suhail Zubairy

Optics CommunicationsMay 1, 19896 citations

R

resonance) (time of collision at the Weisskopf radius). The dimensionless variable

z

is independent of laser frequency and measures the power dependence of the cross section. It is in fact proportional to $\ensuremath{\int}{\ensuremath{-}\ensuremath{\infty}}^{t}\frac{{C}_{3}{E}_{0}\mathrm{dt}}{R{(t)}^{3}}$ evaluated at an impact parameter given by the ${b}_{\ensuremath{\nu}}={(\frac{{C}_{6}}{v})}^{\frac{1}{5}}\ensuremath{\propto}$ Weisskopf radius = impact parameter where the phase shift due to the Van der Waals potential becomes $\ensuremath{\pi}$. Above,

\frac{{C}_{3}{E}_{0}}{{R}^{3}}

is the coupling parameter at intranuclear separation

R

and

{E}_{0}

is the laser field amplitude. The cross section is of the form $\ensuremath{\sigma}={(\frac{|{C}_{6}|}{v})}^{\frac{2}{5}}H(d,z)$, where

H(d,z)

is tabulated in detail. For large laser fields (i.e.,

z>2

), the line shape for collisions at a particular relative velocity

v

, laser field amplitude

{E}_{0}

, and detuning (from the large-

R

resonance frequency), $\ensuremath{\sigma}$ becomes symmetric about $\ensuremath{\delta}=0$ with the width decreasing with increasing laser power. The physical reason for the symmetric

H(d,z)

at large

z

is shown to be the decreased importance of curve-crossing effects for large positive

d

corresponding to the onset of adiabatic behavior and the increased importance of contributions to $\ensuremath{\sigma}$ from such large impact parameters that the Van der Waals shifts can be neglected. Correspondingly, at large

z

the linewidth is due entirely to time-of-collision effects. When $z\ensuremath{\ge}2$, both the long-range version of the atom-atom interaction and the assumption of straight-line orbits are excellent because of the dominant contribution to $\ensuremath{\delta}$ from impact parameters > 15 \AA{}.