The thermally averaged collision-broadened line shape is written in terms of a detuning-dependent broadening rate ${\ensuremath{\gamma}}_{c}(\ensuremath{\Delta})$ which is evaluated numerically for van der Waals potentials using classical straight trajectories. The results are presented in terms of reduced variables that make it easy to calculate the line shape for any system with arbitrary van der Waals coefficient and temperature. The results show how the line shape makes a smooth transition from a Lorentzian profile in the impact region to the dramatically asymmetric far line wings. The transition zone is characterized by $|\ensuremath{\Delta}|{T}_{d}\ensuremath{\sim}1$, where $\ensuremath{\Delta}$ is the frequency detuning from resonance and ${T}_{d}$ is a characteristic collision duration. The lowest-order correction to the Lorentzian line shape due to finite collision duration describes the dominant behavior for $|\ensuremath{\Delta}|{T}_{d}\ensuremath{\sim}1$. The numerical results are compared with analytic approximations and recent experiments. Averaging over a thermal distribution of relative velocities is shown to alter the line-shape asymmetry substantially, improving agreement between theory and experiment. The temperature dependence of the overall line shape is presented and discussed.The thermally averaged collision-broadened line shape is written in terms of a detuning-dependent broadening rate ${\ensuremath{\gamma}}_{c}(\ensuremath{\Delta})$ which is evaluated numerically for van der Waals potentials using classical straight trajectories. The results are presented in terms of reduced variables that make it easy to calculate the line shape for any system with arbitrary van der Waals coefficient and temperature. The results show how the line shape makes a smooth transition from a Lorentzian profile in the impact region to the dramatically asymmetric far line wings. The transition zone is characterized by $|\ensuremath{\Delta}|{T}_{d}\ensuremath{\sim}1$, where $\ensuremath{\Delta}$ is the frequency detuning from resonance and ${T}_{d}$ is a characteristic collision duration. The lowest-order correction to the Lorentzian line shape due to finite collision duration describes the dominant behavior for $|\ensuremath{\Delta}|{T}_{d}\ensuremath{\sim}1$. The numerical results are compared with analytic approximations and recent experiments. Averaging over a thermal distribution of relative velocities is shown to alter the line-shape asymmetry substantially, improving agreement between theory and experiment. The temperature dependence of the overall line shape is presented and discussed.

Physical Review AJan 1, 198446 citations

Line-shape analysis of resonant energy transfer collisions

James Veale, W. Anderson, M. Gatzke +2 more

We have investigated the resonant collision process 26s+24d\ensuremath{\rightarrow}26p+25p in K, which occurs when the 26s and 24d states are tuned by a static electric field so that the intervals 26s-26p and 24d-25p are equal. Resonant collision line shapes are observed and analyzed for three collision velocity distributions: a thermal beam, a small band of velocities in a laser-cooled beam, and two well-separated velocity groups in a laser-cooled beam. Collisions between atoms with a broad distribution of relative velocities produce cusp line shapes. In contrast, collisions occurring between atoms in two well-defined velocity groups produce approximately Lorentzian line shapes. \textcopyright{} 1996 The American Physical Society.We have investigated the resonant collision process 26s+24d\ensuremath{\rightarrow}26p+25p in K, which occurs when the 26s and 24d states are tuned by a static electric field so that the intervals 26s-26p and 24d-25p are equal. Resonant collision line shapes are observed and analyzed for three collision velocity distributions: a thermal beam, a small band of velocities in a laser-cooled beam, and two well-separated velocity groups in a laser-cooled beam. Collisions between atoms with a broad distribution of relative velocities produce cusp line shapes. In contrast, collisions occurring between atoms in two well-defined velocity groups produce approximately Lorentzian line shapes. \textcopyright{} 1996 The American Physical Society.

Physical Review AAug 1, 19966 citations

Transitions in Atom-Atom Collisions Produced by a Dipole-Dipole Interaction

G. Peach

peacJan 1, 19750 citations

ac Stark splitting in intense stochastic driving fields with Gaussian statistics and non-Lorentzian line shape

P. Zoller, G. Alber, R. Salvador

Lorentzian models for laser line shapes lead to qualitatively incorrect results for off-resonance excitation of atoms. This paper is the first attempt to present a theory of the nonperturbative interaction of an atom with a chaotic field (representing multimode laser radiation having strong amplitude fluctuations) with a line shape falling off faster than a Lorentzian. To this end we suggest a stochastic Markovian model for a non-Lorentzian chaotic field. To solve the multiplicative stochastic differential equations describing the atom-field interaction we propose a "marginal characteristic function approach." This not only reproduces our earlier results in a more elegant way and establishes the relationship between approaches used by other authors in a different context, but also provides the simplest possible basis for our present discussion of ac Stark splitting in double optical resonance. While for a chaotic field with a Lorentzian line shape the asymmetry of the two-peaked off-resonance spectrum is reversed for all values of the detuning compared with the monochromatic case, our present model predicts a reversed peak asymmetry only for detunings smaller than a few laser bandwidths in agreement with experiment. The on-resonance spectrum is dominated by the amplitude fluctuations and is only weakly affected by changes of the spectral line shape of the laser.Lorentzian models for laser line shapes lead to qualitatively incorrect results for off-resonance excitation of atoms. This paper is the first attempt to present a theory of the nonperturbative interaction of an atom with a chaotic field (representing multimode laser radiation having strong amplitude fluctuations) with a line shape falling off faster than a Lorentzian. To this end we suggest a stochastic Markovian model for a non-Lorentzian chaotic field. To solve the multiplicative stochastic differential equations describing the atom-field interaction we propose a "marginal characteristic function approach." This not only reproduces our earlier results in a more elegant way and establishes the relationship between approaches used by other authors in a different context, but also provides the simplest possible basis for our present discussion of ac Stark splitting in double optical resonance. While for a chaotic field with a Lorentzian line shape the asymmetry of the two-peaked off-resonance spectrum is reversed for all values of the detuning compared with the monochromatic case, our present model predicts a reversed peak asymmetry only for detunings smaller than a few laser bandwidths in agreement with experiment. The on-resonance spectrum is dominated by the amplitude fluctuations and is only weakly affected by changes of the spectral line shape of the laser.

Physical Review AJul 1, 198185 citations

{T}_{d}

is a characteristic collision duration. The lowest-order correction to the Lorentzian line shape due to finite collision duration describes the dominant behavior for $|\ensuremath{\Delta}|{T}_{d}\ensuremath{\sim}1$. The numerical results are compared with analytic approximations and recent experiments. Averaging over a thermal distribution of relative velocities is shown to alter the line-shape asymmetry substantially, improving agreement between theory and experiment. The temperature dependence of the overall line shape is presented and discussed.