Experimental line profiles and integrated intensities for backscattered and forward-scattered resonance radiation using white-light excitation are compared with theory for Na densities between ${10}^{19}$ and ${10}^{22}$ atoms/ ${\mathrm{m}}^{3}$ . Absorption measurements are used to verify linewidth and line-wing asymmetry parameters and Na-vapor densities. The scattered spectral intensities are normalized to the incident flux using calibrated diffusers. Measurements of scattered intensities were also made as ${\mathrm{N}}_{2}$ was added to the Na. The line profiles and integrated intensities were calculated using a model which assumes complete redistribution of the radiation scattered by an atom and takes into account both radiative and nonradiative transport of the resonance excitation. The theory includes the effects of quenching by ${\mathrm{Na}}_{2}$ and by admixed ${\mathrm{N}}_{2}$ . With the white-light excitation used in these experiments the radiative transport is found to dominate the nonradiative transport except at wavelengths very near line center. The agreement between experimental and theoretical line profiles is good at high sodium densities (\ensuremath{\sim} 5 \ifmmode\times\else\texttimes\fi{} ${10}^{21}$ atoms/ ${\mathrm{m}}^{3}$ ) where instrumental resolution is not a serious limitation. The agreement between experimental and theoretical integrated intensities is within experimental error for Na densities of (1-10) \ifmmode\times\else\texttimes\fi{} ${10}^{19}$ and (2-5) \ifmmode\times\else\texttimes\fi{} ${10}^{21}$ atoms/ ${\mathrm{m}}^{3}$ . At the intermediate densities the approximately 20% discrepancy may be caused by the incomplete redistribution of radiation in the scattering process.Experimental line profiles and integrated intensities for backscattered and forward-scattered resonance radiation using white-light excitation are compared with theory for Na densities between ${10}^{19}$ and ${10}^{22}$ atoms/${\mathrm{m}}^{3}$. Absorption measurements are used to verify linewidth and line-wing asymmetry parameters and Na-vapor densities. The scattered spectral intensities are normalized to the incident flux using calibrated diffusers. Measurements of scattered intensities were also made as ${\mathrm{N}}_{2}$ was added to the Na. The line profiles and integrated intensities were calculated using a model which assumes complete redistribution of the radiation scattered by an atom and takes into account both radiative and nonradiative transport of the resonance excitation. The theory includes the effects of quenching by ${\mathrm{Na}}_{2}$ and by admixed ${\mathrm{N}}_{2}$. With the white-light excitation used in these experiments the radiative transport is found to dominate the nonradiative transport except at wavelengths very near line center. The agreement between experimental and theoretical line profiles is good at high sodium densities (\ensuremath{\sim} 5 \ifmmode\times\else\texttimes\fi{} ${10}^{21}$ atoms/${\mathrm{m}}^{3}$) where instrumental resolution is not a serious limitation. The agreement between experimental and theoretical integrated intensities is within experimental error for Na densities of (1-10) \ifmmode\times\else\texttimes\fi{} ${10}^{19}$ and (2-5) \ifmmode\times\else\texttimes\fi{} ${10}^{21}$ atoms/${\mathrm{m}}^{3}$. At the intermediate densities the approximately 20% discrepancy may be caused by the incomplete redistribution of radiation in the scattering process.

Physical Review AJan 1, 19826 citations

High Excitation Effects and Nonlinear Optics

Springer eBooksJan 1, 20060 citations

Breakdown of the impact approximation as seen in collision broadening at high densities of the (6p7s)P103 state of lead

Joshua B. Halpern, Ahmed Baghdadi, E. B. Saloman

The Hanle effect has been used to measure the resonant pressure broadening of the $(6p7s)^{3}P_{1}^{0}$ excited state of lead over a density range from ${10}^{14}$ to 4 \ifmmode\times\else\texttimes\fi{} ${10}^{16}$ atom/ ${\mathrm{cm}}^{3}$ . Below ${10}^{16}$ atom/ ${\mathrm{cm}}^{3}$ the results agree with theories based on the impact approximation and the experimental results of Happer and Saloman. For densities above ${10}^{16}$ atom/ ${\mathrm{cm}}^{3}$ it is shown that the broadening should have the form $\overline{v}{\ensuremath{\sigma}}_{0}^{(L)}[N\ensuremath{-}\ensuremath{\beta}{N}^{2}]$, where $\overline{v}$ is the mean relative velocity of the atoms, ${\ensuremath{\sigma}}_{0}^{(L)}$ is the resonant-collision-broadening cross section for the L th multipole element of the excited-state density matrix, $N$ is the atomic density, and $\ensuremath{\beta}$ is a measure of the correlation of the atoms which represents the breakdown of the impact approximation. $\ensuremath{\beta}$ has been determined to be equal to 3.8(6) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}18}$ ${\mathrm{cm}}^{3}$ .The Hanle effect has been used to measure the resonant pressure broadening of the $(6p7s)^{3}P_{1}^{0}$ excited state of lead over a density range from ${10}^{14}$ to 4 \ifmmode\times\else\texttimes\fi{} ${10}^{16}$ atom/${\mathrm{cm}}^{3}$. Below ${10}^{16}$ atom/${\mathrm{cm}}^{3}$ the results agree with theories based on the impact approximation and the experimental results of Happer and Saloman. For densities above ${10}^{16}$ atom/${\mathrm{cm}}^{3}$ it is shown that the broadening should have the form $\overline{v}{\ensuremath{\sigma}}_{0}^{(L)}[N\ensuremath{-}\ensuremath{\beta}{N}^{2}]$, where $\overline{v}$ is the mean relative velocity of the atoms, ${\ensuremath{\sigma}}_{0}^{(L)}$ is the resonant-collision-broadening cross section for the L th multipole element of the excited-state density matrix, $N$ is the atomic density, and $\ensuremath{\beta}$ is a measure of the correlation of the atoms which represents the breakdown of the impact approximation. $\ensuremath{\beta}$ has been determined to be equal to 3.8(6) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}18}$ ${\mathrm{cm}}^{3}$.

Physical Review AFeb 1, 19741 citation

THEORY OF DENSE NONEQUILIBRIUM EXCITON SYSTEMS

Wilfried Schäfer

Elsevier eBooksJan 1, 19887 citations

Simulation of a strong van der Waals blockade in a dense ultracold gas

J V Hernández, F. Robicheaux

We report on simulations involving the blockade effect on a dense ultracold gas. The blockade effect is seen when the interaction energy between two excited Rydberg atoms is large enough to shift the two-excitation state out of resonance. In this paper we investigate a system that exhibits a strong van der Waals blockade, where only one out of thousands of atoms can be excited per blockade volume. With such a high number of atoms blockaded, the collective oscillation rate of an ensemble of atoms is much faster than the single atom oscillation rate. We examine the effects of this high density and the effects of a non-uniform density distribution as commonly seen in a magneto-optical trap (MOT). We use three different models and compare them to recent experimental data. The agreement between theory and experiment, although qualitative, suggests that the non-uniformity of the density within a blockade region presents a new challenge to theoretical models.We report on simulations involving the blockade effect on a dense ultracold gas. The blockade effect is seen when the interaction energy between two excited Rydberg atoms is large enough to shift the two-excitation state out of resonance. In this paper we investigate a system that exhibits a strong van der Waals blockade, where only one out of thousands of atoms can be excited per blockade volume. With such a high number of atoms blockaded, the collective oscillation rate of an ensemble of atoms is much faster than the single atom oscillation rate. We examine the effects of this high density and the effects of a non-uniform density distribution as commonly seen in a magneto-optical trap (MOT). We use three different models and compare them to recent experimental data. The agreement between theory and experiment, although qualitative, suggests that the non-uniformity of the density within a blockade region presents a new challenge to theoretical models.

Journal of Physics B Atomic Molecular and Optical PhysicsFeb 11, 200819 citations

Experimental line profiles and integrated intensities for backscattered and forward-scattered resonance radiation using white-light excitation are compared with theory for Na densities between

{10}^{19}

and

{10}^{22}

atoms/

{\mathrm{m}}^{3}

. Absorption measurements are used to verify linewidth and line-wing asymmetry parameters and Na-vapor densities. The scattered spectral intensities are normalized to the incident flux using calibrated diffusers. Measurements of scattered intensities were also made as

{\mathrm{N}}_{2}

was added to the Na. The line profiles and integrated intensities were calculated using a model which assumes complete redistribution of the radiation scattered by an atom and takes into account both radiative and nonradiative transport of the resonance excitation. The theory includes the effects of quenching by

{\mathrm{Na}}_{2}

and by admixed

{\mathrm{N}}_{2}

. With the white-light excitation used in these experiments the radiative transport is found to dominate the nonradiative transport except at wavelengths very near line center. The agreement between experimental and theoretical line profiles is good at high sodium densities (\ensuremath{\sim} 5 \ifmmode\times\else\texttimes\fi{}

{10}^{21}

atoms/

{\mathrm{m}}^{3}

) where instrumental resolution is not a serious limitation. The agreement between experimental and theoretical integrated intensities is within experimental error for Na densities of (1-10) \ifmmode\times\else\texttimes\fi{}

{10}^{19}

and (2-5) \ifmmode\times\else\texttimes\fi{}

{10}^{21}

atoms/

{\mathrm{m}}^{3}

. At the intermediate densities the approximately 20% discrepancy may be caused by the incomplete redistribution of radiation in the scattering process.

The Hanle effect has been used to measure the resonant pressure broadening of the

(6p7s)^{3}P_{1}^{0}

excited state of lead over a density range from

{10}^{14}

to 4 \ifmmode\times\else\texttimes\fi{}

{10}^{16}

atom/

{\mathrm{cm}}^{3}

. Below

{10}^{16}

atom/

{\mathrm{cm}}^{3}

the results agree with theories based on the impact approximation and the experimental results of Happer and Saloman. For densities above

{10}^{16}

atom/

{\mathrm{cm}}^{3}

it is shown that the broadening should have the form $\overline{v}{\ensuremath{\sigma}}_{0}^{(L)}[N\ensuremath{-}\ensuremath{\beta}{N}^{2}]$, where

\overline{v}

is the mean relative velocity of the atoms, ${\ensuremath{\sigma}}_{0}^{(L)}$ is the resonant-collision-broadening cross section for the L th multipole element of the excited-state density matrix,

N

is the atomic density, and $\ensuremath{\beta}$ is a measure of the correlation of the atoms which represents the breakdown of the impact approximation. $\ensuremath{\beta}$ has been determined to be equal to 3.8(6) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}18}$

{\mathrm{cm}}^{3}