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Physical Review Letters

Elastic Collision Kernels: Theoretical Determination and Direct Observation by Use of Time-Resolved Saturation Spectroscopy in Metastable Neon

Michel Gorlicki, C. Lerminiaux, M. Dumont

Published Nov 8, 1982• 23 citations
Publisher

Abstract

Collision kernels describing elastic collision effects in saturation spectroscopy are completely calculated for the metastable $^{3}P_{0}$ state of neon, starting from true experiment-deduced potentials. Collision processes with and without metastability exchange are respectively considered. A direct observation of these two kernels is provided by a two-laser time-resolved saturated absorption experiment. They are in good agreement with theory.

DOI
10.1103/physrevlett.49.1394

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Cold collisions of metastable neon atoms

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In this thesis we investigate theoretically the cold collision properties of metastable neon (Ne*). The collisions of metastable rare gases (Rg*) exhibit a plethora of interesting phenomena: Due to the high internal excitation energies of the metastable atoms ionization processes are very likely. The produced ions can be detected with single-ion efficiency in the experiment. In experiments with atomic Rg* gases at cold temperatures T~1 mK, this allows for in-situ monitoring of the real-time dynamics of the atomic gas and for example for the study of two-particle correlations. Furthermore, in cold Rg* gases one can examine the prospects of creating a Bose-Einstein condensate or a degenerate Fermi gas of Rg*. Ne* is a promising candidate for Bose-Einstein condensation and in the group of G. Birkl the properties of cold gases of Ne* are investigated experimentally. Two-body loss rate coefficients due to the ionization processes and elastic cross sections have been measured. It is useful to complement the experimental measurements with a theoretical study in order to obtain a better understanding of the cold Ne* gases and the collision physics of Ne*. At the low temperatures of the atomic gases, these gases are dilute with particle number densities of n~10^9 cm^{-3}. For these low densities, the behavior of the gas is determined mainly by two-body collision physics which is solved by quantum scattering theory in terms of the S matrix. The collision physics is given by short-range interactions and long-range interactions of the atoms. The short-range and long-range interaction potentials of Ne* have been calculated in the molecular basis of Ne2. In this thesis we first calculate short-range and long-range interactions of atoms and molecular basis states of diatomic molecules with a simpler electronic structure than Ne* and Ne2 in order to introduce the notation and to discuss the characteristics of the calculated molecular interaction potentials and in order to employ them in the scattering calculations for Ne*. Instead of solving the full scattering equations by taking into account all the molecular interaction potentials, we demonstrate that the collision physics of Ne* can be described in terms of a coupled two-channel model with a single interaction potential only which describes the elastic scattering of Ne*. In this model, ionization in Ne* collisions is described by the transition of the upper elastic interaction channel to the lower channel, representing the loss or ionization channel. We introduce two versions of the two-channel model in this work. In the first version, the two channels are given by square-well potentials. We can solve the scattering equations analytically and for complex wave numbers k and study the solutions in the complex k plane. With an expansion of the S matrix in terms of its poles in the complex k plane we find a parametrization of the two-body loss rate coefficients. We show that these coefficients describe ionizing collisions of Ne* by comparing them to the experimental measurements and to the numerical results obtained by the two-channel model in the second version. In this second version of the two-channel model, the elastic scattering channel is given by a realistic interaction potential of Ne*, consisting of a calculated short-range and long-range molecular potential, and the loss channel by a model ionization potential. For this model we calculate the two-body loss rate coefficients and the elastic cross sections for the isotope mixtures of Ne* which have been measured experimentally and demonstrate that the free potential parameters can be optimized to the experimental data to achieve very good agreement of the numerical results with the experimental measurements. We discuss the validity of the two-channel model by comparing the results to existing models for cold Rg* collisions and find that the two-channel model of this work is a useful extension to these models.

•Jan 1, 2017•0 citations
Collision kernels describing elastic collision effects in saturation spectroscopy are completely calculated for the metastable 3P0^{3}P_{0}3P0​ state of neon, starting from true experiment-deduced potentials. Collision processes with and without metastability exchange are respectively considered. A direct observation of these two kernels is provided by a two-laser time-resolved saturated absorption experiment. They are in good agreement with theory.
We present a theoretical and experimental study of the time evolution of the saturation-spectroscopy line shape when the saturating beam is suddenly switched on. We consider two metastable levels coupled by two Doppler-broadened transitions with a common excited level. In this special case, the fast transients from the upper level are rapidly damped, and the slow transients from populations and from Raman coherence in the metastable levels are easy to observe and are used for studying the collisional relaxation. For the sake of clarity, the theoretical analysis is developed according to a perturbation calculation. Nevertheless, saturation of the metastable levels must be taken into account in a more realistic theory (velocity-selective optical pumping): We give only a few results that are in excellent agreement with the experiments performed on neon metastable levels 3P0 and 3P2.
A theory of saturation spectroscopy in three-level gas-vapor systems, including collisional effects, is presented. Using a model of collisions in which they are phase interrupting in their effect on level coherences and velocity changing in their effect on level population densities, the authors calculate the absorption profile of a weak probe field on a given transition when an arbitrarily strong pump field acts on a coupled transition. Line shapes are derived for an arbitrary collision kernel describing the velocity-changing collisions, and these line shapes are evaluated for the collision kernel proposed by Keilson and Storer. Various limiting forms for the line shapes are derived and representative line shapes are displayed. Several new features of the line shapes, including collisionally induced increased probe absorption are discussed. The line shapes are seen to reflect the various collisional processes that may occur in atomic or molecular systems.
The collision-induced exothermic fine-structure transition $\mathrm{Ne}(^{3}P_{0})\ensuremath{-}\mathrm{Ne}(^{3}P_{2})$ has been observed in a crossed-effusive-beam experiment, by measuring the time of flight of metastable atoms scattered perpendicularly to the incident-beam plane. In this direction, the elastic scattering is kinematically discriminated. The identification of the transition is achieved by pumping 3P0^{3}P_{0}3P0​ or 3P2^{3}P_{2}3P2​ levels with a cw dye laser.
We investigate heteronuclear collisions in isotope mixtures of laser-cooled metastable (3P2{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2}3P2​) neon. Experiments are performed with spin-polarized atoms in a magnetic trap for all two-isotope combinations of the stable neon isotopes 20{}^{20}20Ne, 21{}^{21}21Ne, and 22{}^{22}22Ne. We determine the rate coefficients for heteronuclear ionizing collisions to ${\ensuremath{\beta}}_{21,20}=(3.9\ifmmode\pm\else\textpm\fi{}2.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ cm3{}^{3}3/s, ${\ensuremath{\beta}}_{22,20}=(2.6\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ cm3{}^{3}3/s, and ${\ensuremath{\beta}}_{21,22}=(3.9\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ cm3{}^{3}3/s. We also study heteronuclear elastic collision processes and give upper bounds for heteronuclear thermal relaxation cross sections. This work significantly extends the limited available experimental data on heteronuclear ionizing collisions for laser-cooled atoms involving one or more rare gas atoms in a metastable state.
In this thesis we investigate theoretically the cold collision properties of metastable neon (Ne*). The collisions of metastable rare gases (Rg*) exhibit a plethora of interesting phenomena: Due to the high internal excitation energies of the metastable atoms ionization processes are very likely. The produced ions can be detected with single-ion efficiency in the experiment. In experiments with atomic Rg* gases at cold temperatures T~1 mK, this allows for in-situ monitoring of the real-time dynamics of the atomic gas and for example for the study of two-particle correlations. Furthermore, in cold Rg* gases one can examine the prospects of creating a Bose-Einstein condensate or a degenerate Fermi gas of Rg*. Ne* is a promising candidate for Bose-Einstein condensation and in the group of G. Birkl the properties of cold gases of Ne* are investigated experimentally. Two-body loss rate coefficients due to the ionization processes and elastic cross sections have been measured. It is useful to complement the experimental measurements with a theoretical study in order to obtain a better understanding of the cold Ne* gases and the collision physics of Ne*. At the low temperatures of the atomic gases, these gases are dilute with particle number densities of n~10^9 cm^{-3}. For these low densities, the behavior of the gas is determined mainly by two-body collision physics which is solved by quantum scattering theory in terms of the S matrix. The collision physics is given by short-range interactions and long-range interactions of the atoms. The short-range and long-range interaction potentials of Ne* have been calculated in the molecular basis of Ne2. In this thesis we first calculate short-range and long-range interactions of atoms and molecular basis states of diatomic molecules with a simpler electronic structure than Ne* and Ne2 in order to introduce the notation and to discuss the characteristics of the calculated molecular interaction potentials and in order to employ them in the scattering calculations for Ne*. Instead of solving the full scattering equations by taking into account all the molecular interaction potentials, we demonstrate that the collision physics of Ne* can be described in terms of a coupled two-channel model with a single interaction potential only which describes the elastic scattering of Ne*. In this model, ionization in Ne* collisions is described by the transition of the upper elastic interaction channel to the lower channel, representing the loss or ionization channel. We introduce two versions of the two-channel model in this work. In the first version, the two channels are given by square-well potentials. We can solve the scattering equations analytically and for complex wave numbers k and study the solutions in the complex k plane. With an expansion of the S matrix in terms of its poles in the complex k plane we find a parametrization of the two-body loss rate coefficients. We show that these coefficients describe ionizing collisions of Ne* by comparing them to the experimental measurements and to the numerical results obtained by the two-channel model in the second version. In this second version of the two-channel model, the elastic scattering channel is given by a realistic interaction potential of Ne*, consisting of a calculated short-range and long-range molecular potential, and the loss channel by a model ionization potential. For this model we calculate the two-body loss rate coefficients and the elastic cross sections for the isotope mixtures of Ne* which have been measured experimentally and demonstrate that the free potential parameters can be optimized to the experimental data to achieve very good agreement of the numerical results with the experimental measurements. We discuss the validity of the two-channel model by comparing the results to existing models for cold Rg* collisions and find that the two-channel model of this work is a useful extension to these models.