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The Journal of Chemical Physics

Trapping hydrogen atoms from a neon-gas matrix: A theoretical simulation

S. Bovino, P. Zhang, Vasili A. Kharchenko, A. Dalgarno

Published Aug 4, 2009• 16 citations
Publisher

Abstract

Hydrogen is of critical importance in atomic and molecular physics and the development of a simple and efficient technique for trapping cold and ultracold hydrogen atoms would be a significant advance. In this study we simulate a recently proposed trap-loading mechanism for trapping hydrogen atoms released from a neon matrix. Accurate ab initio quantum calculations are reported of the neon-hydrogen interaction potential and the energy- and angular-dependent elastic scattering cross sections that control the energy transfer of initially cold atoms are obtained. They are then used to construct the Boltzmann kinetic equation, describing the energy relaxation process. Numerical solutions of the Boltzmann equation predict the time evolution of the hydrogen energy distribution function. Based on the simulations we discuss the prospects of the technique.

DOI
10.1063/1.3180822

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In this paper, we report on our recent advances on a new trap loading mechanism for neutral atoms. The idea is based on our recently published results for chromium spectroscopy of atoms released from a solid neon matrix at cryogenic temperatures. The proposed trap loading mechanism consists of magnetically capturing the low-energy fraction of paramagnetic atoms being released from the matrix, while the host Ne atoms stick to the walls. Two different designs are described: one with a superconducting magnet producing a trap depth of 3 T and another with a superconducting dynamically switched magnet that generates a trap depth of about 1 T. Some preliminary results are presented.

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Hydrogen is of critical importance in atomic and molecular physics and the development of a simple and efficient technique for trapping cold and ultracold hydrogen atoms would be a significant advance. In this study we simulate a recently proposed trap-loading mechanism for trapping hydrogen atoms released from a neon matrix. Accurate ab initio quantum calculations are reported of the neon-hydrogen interaction potential and the energy- and angular-dependent elastic scattering cross sections that control the energy transfer of initially cold atoms are obtained. They are then used to construct the Boltzmann kinetic equation, describing the energy relaxation process. Numerical solutions of the Boltzmann equation predict the time evolution of the hydrogen energy distribution function. Based on the simulations we discuss the prospects of the technique.
We have studied the velocity distribution of chromium atoms released from a solid neon matrix at cryogenic temperatures via Doppler spectroscopy. The Ne matrix is grown by directing a small flux of gas onto a cold substrate, while Cr atoms are simultaneously implanted by laser ablation, with the resultant plume directed toward the growing matrix. The atoms are then released by a heat pulse. We have observed neutral Cr atoms at temperatures around 13K13\phantom{\rule{0.3em}{0ex}}\mathrm{K}13K with densities close to ${10}^{12}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The released atoms have a large initial drift velocity, explained by simple kinetic theory arguments, due to the light species' drag force. The scheme could be adapted to produce cryogenic beams of atoms, molecules, and possibly ions, for collisional studies and spectroscopy. However, our main motivation was the construction of a hydrogen trap, and here we discuss the prospects and problems of using this technique for this purpose.
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.
Ultracold hydrogen offers unique possibilities for precision spectroscopy, studies of atomic interactions, and the creation of quantum fluids containing mixtures of hydrogen and deuterium. Current techniques for trapping and cooling hydrogen have produced large condensates with N ∼ 109 atoms, but suffer from a variety of experimental limitations. Among these are the slow evaporative cooling rate due to the small H–H elastic-scattering cross section, the need for a superfluid helium film in the initial thermalization process, a geometry that severely limits detection efficiency, and the inability to trap deuterium. We are constructing a new apparatus based on buffer-gas cooling that will overcome these problems. To accelerate evaporative cooling, the thermalization rate is increased by simultaneously loading lithium and hydrogen into a 4.2 T anti-Helmholtz trap. Lithium accelerates evaporative cooling because the Li–H elastic-scattering cross section is ∼1200 times larger than that of H–H. Hydrogen and lithium will be produced by laser ablation of solid LiH in a 3He buffer gas held at temperatures of ∼350 mK. Because no wall collisions are needed for initial thermalization, ablating a solid sample of LiD should enable studies of deuterium. The apparatus is in the final stages of construction. We report on results of initial tests and discuss the new scientific opportunities made possible by this approach.PACS No.: 32.80.Pj
The elastic scattering of two hydrogen atoms interacting at very small energies is explored numerically using the most accurate potential-energy curves available for the X $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ and $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{+}$ states of H2{\mathrm{H}}_{2}H2​. The scattering lengths and low-temperature-averaged cross sections are determined and compared with previous calculations. The scattering lengths are 0.41a0{\mathit{a}}_{0}a0​ for the singlet case and 1.91a0{\mathit{a}}_{0}a0​ for the triplet. The predicted total triplet cross section at 2 K is 5.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ cm2{\mathrm{cm}}^{2}cm2 but it could be lower, at 4.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ cm2{\mathrm{cm}}^{2}cm2, with a different fit to the triplet potential between 12a0{\mathit{a}}_{0}a0​ and 15a0{\mathit{a}}_{0}a0​. A more accurate triplet-state potential is needed at these separations.
We apply kinetic theory to the problem of evaporative cooling of a dilute collisional gas in a trap. Assuming ``sufficient ergodicity'' (phase-space distribution only a function of energy) and s-wave collisions with an energy-independent cross section, an equation for the evolution of the energy distribution of trapped atoms is derived for arbitrary trap shapes. Numerical integration of this kinetic equation demonstrates that during evaporation the gas is accurately characterized by a Boltzmann distribution of atom energies, truncated at the trap depth. Adopting the assumption of a truncated Boltzmann distribution, closed expressions are obtained for the thermodynamic properties of the gas as well as for the particle and energy loss rates due to evaporation. We give analytical expressions both for power-law traps and for a realistic trapping potential (Ioffe quadrupole trap). As an application, we discuss the evaporative cooling of trapped atomic hydrogen gas. \textcopyright{} 1996 The American Physical Society.
In this paper, we report on our recent advances on a new trap loading mechanism for neutral atoms. The idea is based on our recently published results for chromium spectroscopy of atoms released from a solid neon matrix at cryogenic temperatures. The proposed trap loading mechanism consists of magnetically capturing the low-energy fraction of paramagnetic atoms being released from the matrix, while the host Ne atoms stick to the walls. Two different designs are described: one with a superconducting magnet producing a trap depth of 3 T and another with a superconducting dynamically switched magnet that generates a trap depth of about 1 T. Some preliminary results are presented.