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arXiv:physics/9902053 · Physical Review A

Collisions of cold magnesium atoms in a weak laser field

Mette Machholm, Paul S. Julienne, Kalle‐Antti Suominen

Published Jun 1, 1999• 29 citations
arXivHTMLPDF

Abstract

We use quantum scattering methods to calculate the light-induced collisional loss of laser-cooled and trapped magnesium atoms for detunings up to 30 atomic linewidths to the red of the ${}^{1}{S}_{0}{\ensuremath{-}}^{1}{P}_{1}$ cooling transition. Magnesium has no hyperfine structure to complicate the theoretical studies. We evaluate both the radiative and nonradiative mechanisms of trap loss. The radiative escape mechanism via allowed ${}^{1}{\ensuremath{\Sigma}}_{u}$ excitation is dominant for more than about one atomic linewidth detuning. Molecular vibrational structure due to photoassociative transitions to bound states begins to appear beyond about ten linewidths detuning.

DOI
10.1103/physreva.59.r4113

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We use quantum scattering methods to calculate the light-induced collisional loss of laser-cooled and trapped magnesium atoms for detunings up to 30 atomic linewidths to the red of the 1S0\ensuremath−1P1{}^{1}{S}_{0}{\ensuremath{-}}^{1}{P}_{1}1S0​\ensuremath−1P1​ cooling transition. Magnesium has no hyperfine structure to complicate the theoretical studies. We evaluate both the radiative and nonradiative mechanisms of trap loss. The radiative escape mechanism via allowed 1\ensuremathΣu{}^{1}{\ensuremath{\Sigma}}_{u}1\ensuremathΣu​ excitation is dominant for more than about one atomic linewidth detuning. Molecular vibrational structure due to photoassociative transitions to bound states begins to appear beyond about ten linewidths detuning.
We calculate the light-induced collisional loss of laser-cooled and trapped magnesium atoms for detunings up to 50 atomic linewidths to the red of the ${}^{1}{S}_{0}{\ensuremath{-}}^{1}{P}_{1}$ cooling transition. We evaluate loss rate coefficients due to both radiative and nonradiative state-changing mechanisms for temperatures at and below the Doppler-cooling temperature. We solve the Schr\"odinger equation with a complex potential to represent spontaneous decay, but also give analytic models for various limits. Vibrational structure due to molecular photoassociation is present in the trap loss spectrum. Relatively broad structure due to absorption to the ${\mathrm{Mg}}_{2}{ }^{1}{\ensuremath{\Sigma}}_{u}$ state occurs for detunings larger than about ten atomic linewidths. A much sharper structure, especially evident at low temperature, occurs even at smaller detunings due to ${\mathrm{Mg}}_{2}{ }^{1}{\ensuremath{\Pi}}_{g}$ absorption, which is weakly allowed due to relativistic retardation corrections to the forbidden dipole transition strength. We also perform model studies for the other alkaline-earth-metal species Ca, Sr, and Ba, and for Yb, and we find similar qualitative behavior as for Mg.
We report Monte Carlo wave function simulation results on cold collisions between magnesium atoms in a strong red-detuned laser field. This is the normal situation, e.g., in magneto-optical traps (MOT). The Doppler limit heating rate due to radiative collisions is calculated for 24Mg^{24}\mathrm{Mg}24Mg atoms in an MOT based on the $^{1}S_{0}\text{\ensuremath{-}}^{1}P_{1}$ atomic laser cooling transition. We find that radiative heating does not seem to affect the Doppler limit in this case. We also describe a channeling mechanism due to the missing QQQ branch in the excitation scheme, which could lead to a suppression of inelastic collisions, and find that this mechanism is not present in our simulation results due to the multistate character of the excitation process.
Inelastic atomic collisions constitute loss mechanisms for neutral atom traps, and the study of trap-loss rates may provide detailed information on the long-range interaction between atoms and on the dynamics of very slow collisions. Gallagher and Pritchard (1989) have given a simple two-state model for such collisions which includes a radiative transition or a single curve crossing at short range representing, for example, fine-structure-changing collisions. In order to better describe the more complicated case found in alkali metals, we have extended this model to include several excited hyperfine structure levels with curve crossings at long range. We find that collisions in a laser field that are capable of expelling atoms from the trap can be suppressed in some laser frequency regions and enhanced in others, in comparison with the predictions of the simple two-state model. Using this model to represent radiative escape via the 2 u potential of alkali dimer molecules we are able to greatly improve agreement between theory and experiment, including new measurements on 85 Rb reported here.
Magnesium atoms are cooled in a magneto-optical trap (MOT) using the 3s2 S0 → 3s3p P1 resonance transition. Magnesium is a simple atom which offers a unique possibility for comparison to the Doppler theory of laser cooling. We measure trap parameters as a function of laser-intensity, -detuning and magnetic field gradient. We find the main features well accounted for by Doppler theory, but temperature measurements gave significant higher values than predicted by the Doppler theory. We also observe radiation pressure effects within the MOT that limit the maximum achievable density. Comparing our results to predictions by models in the literature shows a good agreement. Recently we have improved our set-up and now trap about 150 × 106 atoms.
Measurements of the temperature dependence of trap loss collisions of laser-cooled rubidium atoms are presented. A significant suppression of the rate of collisions between ground- and excited-state atoms is observed for temperatures below $\\sim$70 mu\\mumuK. In such inelastic collisions, the atomic excitation takes place at long range and must survive against spontaneous decay to short range. Our results are consistent with recent predictions for the low temperature suppression of these collisions due to reduced survival of atomic excitation at low collision velocities.^ We report on measurements of trap loss collisions between ultracold Rb atoms which are confined in a magneto-optical trap. Both isotopes sp85\\sp{85}sp85Rb and sp87\\sp{87}sp87Rb have been studied over wide range of trap laser intensities and detunings. The trap loss collision rates exhibit variations over 3 orders of magnitude. We observe significant differences between the isotopes. At large detunings the ability of the trap to recapture products of the hyperfine-changing collisions is significantly diminished. This finding is supported by our numerical simulations of the recapture process. The trap loss rates due to collisions with room temperature background gas have also been measured.^ Using laser light tuned to a repulsive molecular potential, we have been able to suppress inelastic ground-state hyperfine changing collisions between ultracold sp87\\sp{87}sp87Rb atoms. Adiabatic excitation to the repulsive curve alters the atomic trajectories and prevents the atoms from approaching close enough for the hyperfine change to occur. Experimental results show suppressions up to $\\sim$50% and are in reasonable agreement with a simple Landau-Zener model.^ Finally, we have observed a significant cooperative effect in ultracold trap loss collisions induced by two separate lasers. One laser, tuned close to the atomic resonance, excites the atom pair to an attractive potential at long range. The resulting acceleration and deflection give rise to an enhancement in the collisional flux of ground-state atoms reaching short range, as probed by a second laser. Enhancements up to a factor of $\\sim$3 have been observed. ^