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Physica Scripta

Cold Collisions between Laser-Cooled Magnesium Atoms

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

Published Jan 1, 2001• 1 citation
Publisher

Abstract

Light-assisted inelastic cold collisions are the main loss process for neutral atoms trapped and laser cooled in magneto-optical traps. Alkaline earth atoms do not have hyperfine structure, which is expected to make the comparison between theoretical predictions and experimental results much easier, compared to the case of alkali-metal atoms. We present here a numerical calculation for the loss rates in a weak laser field for cold magnesium atoms.

DOI
10.1238/physica.topical.095a00058

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Light-assisted inelastic cold collisions are the main loss process for neutral atoms trapped and laser cooled in magneto-optical traps. Alkaline earth atoms do not have hyperfine structure, which is expected to make the comparison between theoretical predictions and experimental results much easier, compared to the case of alkali-metal atoms. We present here a numerical calculation for the loss rates in a weak laser field for cold magnesium atoms.
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 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.
We show that when cold collisions account for just a few percent of the total loss in magneto-optical traps, as for alkaline-earth metals, their contribution can be obtained by comparing the load and decay quasiexponential curves. We exemplify it by measuring the collision rate coefficient \ensuremath{\beta} for calcium atoms at small trap laser detuning, which confirms the role of the long-lived ${}^{1}{\ensuremath{\Pi}}_{g}$ state at small internuclear separation. Systematic and simpler measurements of \ensuremath{\beta} for alkaline-earth metals are important for cold collision theory, since these elements have nondegenerate ground state and no hyperfine structure. Our method has general applicability and should considerably reduce the experimental challenges associated with these important measurements.
Trap-loss rates due to hyperfine--structure-changing collisions involving cold Na and K atoms in a mixed species magneto-optical trap have been measured. The investigations were performed in the low intensity regime, where hyperfine--structure-changing collision are believed to be the dominant mechanism for atomic losses. Comparison between homonuclear (Na-Na) and heteronuclear (Na-K) collision rate coefficients reveals a higher loss rate in the case of heteronuclear collisions. Results obtained in the regime of low trap laser intensity are compared with existent loss rates for several alkali metals, showing themselves to be in good agreement with those expected.
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.