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arXiv:physics/0103059 · Physical Review A

Calculations of collisions between cold alkaline-earth-metal atoms in a weak laser field

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

Published Aug 20, 2001• 65 citations
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Abstract

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.

DOI
10.1103/physreva.64.033425

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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 1S0\ensuremath−1P1{}^{1}{S}_{0}{\ensuremath{-}}^{1}{P}_{1}1S0​\ensuremath−1P1​ 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 Mg21\ensuremathΣu{\mathrm{Mg}}_{2}{ }^{1}{\ensuremath{\Sigma}}_{u}Mg2​1\ensuremathΣu​ 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 Mg21\ensuremathΠg{\mathrm{Mg}}_{2}{ }^{1}{\ensuremath{\Pi}}_{g}Mg2​1\ensuremathΠg​ 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.
This paper examines two collisional mechanisms by which cold alkali-metal atoms can escape from a neutral-atom trap, due to collison of excited- and ground-state atoms. One is fine-structure-changing collisions, by which the atoms are heated by the amount of the fine-structure splitting. The other produces hot ground-state atoms following emission of a red-shifted photon during the course of a collision. A rate expression is obtained that applies to both normal and ultracold temperatures (1 mK). This expression assumes a canonical distribution of initial states, low-intensity excitation, and a semiclassical treatment of the survival probability relative to excited-state decay during the long time of the ultracold collision, and uses fine-structure-changing probabilities found by quantum scattering calculations. The known properties of the attractive molecular states of the alkaline-metal dimers are used to identify and calculate the probabilities for the specific mechanisms. We conclude that the earlier semiclassical analysis by Dashevskaya [Opt. Spectrosk. 46, 423 (1979)] of the fine-structure-changing mechanisms for the various alkali-metal species is qualitatively correct. We present quantum-mechanical calculations of the rate coefficient for fine-structure-changing collisions between ground- and excited-state Cs atoms from 1000 K to 100 \ensuremath{\mu}K. Collision-rate coefficients for the trap-loss processes are calculated for pairs of Li, Na, K, Rb, and Cs atoms at low temperature. There is a wide variation of predicted loss rate among alkali-metal species from the fastest for K and the slowest for Li. Retardation corrections to molecular lifetimes must be taken into account to predict the correct rate coefficients for Na, K, and Rb. Good agreement is obtained with the observed trap loss rate in a Cs trap.
Radiative emission during cold collisions between trapped laser-cooled Rb atoms and alkaline-earth ions (Ca+^++, Sr+^++, Ba+^++) and Yb+^++, and between Li and Yb+^++, are studied theoretically, using accurate effective-core-potential based quantum chemistry calculations of potential energy curves and transition dipole moments of the related molecular ions. Radiative association of molecular ions is predicted to occur for all systems with a cross section two to ten times larger than the radiative charge transfer one. Partial and total rate constants are also calculated and compared to available experiments. Narrow shape resonances are expected, which could be detectable at low temperature with an experimental resolution at the limit of the present standards. Vibrational distributions are also calculated, showing that the final molecular ions are not created in their ground state level.
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.
Narrow s-wave features with subthermal widths are predicted for the ${}^{1}{\ensuremath{\Pi}}_{g}$ photoassociation spectra of cold alkaline-earth-metal atoms. The phenomenon is explained by numerical and analytical calculations. These show that only a small subthermal range of collision energies near threshold contributes to the s-wave features that are excited when the atoms are very far apart. The resonances survive thermal averaging, and may be detectable for Ca cooled near the Doppler cooling temperature of the $4{}^{1}P\ensuremath{\leftarrow}4{}^{1}S$ laser-cooling transition.