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arXiv:physics/0107051 · Physical Review A

Subthermal linewidths in photoassociation spectra of cold alkaline-earth-metal atoms

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

Published Jan 3, 2002• 16 citations
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Abstract

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.

DOI
10.1103/physreva.65.023401

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Narrow s-wave features with subthermal widths are predicted for the 1\ensuremathΠg{}^{1}{\ensuremath{\Pi}}_{g}1\ensuremathΠg​ 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 41P\ensuremath←41S4{}^{1}P\ensuremath{\leftarrow}4{}^{1}S41P\ensuremath←41S laser-cooling transition.
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.
The properties of photoassociation (PA) spectra near the intercombination line (the weak transition between and states) of group II atoms are theoretically investigated. As an example, we have carried out a calculation for calcium atoms colliding at ultralow temperatures of , , and . Unlike in most current photoassociation spectroscopy, the Doppler effect can significantly affect the shape of the investigated lines. Spectra are obtained using and short-range potentials and long-range van der Waals and resonance dipole potentials. The similar van der Waals coefficients of ground and excited states cause the PA to differ greatly from those of strong, allowed transitions with resonant dipole interactions. The density of spectral lines is lower, the Condon points are at relatively short range, the reflection approximation for the Franck-Condon factors is not applicable, and the spontaneous decay to bound ground-state molecules is efficient. Finally, the possibility of efficient production of cold molecules is discussed.
It is possible to tune the scattering length for the collision of ultracold ground-state alkaline-earth-metal atoms using an optical Feshbach resonance. This is achieved with a laser far detuned from an excited molecular level near the frequency of the atomic intercombination transition. Simple resonant-scattering theory, illustrated by the example of , allows an estimate of the magnitude of the effect. Unlike alkali metal species, large changes of the scattering length are possible while atom loss remains small, because of the very narrow linewidth of the molecular photoassociation transition. This raises prospects for control of atomic interactions for a system without magnetically tunable Feshbach resonance levels.
We present the first measurement of a photoassociative spectrum of an alkaline earth element near the dissociation limit. The observed spectrum of Ca2 formed from cold atoms shows the regular vibrational series with the characteristic spacing of the 1/R3 asymptotic potential. The interpretation is in principle simplified compared to previous measurements on alkali metals by the nondegenerate ground state and the missing hyperfine structure of 40Ca. As an example, we derive the natural decay rate of the excited atomic 4p 1P1 state from the positions of the observed vibrational and rotational resonances with reduced uncertainty compared to previous measurements.
Quench cooling is a promising technique to reach ultra-cold temperatures in alkaline-earth atoms by Doppler cooling on ultra-narrow transitions. The principles of quench cooling are derived from an effective two-level system with a linewidth adjustable by the quenching laser. A tunable linewidth reconciles the contradictory requirements of a fast cooling rate and a high velocity selectivity at high and low temperatures, respectively. In this paper, we investigate the efficiency of quench cooling in alkaline-earth systems. We present a one-dimensional analytical description of the quenching process. Cooling and trapping in three dimensions is studied with semi-classical Monte Carlo simulations. Our results for magnesium indicate a loading efficiency of up to 40% of pre-cooled atoms at 2 mK into a QuenchMOT. Final temperatures of 9µ K and an increase in phase-space density by almost five orders of magnitude are observed in the simulations.