LASER COOLING OF TRAPPED IONS WITH POLARIZATION GRADIENTS

Laser cooling of a single trapped ion with Zeeman substructure below t he Doppler limit is considered theoretically. The laser field consists of two counterpropagating beams linearly polarized in different direc tions, and the internal atomic transition is J(g) = 1/2 --> J(e) = 3/2 . The ion is assumed to be localized to spatial dimensions smaller tha n the optical wavelength (Lamb-Dicke limit) and placed at a specific p osition with respect to the laser beams. Under the assumption that the rate for optical pumping between the atomic ground states defines the smallest time constant in the system, analytic expressions for the fi nal energy and the cooling rates are derived, with both a semiclassica l and a full quantum treatment. The results show that laser cooling of a trapped ion using polarization gradients leads to very low energies . These energies are insensitive to the precise localization of the io n with respect to the lasers, the angle between the direction of the p olarizations of the laser beams, and the detuning of the cooling laser .