SEMICLASSICAL LASER-COOLING THEORY FOR A TRAPPED MULTISTATE ION

We present a semiclassical laser-cooling theory for an ion bound in a quadratic potential well, allowing for an arbitrary internal level scheme of the ion and an arbitrary polarization of the light field. The special case that the ion moves in a region much smaller than the wavelength of the exciting light (Lamb-Dicke limit), as well as an additional low-intensity limit, are worked out in detail. Explicit general expressions are given for the damping and diffusion tensors of the center-of-mass motion of the ion, and the light-induced renormalization of the mechanical oscillation frequencies is discussed. The formalism is implemented analytically using a computer program MATHEMATICA for an ion with a j = 1/2 --> j = 3/2 transition moving in a one-dimensional optical molasses consisting of two counterpropagating laser beams with perpendicular linear polarizations (lin perpendicular-to lin). For a weakly bound ion at negligible saturation, the greatest lower limit of excitation energy turns out to be (33/20)1/2-1/2 almost-equal-to 0.78 vibrational quanta above the zero-point energy.