THE EFFECT OF THE LASER MODE STRUCTURE ON THE SIDE-BAND SPECTRUM OF STORED IONS
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abstract
The optical absorption spectrum of ions oscillating in a three-dimensional harmonic trap is calculated for laser excitation. The effect of the mode structure of the laser beam employed, in particular the case of the TEM 00 mode used in most experiments is considered. The spectrum contains many sidebands, besides the central transition frequency, generated by all combinations of the ion oscillation frequencies in the three orthogonal directions of motion, even when the laser is directed along the trap axis or is incident in the radial plane, and even when perfect symmetry of the trapping fields is assumed. It is shown that this coupling between the axial and radial frequencies is due to the Gaussian mode structure of the laser beam. In laser spectroscopy of ions trapped in a real radio frequency (rf) trap, energy transfer between the ion motional degrees of freedom is therefore caused by the mode structure of the laser beam and, as previously assumed, by asymmetries of the pseudopotential well and for more than one ion in the trap by ion space charge fields. The ion motion coupling due to the laser mode structure is of particular significance during the initial phases of laser cooling experiments when comparatively hot ions sample a distance comparable to the waist of the collimated laser beams and when this distance is of the order of the optical wavelength.
