Laser-induced excitation and deexcitation of a strongly bound, cold tr
apped ion on the vibrational sidebands is analyzed, assuming the detec
tion of quantized fluorescence. The laser couples to oscillations in o
ne, two or three spatial directions. Sideband absorption is found to p
roduce non-classical states of the oscillator which affect the ensuing
emission. Sideband strengths and excitation spectra are calculated fo
r a number of limiting cases. Repeated null fluorescence observation l
eads to cooling of the ion and possibly to vibrational Fock states.