Abstract
An individual barium ion, continuously observed by laser fluorescence, has been isolated in a Paul rf quadrupole trap at room temperature. By optical sideband cooling its microscopically measured image has been reduced in thickness to \ensuremath{\sim} 2 \ensuremath{\mu}m in the object plane, the diffraction limit. Estimated ion temperatures reached are ${T}_{i}\ensuremath{\simeq}10 \mathrm{to} <36$ mK. With cooling, the ion could be held indefinitely, without cooling \ensuremath{\sim} 30 s. In the future the technique seems capable of attaining kinetic temperatures \ensuremath{\sim} ${10}^{\ensuremath{-}8}$ K, much lower than realized so far by other means, with corresponding far-reaching implications.
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