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Preparing Single Ions in m=0 States in the Lamb-Dicke Regime

When a trapped ion is used for optical frequency standards, it is usually cooled by laser radiation and then pumped to the m=0 state. However, simple laser cooling cannot be applied to some ion species due to the formation of the dark state. This paper shows theoretically that such ions can also be cooled to the Doppler limit and can be prepared in the m=0 state by three laser beams with different polarizations and frequency detunings.