  Highest resolution laser spectroscopy has generally been limited to single
trapped ion systems due to rapid decoherence which plagues neutral atom
ensembles. Here, precision spectroscopy of ultracold neutral atoms confined in
a trapping potential shows superior optical coherence without any deleterious
effects from motional degrees of freedom, revealing optical resonance
linewidths at the hertz level with an excellent signal to noise ratio. The
resonance quality factor of 2.4 x 10^{14} is the highest ever recovered in any
form of coherent spectroscopy. The spectral resolution permits direct
observation of the breaking of nuclear spin degeneracy for the 1S0 and 3P0
optical clock states of 87Sr under a small magnetic bias field. This optical
NMR-like approach allows an accurate measurement of the differential Lande
g-factor between the two states. The optical atomic coherence demonstrated for
collective excitation of a large number of atoms will have a strong impact on
quantum measurement and precision frequency metrology.
