We propose a scheme to perform optical pulses that suppress the effect of photon recoil by three orders of magnitude compared to ordinary pulses in the Lamb-Dicke regime. We derive analytical insight about the fundamental limits to the fidelity of optical qubits for trapped atoms and ions. This paves the way towards applications in quantum computing for realizing $>1000$ of gates with an overall fidelity above 99\%.
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.