We perform entanglement of spin and motional degrees of freedom of a single,
ground-state trapped ion through the application of a 16 ps laser pulse. The
duration of the interaction is significantly shorter than both the motional
timescale (≈10μs) and spin precession timescale (≈10
ns), demonstrating that neither sets a fundamental speed limit on this
operation for quantum information processing. Entanglement is demonstrated
through the collapse and revival of spin coherence as the spin components of
the wavefunction separate and recombine in phase space. We infer the fidelity
of these single qubit operations to be 97(3)%.Comment: 5 pages, 4 figure