  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 ($30$ $\mu$s) and spin precession timescale ($1$ 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 $(97^{+3}_{-4})\%$.
