A single $16$~ps laser pulse performs single qubit rotations as well as generates entanglement of the spin and motional degrees of freedom in a single, trapped ${}^{138}$Ba${}^+$ ion. The fidelity of these single qubit rotations was found to be consistent with 100\%, $(97^{+3}_{-4})\%$. Entanglement is demonstrated through the collapse and revival of spin coherence as the spin components of the wavefunction separate and recombine in phase space.