  Trapped ions are a well-studied and promising system for the realization of a
scalable quantum computer. Faster quantum gates would greatly improve the
applicability of such a system and allow for greater flexibility in the number
of calculation steps. In this paper we present a pulsed laser system,
delivering picosecond pulses at a repetition rate of 5 GHz and resonant to the
S$_{1/2}$ to P$_{3/2}$ transition in Ca$^+$ for coherent population transfer to
implement fast phase gate operations. The optical pulse train is derived from a
mode-locked, stabilized optical frequency comb and inherits its frequency
stability. Using a single trapped ion, we implement three different techniques
for measuring the ion-laser coupling strength and characterizing the pulse
train emitted by the laser, and show how all requirements can be met for an
implementation of a fast phase gate operation.
