  We present measurements of the pulse length of ultracold electron bunches
generated by near-threshold two-photon photoionization of a laser-cooled gas.
The pulse length has been measured using a resonant $3$ GHz deflecting cavity
in TM$_{110}$ mode. We have measured the pulse length in three ionization
regimes. The first is direct two-photon photoionization using only a $480$ nm
femtosecond laser pulse, which results in short ($\sim 15$ ps) but hot ($\sim
10^{4}$ K) electron bunches. The second regime is just-above-threshold
femtosecond photoionization employing the combination of a continuous-wave
$780$ nm excitation laser and a tunable $480$ nm femtosecond ionization laser
which results in both ultracold ($\sim 10$ K) and ultrafast ($\sim 25$ ps)
electron bunches. These pulses typically contain $\sim 10^{3}$ electrons and
have an rms normalized transverse beam emittance of $1.5\pm0.1$ nm$\cdot$rad.
The measured pulse lengths are limited by the energy spread associated with the
longitudinal size of the ionization volume, as expected. The third regime is
just-below-threshold ionization which produces Rydberg states which slowly
ionize on microsecond time scales.
