  Revealing the ultrafast dynamics of three-dimensional (3D) Dirac fermions
upon photoexcitation is critical for both fundamental science and device
applications. So far, how the cooling of 3D Dirac fermions differs from that of
two-dimensional (2D) Dirac fermions and whether there is population inversion
are fundamental questions that remain to be answered. Here we reveal the
ultrafast dynamics of Dirac fermions in a model 3D Dirac semimetal Cd$_3$As$_2$
by ultrafast time- and angle-resolved photoemission spectroscopy (TrARPES) with
a tunable probe photon energy from 5.3 - 6.9 eV. The energy- and
momentum-resolved relaxation rate shows a linear dependence on the energy,
suggesting Dirac fermion cooling through intraband relaxation. Moreover, a
population inversion is reported based on the observation of accumulated
photoexcited carriers in the conduction band with a lifetime of $\tau_n$ = 3.0
ps. Our work provides direct experimental evidence for a long-lived population
inversion in a 3D Dirac semimetal, which is in contrast to 2D graphene where
the interband relaxation occurs on a much faster timescale.
