  Hole spins in semiconductors are a potential qubit alternative to electron
spins. In nuclear-spin-rich host crystals like GaAs, the hyperfine interaction
of hole spins with nuclei is considerably weaker than that for electrons,
leading to potentially longer coherence times. Here we demonstrate optical
pumping and coherent population trapping for acceptor-bound holes in a strained
GaAs epitaxial layer. We find $\mu$s-scale longitudinal spin relaxation time
T$_1$ and an inhomogeneous dephasing time T$_2^*$ of $\sim$7~ns. We attribute
the spin relaxation mechanism to a combination effect of a hole-phonon
interaction through the deformation potentials and a heavy-hole light-hole
mixing in an in-plane magnetic field. We attribute the short T$_2^*$ to
g-factor broadening due to strain inhomogeneity. T$_1$ and T$_2^*$ are
quantitatively calculated based on these mechanisms and compared with the
experimental results. While the hyperfine-mediated decoherence is mitigated,
our results highlight the important contribution of strain to relaxation and
dephasing of acceptor-bound hole spins.
