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.
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