  As a unique feature, the $^{229}$Th nucleus has an isomeric transition in the
vacuum ultraviolet that can be accessed by optical lasers. The interference
effects occurring in the interaction between coherent optical light and an
ensemble of $^{229}$Th nuclei are investigated theoretically. We consider the
scenario of nuclei doped in vacuum ultraviolet-vacuum ultraviolet transparent
crystals and take into account the effect of different doping sites and
therefore different lattice fields that broaden the nuclear transition width.
This effect is shown to come in interplay with interference effects due to the
hyperfine splitting of the ground and isomeric nuclear states. We investigate
possible experimentally available situations involving two-, three- and
four-level schemes of quadrupole sublevels of the ground and isomeric nuclear
states coupling to one or two coherent fields. Specific configurations which
offer clear signatures of the isomer excitation advantageous for the more
precise experimental determination of the transition energy are identified.
Furthermore, it is shown that population trapping into the isomeric state can
be achieved. This paves the way for further nuclear quantum optics applications
with $^{229}$Th such as nuclear coherent control.
