  In the present work we consider models of quantum droplets in the presence of
a defect in the form of a laser beam moving through the respective condensates
including the Lee-Huang-Yang correction. Our analysis features separately an
exploration of the existence, stability, bifurcations and dynamics in 1D, 2D
and 3D settings. In the absence of an analytical solution of the problem, we
provide an analysis of the speed of sound and observe how the states traveling
with the defect may feature a saddle-center bifurcation as the speed or the
strength of the defect is modified. Relevant bifurcation diagrams are
constructed systematically, and the unstable states, as well as the dynamics
past the existence of stable states is monitored. The connection of the
resulting states with dark solitonic patterns in 1D, vortical states in 2D and
vortex rings in 3D is accordingly elucidated.
