  We systematically investigate unconventional superfluid phases of fermionic
dipolar particles lying in a double-wire setup with laser-assisted interwire
tunneling. Our numerical simulations, based on the nonlocal Kohn-Sham
Bogoliubov-de Gennes equation, reveal the existence of a large
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) region with a stripe phase under an
imbalance of particle densities between two wires. When the laser-assisted
interwire tunneling is present, it induces a transition from the FFLO phase to
the topological superfluid phase and the associated Majorana zero modes exhibit
an oscillation structure, which is significantly enhanced by the long-range
nature of the interwire dipolar interaction. This distinguishes itself from the
results obtained with usual contact interaction and offers new opportunities
for manipulating and reshaping Majorana zero modes by adjusting the degree of
the nonlocality and the interwire separation.
