Bose-Fermi Mixtures Of Self-Assembled Filaments Of Fermionic Polar Molecules

Fermionic polar molecules in deep one-dimensional (1D) optical lattices may form self-assembled filaments when the electric dipoles are oriented along the lattice axis. These composites are bosons or fermions depending on the number of molecules per chain, leading to a peculiar and complex Bose-Fermi mixture, which we discuss in detail for the simplest case of a three-well potential. We show that the interplay among filament binding energy, transverse filament modes, and trimer Fermi energy leads to a rich variety of possible scenarios ranging from a degenerate Fermi gas of trimers to a binary mixture of two different types of bosonic dimers. We study the intriguing zero-temperature and finite-temperature physics of these composites for the particular case of an ideal filament gas loaded in 1D sites, and we discuss possible methods to probe these chain mixtures.