Ultra-cold atomic and molecular gases offer a unique possibility to realize a range of novel interacting many-body systems.

While in solid state systems electrons interact via the long-range Coulomb interactions, the inter- actions in cold gases are essentially local. However, the use of dipolar atoms or molecules allows one to surmount this limitation. Arrays of onedimensional chains of cold gases can be realized using optical lattices. The dipolar interactions lead to a coupling between the and, due to the anisotropy of the interactions, a rich phase diagram. Our first studies addressed bosons in planar arrays of one-dimensional tubes. We find a sliding Luttinger liquid and various ordered phases.

One aspect of cold atomic gases that often is deliberately ignored is the inhomogeneity of the system due to the trap potential. Further inhomogeneities can be achieved by applying inhomogeneous magnetic fields which affect both the single-particle potentials as well as the interaction between particles. The full potential of this additional control parameter has not been explored, yet. We studied the possibility of creating a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase by separating two spin species of trapped fermions using a magnetic field gradient. See K. Sun, JSM, D.S. Sheehy, and S. Vishveshwara, Oscillatory pairing of fermions in spin-split traps, Phys. Rev. A 83, 033608 (2011); arXiv:1009.4476. The FFLO phase, a superfluid phase with spatially varying order parameter and finite magnetization, has been long sought after in solid state systems and recent progress toward realizing it in cold atomic systems has created much excitement.