Using exact continuous quantum Monte Carlo techniques, we study the zero- and finite-temperature properties of a system of harmonically trapped one-dimensional spin- 1 2 fermions with short-range interactions. Motivated by experimental searches for modulated Fulde-Ferrel-Larkin-Ovchinikov states, we systematically examine the impact of a spin imbalance on the density profiles. We quantify the accuracy of the Thomas-Fermi approximation, finding that for sufficiently large particle numbers (N100) it quantitatively reproduces most features of the exact density profile.

We model the impact of final-state interactions on the radio frequency spectrum of a strongly interacting two-component superfluid Fermi gas. In addition to a broad asymmetric peak coming from the breakup of Cooper pairs, we find that, for appropriate parameters, one can observe a sharp symmetric "bound-bound" spectral line coming from the conversion of Cooper pairs in one channel to pairs or molecules in another. © 2008 The American Physical Society.

We study vortex-lattice phases for a Bose gas trapped in a rotating optical-lattice near the superfluid-Mott-insulator transition. We find a series of abrupt structural phase transitions where vortices are pinned with their cores only on plaquettes or only on sites. We discuss connections between these vortex structures and the Hofstadter-butterfly spectrum of free particles on a rotating lattice. © 2008 The American Physical Society.