We study theoretically the few-body dynamics of atoms which leak out of a trap by tunneling through a thin barrier. We consider the two cases of bosons with strongly repulsive contact interactions and spinless fermions with strongly attractive contact interactions (Bose and Fermi Tonk-Girardeau gases, respectively). The tunneling is studied as a function of the number of particles
N and the barrier opacity. The fermionic case reproduces a nonexponential decay of a single particle, but with a signal enhanced by a factor of
N. In the bosonic case, we find a different regime of nonexponential decay due to the contribution of different resonances of the trap. The relevant physical realization is that of atoms confined to an optical box with an end-cap laser barrier, and the prospects for future experiments are discussed.
Dilute atomic Fermi gases are the subject of much current theoretical and experimental interest. Atomic gases have been cooled to temperatures much lower than the Fermi energy, and initial measurements of their properties have been achieved. We describe Quantum Monte Carlo calculations of the ground‐state properties of these intriguing systems, from the weak‐coupling regime described by BCS theory to the strong‐coupling regime where the atoms pair into weakly‐interacting dimers. We describe ground‐state properties and also calculations of the lowest spin‐excitations in these systems. Important directions for future work are also highlighted.