Universal properties of a trapped two-component Fermi gas at unitarity

We treat the trapped two-component Fermi system, in which unlike fermions interact through a two-body short-range potential having no bound state but an infinite scattering length. By accurately solving the Schroedinger equation for up to N=6 fermions, we show that no many-body bound states exist other than those bound by the trapping potential, and we demonstrate unique universal properties of the system: Certain excitation frequencies are separated by $2\hbar\omega$, the wavefunctions agree with analytical predictions and a virial theorem is fulfilled. Further calculations up to N=30 determine the excitation gap, an experimentally accessible universal quantity, and it agrees with recent predictions based on a density functional approach.