Trapped Fermi gases

Trapped degenerate atomic gases provide exciting opportunities for the manipulation and quantitative study of quantum statistical effects, such as the strikingly direct observation of Bose-Einstein condensation @1–3#. Although perhaps not as dramatic as the phase transition associated with bosons, the behavior of trapped Fermi gases also merits attention, both as a degenerate quantum system in its own right and as a possible precursor to a paired Fermi condensate at lower temperatures @4#. The ideal Fermi gas is an old and well-understood problem; there are many familiar systems where the noninteracting Fermi gas is a good zeroth-order approximation. Unlike electrons in atoms and metals, and nucleons in nuclei, however, the trapped atomic gases of Refs. @1–3# are dilute. The effects of predominantly short-ranged atom-atom interactions are therefore weak. For dilute, spin-polarized Fermi gases, the s-wave scattering amplitude ~which would dominate the behavior of a comparable gas of distinguishable particles! vanishes due to the antisymmetry of the manyfermion wave function. The next leading order, p-wave scattering is small at low energy, and can be neglected @5#. At low temperatures, both the Bose @6# and Fermi @7# gases are expanded relative to a classical gas at the same temperature. For fermions, however, this effect is due to the Pauli exclusion principle rather than atom-atom interactions. While in the Bose case a phase transition separates the degenerate and classical regimes, a trapped Fermi gas undergoes a gradual crossover between the classical limit and the compact Fermi sea. Harmonic traps provide a particularly simple realization of the confined Fermi system. In this paper we calculate the chemical potential, specific heat, and spatial and momentum distributions of a harmonically trapped, spin-polarized, ideal Fermi gas. These properties are described by universal scaling functions for any number of particles. We show that the observation of the spatial distribution of the trapped cloud would provide an explicit visualization of a real-space ‘‘Fermi sea.’’