Theory of output coupling for trapped fermionic atoms (16 pages)

We develop a dynamic theory of output coupling for fermionic atoms initially confined in a magnetic trap. We consider an exactly soluble one-dimensional model, with a spatially localized {delta}-type coupling between the atoms in the trap and a continuum of free-particle external modes. The transient dynamics of the atoms, as they leave the trap, is investigated in detail. Two important special cases are considered for the confinement potential: the infinite box and the harmonic oscillator. We establish that in both cases a bound state of the coupled system appears for any value of the coupling constant, implying that the trap population does not vanish in the infinite-time limit. For weak coupling, the infinite-time spectral distribution of the outgoing atoms exhibits peaks corresponding to the initially occupied energy levels in the trap; the heights of these peaks increase with the energy. As the coupling gets stronger, the infinite-time spectral distribution is displaced towards dressed energies of the fermions in the trap. The corresponding dressed states result from the coupling between the unperturbed fermionic states in the trap, mediated by the coupling between these states and the continuum. In the strong-coupling limit, there is a reinforcement of the lowest-energy dressed mode, whichmore » contributes to the spectral distribution of the outgoing beam more strongly than the other modes. This effect is especially pronounced for the one-dimensional box, which indicates that the efficiency of the mode-reinforcement mechanism depends on the steepness of the confinement potential. In this case, a quasimonochromatic antibunched atomic beam is obtained. Results for a bosonic sample are also shown for comparison.« less