Scattering and binding of different atomic species in a one-dimensional optical lattice

The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average discrete coordinates applies and makes the problem analytically tractable, and we present a number of new results and features compared to the case of identical atoms.Comment: 5 pages, 4 figure

Feshbach Molecules in a One-dimensional Optical Lattice

We present the theory of a pair of atoms in a one-dimensional optical lattice interacting via a narrow Feshbach resonance. Using a two-channel description of the resonance, we derive analytic results for the scattering states inside the continuum band and the discrete bound states outside the band. We identify a Fano resonance profile, and the survival probability of a molecule when swept through the Bloch band of scattering states by varying an applied magnetic field. We discuss how these results may be used to investigate the importance of the structured nature of the continuum in experiments.Comment: 4 pages, 3 figure

Two-channel Feshbach physics in a structured continuum

We analyze the scattering and bound state physics of a pair of atoms in a one-dimensional optical lattice interacting via a narrow Feshbach resonance. The lattice provides a structured continuum allowing for the existence of bound dimer states both below and above the continuum bands, with pairs above the continuum stabilized by either repulsive interactions or their center of mass motion. Inside the band the Feshbach coupling to a closed channel bound state leads to a Fano resonance profile for the transmission, which may be mapped out by RF- or photodissociative spectroscopy. We generalize the scattering length concept to the one-dimensional lattice, where a scattering length may be defined at both the lower and the upper continuum thresholds. As a function of the applied magnetic field the scattering length at either band edge exhibits the usual Feshbach divergence when a bound state enters or exits the continuum. Near the scattering length divergences the binding energy and wavefunction of the weakly bound dimer state acquires a universal form reminiscent of those of free-space Feshbach molecules. We give numerical examples of our analytic results for a specific Feshbach resonance, which has been studied experimentally.Comment: 18 pages, 9 embedded figure

Static Properties of Trapped Bose-Fermi Mixed Condensate of Alkali Atoms

Static properties of a bose-fermi mixture of trapped potassium atoms are studied in terms of coupled Gross-Pitaevskii and Thomas-Fermi equations for both repulsive and attractive bose-fermi interatomic potentials. Qualitative estimates are given for solutions of the coupled equations, and the parameter regions are obtained analytically for the boson-density profile change and for the boson/fermion phase separation. Especially, the parameter ratio $R_{int}$ is found that discriminates the region of the large boson-profile change. These estimates are applied for numerical results for the potassium atoms and checked their consistency. It is suggested that a small fraction of fermions could be trapped without an external potential for the system with an attractive boson-fermion interaction.Comment: 8 pages,5 figure

Ground-state properties of trapped Bose-Fermi mixtures: role of exchange-correlation

We introduce Density Functional Theory for inhomogeneous Bose-Fermi mixtures, derive the associated Kohn-Sham equations, and determine the exchange-correlation energy in local density approximation. We solve numerically the Kohn-Sham system and determine the boson and fermion density distributions and the ground-state energy of a trapped, dilute mixture beyond mean-field approximation. The importance of the corrections due to exchange--correlation is discussed by comparison with current experiments; in particular, we investigate the effect of of the repulsive potential energy contribution due to exchange--correlation on the stability of the mixture against collapse.Comment: 6 pages, 4 figures (final version as published in Physical Review

Zero-temperature phase diagram of binary boson-fermion mixtures

We calculate the phase diagram for dilute mixtures of bosons and fermions at zero temperature. The linear stability conditions are derived and related to the effective boson-induced interaction between the fermions. We show that in equilibrium there are three possibilities: a) a single uniform phase, b) a purely fermionic phase coexisting with a purely bosonic one and c) a purely fermionic phase coexisting with a mixed phase.Comment: 8 pages, revtex, 3 postscript figures; NORDITA-1999/71 C

Finite temperature effects on the collapse of trapped Bose-Fermi mixtures

By using the self-consistent Hartree-Fock-Bogoliubov-Popov theory, we present a detailed study of the mean-field stability of spherically trapped Bose-Fermi mixtures at finite temperature. We find that, by increasing the temperature, the critical particle number of bosons (or fermions) and the critical attractive Bose-Fermi scattering length increase, leading to a significant stabilization of the mixture.Comment: 5 pages, 4 figures; minor changes, proof version, to appear in Phys. Rev. A (Nov. 1, 2003