Controlled collisions of two ultracold atoms in separate harmonic traps

Abstract

We consider controlled collisions between two ultracold atoms guided by external harmonic potentials. We derive analytical solutions of the Schroedinger equation for this system, and investigate the properties of eigenergies and eigenstates for different trap geometries as a function of a trap separation and of the scattering length. When varying the trap separation the energy spectrum exhibits avoided crossings, corresponding to trap-induced shape resonances. Introducing an energy-dependent scattering length we investigate the behavior of the system in the vicinity of a magnetic Feshbach resonance. Finally, we illustrate our analytical results with two examples: the quantum phase gate controlled by the external magnetic field, and a scheme for a coherent transport of atoms in optical lattices into higher Bloch bands.

11 pages, 11 figures

References in corpus (8)

• Theory of ultracold Fermi gases
• Controlled exchange interaction between pairs of neutral atoms in an optical lattice
• Ultracold heteronuclear molecules in a 3D optical lattice
• Molecules of Fermionic Atoms in an Optical Lattice
• Quantum theory of ultracold atom-ion collisions
• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• Controlled collisions of a single atom and ion guided by movable trapping potentials
• A quasi-Hermitian pseudopotential for higher partial wave scattering