Controlled collisions of two ultracold atoms in separate harmonic traps

TL;DR

This paper provides analytical solutions for controlled collisions of two ultracold atoms in separate harmonic traps, exploring energy spectra, resonances, and applications in quantum gates and atom transport.

Contribution

It introduces analytical models for atom collisions in harmonic traps, including effects of trap separation and Feshbach resonances, with applications in quantum information.

Findings

Energy spectrum shows avoided crossings and trap-induced shape resonances.

Analytical solutions describe eigenstates and energies for various trap geometries.

Illustrates applications in quantum gates and coherent atom transport.

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.