Heteronuclear molecules in an optical lattice: Theory and experiment

TL;DR

This paper combines theoretical modeling and experimental data analysis to study heteronuclear molecules in an optical lattice, focusing on energy spectra, rf association efficiency, and lifetime near Feshbach resonances for K-40 and Rb-87.

Contribution

It introduces an exact diagonalization method that accounts for coupling between center-of-mass and relative motion in heteronuclear systems with different trap frequencies.

Findings

Accurate energy spectrum calculations matching experimental data.

Precise determination of Feshbach resonance position.

Effective treatment of lattice anharmonicity and particle interactions.

Abstract

We study properties of two different atoms at a single optical lattice site at a heteronuclear atomic Feshbach resonance. We calculate the energy spectrum, the efficiency of rf association and the lifetime as a function of magnetic field and compare the results with the experimental data obtained for K-40 and Rb-87 [C. Ospelkaus et al., Phys. Rev. Lett. 97, 120402 (2006)]. We treat the interaction in terms of a regularized delta function pseudopotential and consider the general case of particles with different trap frequencies, where the usual approach of separating center-of-mass and relative motion fails. We develop an exact diagonalization approach to the coupling between center-of-mass and relative motion and numerically determine the spectrum of the system. At the same time, our approach allows us to treat the anharmonicity of the lattice potential exactly. Within the pseudopotential model, the center of the Feshbach resonance can be precisely determined from the experimental data.