Born-Oppenheimer description of two atoms in a combined oscillator and lattice trap

TL;DR

This paper applies a Born-Oppenheimer-like approximation to analyze the quantum states of two atoms in a combined harmonic oscillator and lattice trap, revealing a separation of motion scales under strong attraction.

Contribution

It introduces a novel application of the Born-Oppenheimer approximation to a two-atom system in a combined trap, highlighting the separation of time scales.

Findings

Separation of relative and center-of-mass motion under strong attraction

Representation of equations in momentum space for tight-binding regime

Validation of the Born-Oppenheimer approximation in this quantum system

Abstract

We analyze the quantum states of two atoms in a combined harmonic oscillator and periodic lattice trap in one spatial dimension. In the case of tight-binding and only nearest neighbor tunneling, the equations of motion are conveniently represented in the momentum representation. We show that in the case of strong attraction between the particles, the different time scales of relative and center-of-mass motion validate a separation of the problem similar to the Born-Oppenheimer approximation applied in the description of electronic and nuclear motion in molecules.