Two Atoms in a Double Well: An Exact Solution

TL;DR

This paper presents an exact solution for two atoms in a double well, revealing interaction-dependent occupation probabilities and tunneling dynamics, advancing understanding beyond simplified models.

Contribution

It introduces an exact Bethe ansatz-based model for two atoms in a double well, providing detailed insights into their tunneling behavior and state occupations.

Findings

Occupation probability depends on interaction strength.

Tunneling transfers probabilities between double and single occupancy.

Exact solutions differ from previous two-mode models.

Abstract

We propose to experimentally realize an odd parity eigenstate $\left\vert b\right\rangle $ of two atoms in the double well. The occupation probability of this state shows evident dependence on the interaction, distinct from the result of two-mode model adopted in the Heidelberg experiment. The tunneling dynamics of two atoms starting from the $NOON$ state with infinite barrier height can be derived from the exactly solved model of $\delta $-barrier split double well based on a Bethe ansatz type hypothesis of the wave functions. We find that the single particle tunneling transfer the probabilities between double occupancy and single occupancy of each well.