Analytical solution of a double-well Bose-Einstein Condensate

TL;DR

This paper presents an analytical solution for the Hamiltonian of a double-well Bose-Einstein Condensate in the two-mode approximation, including cases with asymmetry and small overlaps, advancing theoretical understanding of such systems.

Contribution

It provides an exact diagonalization method for the BEC Hamiltonian in asymmetric double-well traps, extending previous models and incorporating perturbative corrections.

Findings

Hamiltonian is exactly diagonalizable for small mode overlaps

Perturbation theory accounts for larger overlaps and symmetric traps

Analytical solutions enhance understanding of BEC dynamics in double wells

Abstract

We introduce a microscopic computation which shows that the Hamiltonian of a Bose-Einstein Condensate can be analytically solved in the two-mode approximation, in particular, in the case of an asymmetric double-well condensate in the dilute regime. Our model is exactly diagonalisable when the overlap of the quasilocalized modes in each well is small enough with respect to the trap asymmetry. For larger overlaps or highly symmetric traps, our diagonalisable Hamiltonian acquires extra terms that we treat within perturbation theory.