Macroscopic quantum bound states of Bose Einstein condensates in optical lattices

TL;DR

This paper explores localized ground states of Bose-Einstein condensates in optical lattices, revealing how interactions lead to bound states that are exact solitons of the Gross-Pitaevskii equation, with implications for soliton delocalization.

Contribution

It introduces a self-consistent linear Schrödinger framework to identify bound states as exact GPE solitons, linking linear spectrum gaps to nonlinear localized states.

Findings

Bound states form in forbidden spectral zones depending on interaction type.

These states are exact solitons of the GPE.

Implications for soliton delocalization transitions in higher dimensions.

Abstract

We discuss localized ground states of the periodic Gross-Pitaevskii equation in the framework of a quantum linear Schr\"odinger equation with effective potential determined in self-consistent manner. We show that depending on the interaction among the atoms being attractive or repulsive, bound states of the linear self consistent problem are formed in the forbidden zones of the linear spectrum below or above the energy bands. These eigenstates are shown to be exact solitons of the GPE equation. The implications of this bound state interpretation on the existence of a delocalization transition for multidimensional solitons is briefly discussed.