The nature of self-localization of Bose-Einstein condensates in deep optical lattices

TL;DR

This paper investigates the self-localization transition of Bose-Einstein condensates in deep optical lattices, revealing it as a self-trapping crossover driven by the Peierls-Nabarro barrier, with implications for experimental control of quantum states.

Contribution

It identifies the Peierls-Nabarro barrier as the key factor behind the self-localization crossover in BECs within optical lattices, linking mean-field and beyond mean-field behaviors.

Findings

Self-localization is a self-trapping crossover in BECs.

The Peierls-Nabarro barrier determines the stability of self-trapped states.

The crossover sharpens beyond mean-field, affecting condensate coherence.

Abstract

We analyze the nature of a novel type of self-trapping transition called self-localization (SL) of Bose-Einstein condensates in one-dimensional optical lattices in the presence of weak local dissipation. SL has recently been observed in several studies based upon the discrete nonlinear Schr\"odinger equation (DNLS), however, its origin is hitherto an open question. We show that SL is based upon a self-trapping crossover in the system. Furthermore, we establish that the origin of the crossover is the Peierls-Nabarro barrier, an energy threshold describing the stability of self-trapped states. Beyond the mean-field description the crossover becomes even sharper which is also reflected by a sudden change of the coherence of the condensate. While we expect that the crossover can be readily studied in current experiments in deep optical lattices, our results allow for the preparation of robust and long-time coherent quantum states.