Persistence of mean-field features in the energy spectrum of small arrays of Bose-Einstein condensates

TL;DR

This paper investigates how mean-field features persist in the energy spectra of small Bose-Einstein condensate arrays, specifically dimers and trimers, bridging classical mean-field dynamics and quantum energy levels.

Contribution

It extends mean-field analysis of dimer and trimer systems to asymmetric cases and explores the quantum spectrum, highlighting the link between classical fixed points and quantum states.

Findings

Mean-field features persist in asymmetric dimers.

Mapping between dimer and trimer aids spectral analysis.

Quantum energy levels relate to classical fixed points.

Abstract

The Bose-Hubbard Hamiltonian capturing the essential physics of the arrays of interacting Bose-Einstein condensates is addressed, focusing on arrays consisting of two (dimer) and three (trimer) sites. In the former case, some results concerning the persistence of mean-field features in the energy spectrum of the symmetric dimer are extended to the asymmetric version of the system, where the two sites are characterized by different on-site energies. Based on a previous systematic study of the mean-field limit of the trimer, where the dynamics is exhaustively described in terms of its fixed points for every choice of the significant parameters, an interesting mapping between the dimer and the trimer is emphasized and used as a guide in investigating the persistence of mean-field features in the rather complex energy spectrum of the trimer. These results form the basis for the systematic investigation of the purely quantum trimer extending and completing the existing mean-field analysis. In this respect we recall that, similar to larger arrays, the trimer is characterized by a non-integrable mean-field dynamics featuring chaotic trajectories. Hence, the correspondence between mean-field fixed points and quantum energy levels emphasized in the present work may provide a key to investigate the quantum counterpart of classical instability.