Stability of Bose-Einstein condensates in a circular array

TL;DR

This paper analyzes the stability and excitation spectrum of Bose-Einstein condensates in a circular array using the Bose-Hubbard model and Bogoliubov theory, revealing conditions for superflow stability.

Contribution

It provides a detailed theoretical analysis of superfluid stability in circular arrays, deriving the excitation spectrum and identifying stable superflow regions.

Findings

Superflow condensates exist only in the central Brillouin zone region.

Excitation spectra show doublets due to paired quasimomenta.

Superflow in outer Brillouin zone regions is energetically unstable.

Abstract

The properties of the superfluid phase of ultra cold bosonic atoms loaded in a circular array are investigated in the framework of the Bose-Hubbard model and the Bogoliubov theory. We derive and solve the Gross-Pitaevskii equation of the model to find that the atoms condense in states of well-defined quasimomentum. A detailed analysis of the coupling structure in the effective quadratic grand-canonical Hamiltonian shows that only pairs of distinct and identical quasimomenta are coupled. Solving the corresponding Bogoliubov-de Gennes equations we see that each pair of distinct quasimomenta gives raise to doublets in the excitation energy spectrum and that the quasimomenta of the zero-energy mode and of the occupied state in the condensates are identical. The dynamical and energetic stabilities of the condensates are determined by studying the behavior of the elementary excitations in the control parameters space. Our investigation establishes that superflow condensates exists only in the central region of the first Brillouin zone whereas there is none in the last quarters since they are energetically unstable, independently of the control parameters.