Phonon-like excitations in the two-state Bose-Hubbard model

TL;DR

This paper investigates phonon-like collective excitations in a two-state Bose-Hubbard model, revealing how their spectrum varies with phase, temperature, and chemical potential using the random phase approximation.

Contribution

It introduces a two-level Bose-Hubbard model analysis of phonon-like excitations, including the effects of Bose-Einstein condensation and interactions, within the random phase approximation.

Findings

Normal phase has one exciton-like band

Condensed phase shows an additional excitation band

Spectral properties depend on chemical potential and temperature

Abstract

The spectrum of phonon-like collective excitations in the system of Bose-atoms in optical lattice (more generally, in the system of quantum particles described by the Bose-Hubbard model) is investigated. Such excitations appear due to displacements of particles with respect to their local equilibrium positions. The two-level model taking into account the transitions of bosons between the ground state and the first excited state in potential wells, as well as interaction between them, is used. Calculations are performed within the random phase approximation in the hard-core boson limit. It is shown that excitation spectrum in normal phase consists of the one exciton-like band, while in the phase with BE condensate an additional band appears. The positions, spectral weights and widths of bands strongly depend on chemical potential of bosons and temperature. The conditions of stability of a system with respect to the lowering of symmetry and displacement modulation are discussed.