Effects of Inhomogeneity on the Spectrum of the Mott-Insulator State

TL;DR

This paper explores how inhomogeneity from an external potential affects the spectral properties and phase transitions of ultracold bosons in a 1D optical lattice, revealing coexistence of localized and delocalized regions.

Contribution

It introduces a model capturing quasi phase transitions induced by external potentials and clarifies the microscopic mechanisms behind these phenomena.

Findings

External potential induces coexistence of localized and delocalized regions.

A simplified Fock state model describes energy gap and particle fluctuations.

Symmetry influences the energy gap behavior as potential depth varies.

Abstract

We investigate the existence of quantum {\it quasi} phase transitions for an ensemble of ultracold bosons in a one-dimensional optical lattice, performing exact diagonalizations of the Bose-Hubbard Hamiltonian. When an external parabolic potential is added to the system {\it quasi} phase transitions are induced by the competition of on-site mean-field energy, hopping energy, and energy offset among lattice sites due to the external potential and lead to the coexistence of regions of particle localization and delocalization in the lattice. We clarify the microscopic mechanisms responsible for these {\it quasi} phase transitions as a function of the depth of the external potential when the on-site mean-field energy is large compared to the hopping energy. In particular, we show that a model Hamiltonian involving a few Fock states can describe the behavior of energy gap, mean particle numbers per site, and number fluctuations per site almost quantitatively. The role of symmetry on the gap as a function of the depth of the external trapping potential is elucidated. We discuss possible experimental signatures of {\it quasi} phase transitions studying the single particle density matrix and explain microscopically the occurrence of local maxima in the momentum distribution. The role of a thermal population of the excited states on the momentum distribution is discussed.