Mott Domains of Bosons Confined on Optical Lattices

TL;DR

This paper investigates how Mott insulating phases in bosonic systems on optical lattices are affected by trapping potentials, revealing persistent Mott behavior over a range of fillings and implications for experiments.

Contribution

It demonstrates that Mott phases persist under trapping potentials and are not characterized by a traditional quantum phase transition, extending understanding to higher dimensions.

Findings

Mott behavior persists over a range of incommensurate fillings with a trap.

The transition to Mott insulator is not a traditional quantum phase transition.

Qualitative results are similar in higher dimensions.

Abstract

In the absence of a confining potential, the boson Hubbard model in its ground state is known to exhibit a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong on-site repulsion. In this paper, we use quantum Monte Carlo simulations to study the ground state of the one dimensional bosonic Hubbard model in a trap. We show that some, but not all, aspects of the Mott insulating phase persist when a confining potential is present. The Mott behavior is present for a continuous range of incommensurate fillings, a very different situation from the unconfined case. Furthermore the establishment of the Mott phase does not proceed via a quantum phase transition in the traditional sense. These observations have important implications for the interpretation of experimental results for atoms trapped on optical lattices. Initial results show that, qualitatively, the same results persist in higher dimensions.