Superfluid to Mott-insulator transition of cold atoms in optical lattices

TL;DR

This paper reviews the superfluid to Mott-insulator transition in cold atoms within optical lattices, discussing experimental signatures, theoretical models, and critical behaviors, highlighting challenges in understanding certain excitation modes.

Contribution

It provides a comprehensive review of the transition, emphasizing the limitations of traditional theories and connecting experimental observations with advanced non-perturbative approaches.

Findings

Experimental signatures of the transition are summarized.

RPA theory predicts a gapped mode in the superfluid phase.

Critical behavior involves complex infrared dynamics.

Abstract

We review the superfluid to Mott-insulator transition of cold atoms in optical lattices. The experimental signatures of the transition are discussed and the RPA theory of the Bose-Hubbard model briefly described. We point out that the critical behavior at the transition, as well as the prediction by the RPA theory of a gapped mode (besides the Bogoliubov sound mode) in the superfluid phase, are difficult to understand from the Bogoliubov theory. On the other hand, these findings appear to be intimately connected to the non-trivial infrared behavior of the superfluid phase as recently studied within the non-perturbative renormalization group.