Mott insulators in an optical lattice with high filling factors

TL;DR

This paper investigates the superfluid to Mott insulator transition in high-filling optical lattices, demonstrating that a single-band Bose-Hubbard model effectively describes the system and revealing challenges in realizing the Mott phase in low-dimensional lattices.

Contribution

It shows that multi-band systems with high filling factors can be effectively modeled by a single-band Bose-Hubbard Hamiltonian, including renormalized parameters and temperature effects.

Findings

Mott insulator phase is harder to realize in 1D and 2D lattices.

Long-wavelength physics is captured by a single-band model despite multi-band filling.

Renormalized tunneling and interaction parameters are derived for the effective model.

Abstract

We discuss the superfluid to Mott insulator transition of an atomic Bose gas in an optical lattice with high filling factors. We show that also in this multi-band situation, the long-wavelength physics is described by a single-band Bose-Hubbard model. We determine the many-body renormalization of the tunneling and interaction parameters in the effective Bose-Hubbard Hamiltonian, and consider the resulting model at nonzero temperatures. We show that in particular for a one or two-dimensional optical lattice, the Mott insulator phase is more difficult to realize than anticipated previously.