Tuning superfluid phases of spin-1 bosons in cubic optical lattice with linear Zeeman effect

TL;DR

This paper develops a Ginzburg-Landau theoretical framework to analyze superfluid phases of spin-1 bosons in a cubic optical lattice under a linear Zeeman effect, revealing the nature of phase transitions at zero temperature.

Contribution

It introduces a Ginzburg-Landau theory for spin-1 Bose-Hubbard model under magnetic field, detailing phase boundaries and transition orders.

Findings

Superfluid-Mott insulator transition is second order.

Superfluid phase transitions can be first or second order.

Phase diagram depends on anti-ferromagnetic interaction and Zeeman effect.

Abstract

We analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons in the presence of an external magnetic field, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. In particular at zero temperature, we determine both the Mott and the superfluid phases for the competition between the anti-ferromagnetic interaction and the linear Zeeman effect within the validity range of the Ginzburg-Landau theory. Moreover, we find that the phase transition between the superfluid and Mott insulator phases is of second order and that the transitions between the respective superfluid phases for anti-ferromagnetic interaction can be both of first and second order.