Ultracold bosons in a synthetic periodic magnetic field: Mott phases and re-entrant superfluid-insulator transitions

TL;DR

This paper investigates how synthetic periodic magnetic fields influence Mott phases and superfluid-insulator transitions of ultracold bosons in a 2D optical lattice, revealing tunable band structures and re-entrant phase transitions.

Contribution

It introduces a model reducing the bosonic Schrödinger equation to a Harper-like equation, enabling analysis of phase diagrams and momentum distributions under synthetic magnetic fields.

Findings

Re-entrant superfluid-insulator transitions induced by magnetic field variations.

Periodic superfluid density patterns with period q or q/2 depending on q.

Tunable energy band minima affecting phase behavior.

Abstract

We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength $p$ and a period $l=qa$, where $q$ is an integer and $a$ is the lattice spacing. We show that the Schr\"odinger equation for the non-interacting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields $q$ energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying $p$ for a given $q$. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the $p$ and $q$ dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several re-entrant field-induced SI transitions for any fixed period $q$. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity $q$ ($q/2$) in real space for odd (even) $q$ and suggest experiments to test our theory.