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

Source: [Ultracold bosons in a synthetic periodic magnetic field: Mott phases and re-entrant superfluid-insulator transitions](<https://www.sota2.com/research/paper/68fa2c411e209131ce84e807>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T15:14:43.140Z

Authors: K. Saha, K. Sengupta, K. Ray

Published: 2010-05-25T03:56:07.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1005.4476>)

[PDF](<https://arxiv.org/pdf/1005.4476.pdf>)