# Spinor bosons in optical superlattices: a numerical study

## TL;DR

This paper numerically investigates the ground states of spin-1 ultracold bosons in a one-dimensional optical superlattice, revealing complex phase diagrams with Mott insulator, superfluid, and charge density wave phases influenced by energy shifts and spin interactions.

## Contribution

It provides a detailed numerical analysis of how energy shifts and spin-dependent interactions shape phase transitions in spinor bosons in optical superlattices, highlighting new phase behaviors.

## Key findings

- Charge density wave phases depend on density and energy shift.
- Quantum phase transitions occur at finite spin-dependent strength.
- Multiple phase transitions observed for different densities.

## Abstract

The ground state of spin-1 ultracold bosons trapped in a periodic one-dimensional optical superlattice is studied. The two sites of the unit cell have an energy shift between them, whose competition with the spin-dependent strength is the main focus of this paper. Charge density wave (CDW) phases appear for semi-integer and integer densities, leading to rich phase diagrams with Mott insulator, superfluid and CDW phases. The spin-dependent interaction favors insulator phases for integer densities and disfavors CDW phases for semi-integer densities, which tend to disappear. Also, quantum phase transitions at finite values of the spin-dependent strength were observed. For integer densities, Mott insulator-superfluid-CDW insulator transitions appear for an energy shift lower (higher) than the local repulsion for the global density $\rho=1$ ($\rho=2$).