Hubbard models and state preparation in an optical Lieb lattice

TL;DR

This paper explores the properties of cold atoms in an optical Lieb lattice, focusing on edge states, many-body phases, and flat band phenomena, providing theoretical groundwork for experimental realization of novel quantum states.

Contribution

It computes localized Wannier functions and Hubbard model coefficients for an optical Lieb lattice, and analyzes many-body phases and flat band effects in 1D and 2D geometries.

Findings

Edge states are robust against interactions in the Lieb lattice.

Strong attractive interactions enhance pair correlations in the Lieb ladder.

The study provides a pathway for experimental exploration of correlated phases in Lieb lattices.

Abstract

Inspired by the growing interest in probing many-body phases in novel two-dimensional lattice geometries we investigate the properties of cold atoms as they could be observed in an optical Lieb lattice. We begin by computing Wannier functions localised at individual sites for a realistic experimental setup, and determining coefficients for a Hubbard-like model. Based on this, we show how experiments could probe the robustness of edge states in a Lieb lattice with diagonal boundary conditions to the effects of interactions and realise strongly correlated many-body phases in this geometry. We then generalise this to interacting particles in a half-filled 1D Lieb ladder, where excitations are dominated by flat band states. We show that for strong attractive interactions, pair correlations are enhanced even when there is strong mixing with the Dirac cone. These findings in 1D raise interesting questions about the phases in the full 2D Lieb lattice which we show can be explored in current experiments.