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.
Highlights
In recent years, there has been much progress in realising and exploring novel lattice geometries using ultra-cold atoms in optical lattices [1, 2], and especially lattices with topological properties [3,4,5,6,7,8,9,10,11,12,13]
We first probe the robustness of edge and corner states in a Lieb lattice with diagonal boundary conditions [19] when weak interactions are introduced, and we investigate the many-body phases manifested in a half-filled 1D Lieb ladder for strong attractive interactions
In reference [15] we showed that a flat band system can host stable bound pairs with a significantly enhanced pair kinetic energy which grows with interaction strength, suggesting that the critical temperature required to realise pair dominated phases may be larger compared to conventional systems and may even grow with increasing interactions
Summary
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Keywords: quantum gases, optical lattice, topological band structure, strongly correlated system, Hubbard model, quantum ladder system, flat band
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