Hubbard parameters for programmable tweezer arrays

Publication Date

1-1-2024

Document Type

Article

Publication Title

Physical Review A

Volume

109

Issue

1

DOI

10.1103/PhysRevA.109.013318

Abstract

The experimental realization of Fermi-Hubbard tweezer arrays opens a new stage for engineering fermionic matter, where programmable lattice geometries and Hubbard model parameters are combined with single-site imaging. In order to use these versatile experimental Fermi-Hubbard models as quantum simulators, it is crucial to know the Hubbard parameters describing them. Here we develop methods to calculate the Hubbard model parameters of arbitrary two-dimensional lattice geometries: The tunneling t, on-site potential V, and interaction U for multiple bands and for both fermions and bosons. We show several examples. One notable finding is that a finite array of equally strong and separated individual tweezer potentials actually sums to give a nonperiodic total potential and thus spatially nonuniform Hubbard parameters. We demonstrate procedures to find trap configurations that equalize these parameters. More generally, these procedures solve the inverse problem of calculating Hubbard parameters: Given desired Hubbard parameters, find trap configurations to realize them. These methods will be critical tools for using tunnel-coupled tweezer arrays.

Funding Number

CMMI-2037545

Funding Sponsor

National Science Foundation

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