Hubbard parameters for programmable tweezer arrays

TL;DR

This paper develops methods to calculate and engineer Hubbard model parameters in programmable tweezer arrays, enabling precise quantum simulation of fermionic and bosonic systems with customizable lattice geometries.

Contribution

It introduces algorithms to determine Hubbard parameters for arbitrary 2D geometries and inverse design procedures to achieve desired parameters in tweezer arrays.

Findings

Finite tweezer arrays produce non-uniform Hubbard parameters.

Procedures to equalize Hubbard parameters across arrays.

Inverse design methods for target Hubbard parameters.

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 non-periodic total potential and thus spatially non-uniform 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.