Hubbard parameters for programmable tweezer arrays

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.

arXiv comment14 pages, 8 figures

References in corpus (41)

• Maximally localized Wannier functions: Theory and applications
• Quantum Simulation
• Realizing a lattice spin model with polar molecules
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Quantum Simulators: Architectures and Opportunities
• Fermi-Hubbard physics with atoms in an optical lattice
• Ultracold Dipolar Gas of Fermionic ${}^{23}$Na${}^{40}$K Molecules in their Absolute Ground State
• Ultracold Atoms in a Tunable Optical Kagome Lattice
• The Hubbard Model
• Nano-Engineering Defect Structures on Graphene
• Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice
• Tunable Superfluidity and Quantum Magnetism with Ultracold Polar Molecules
• Long-range interacting quantum systems
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• Excitation spectrum of a trapped dipolar supersolid and its experimental evidence
• Hong-Ou-Mandel atom interferometry in tunnel-coupled optical tweezers
• Matter-wave diffraction from a quasicrystalline optical lattice
• Interactions Between Rydberg-Dressed Atoms
• Far from equilibrium quantum magnetism with ultracold polar molecules
• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• Experimental Characterization of Two-Particle Entanglement through Position and Momentum Correlations
• A Fermi-Hubbard Optical Tweezer Array
• Fermionic quantum processing with programmable neutral atom arrays
• A two-dimensional programmable tweezer array of fermions
• In-situ equalization of single-atom loading in large-scale optical tweezers arrays
• Microscopic Structure of a Vortex Line in a Superfluid Fermi Gas
• Exotic topological density waves in cold atomic Rydberg fermions
• Parallel assembly of arbitrary defect-free atom arrays with a multi-tweezer algorithm
• Tight binding models for ultracold atoms in honeycomb optical lattices
• Measurement of Identical Particle Entanglement and the Influence of Antisymmetrisation
• Anisotropic optical trapping as a manifestation of the complex electronic structure of ultracold lanthanide atoms: the example of holmium
• Precise Programmable Quantum Simulations with Optical Lattices
• Quench dynamics of Rydberg-dressed bosons on two-dimensional square lattices
• Hubbard Models for Quasicrystalline Potentials
• Observation of brane parity order in programmable optical lattices
• Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials
• Vortex line in a neutral finite-temperature superfluid Fermi gas
• Effective many-body parameters for atoms in non-separable Gaussian optical potentials
• Fermionic Simulators for Enhanced Scalability of Variational Quantum Simulation
• Orbital quantum magnetism in spin dynamics of strongly interacting magnetic lanthanide atoms
• Hubbard models with arbitrary structures in programmable optical lattices

Cited by in corpus (5)

• Ultra-precise holographic optical tweezers array
• Ising phase transitions and thermodynamics of correlated fermions in a two-dimensional spin-dependent lattice potential
• Structural complexity of snapshots of 2D Fermi-Hubbard systems
• Quantum science with arrays of metastable helium-3 atoms
• On the origin of energy gaps in quasicrystalline potentials