Hubbard parameters for programmable tweezer arrays
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914645588049920 |
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| author | Wei, Hao-Tian Ibarra-García-Padilla, Eduardo Wall, Michael L. Hazzard, Kaden R. A. |
| author_facet | Wei, Hao-Tian Ibarra-García-Padilla, Eduardo Wall, Michael L. Hazzard, Kaden R. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03019 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hubbard parameters for programmable tweezer arrays Wei, Hao-Tian Ibarra-García-Padilla, Eduardo Wall, Michael L. Hazzard, Kaden R. A. Quantum Gases Atomic Physics Quantum Physics 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. |
| title | Hubbard parameters for programmable tweezer arrays |
| topic | Quantum Gases Atomic Physics Quantum Physics |
| url | https://arxiv.org/abs/2306.03019 |