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Optical tweezer arrays of neutral atoms provide a versatile platform forquantum simulation due to the range of interactions and Hamiltonians that canbe realized and explored. We propose to simulate a two-component Bose-Hubbardmodel with power-law hopping using arrays of multilevel Rydberg atoms featuringresonant dipolar interactions. The diversity of states that can be used toencode the local Hilbert space of the Bose-Hubbard model enables control of therelative hopping rate of each component and even the realization of spin-fliphopping. We use numerical simulations to show how multilevel Rydberg atomsprovide an opportunity to explore the diverse non-equilibrium quench dynamicsof the model. For example, we demonstrate a separation of the relaxationtimescales of effective spin and charge degrees of freedom, and observe regimesof slow relaxation when the effective hopping rates of the two components arevastly different due to dynamical constraints arising from hardcore bosoninteractions. We discuss the technical details of realizing our proposal instate-of-the-art Rydberg tweezer arrays.

Simulating a two component Bose-Hubbard model with imbalanced hopping in a Rydberg tweezer array