Quantum Simulation of the Hubbard Model with Dopant Atoms in Silicon

TL;DR

This paper demonstrates the quantum simulation of the Hubbard model using subsurface dopants in silicon, achieving single-site resolution and measuring entanglement and interactions relevant for strongly correlated systems.

Contribution

It introduces a novel method for simulating the Hubbard model with dopant atoms in silicon, enabling single-site measurements and tunable interactions.

Findings

Successful simulation of a two-site Hubbard Hamiltonian with atomic resolution.

Quantification of entanglement entropy and Hubbard interactions from quasiparticle tunneling.

Identification of separation-tunable Hubbard interaction strengths suitable for larger arrays.

Abstract

In quantum simulation, many-body phenomena are probed in controllable quantum systems. Recently, simulation of Bose-Hubbard Hamiltonians using cold atoms revealed previously hidden local correlations. However, fermionic many-body Hubbard phenomena such as unconventional superconductivity and spin liquids are more difficult to simulate using cold atoms. To date the required single-site measurements and cooling remain problematic, while only ensemble measurements have been achieved. Here we simulate a two-site Hubbard Hamiltonian at low effective temperatures with single-site resolution using subsurface dopants in silicon. We measure quasiparticle tunneling maps of spin-resolved states with atomic resolution, finding interference processes from which the entanglement entropy and Hubbard interactions are quantified. Entanglement, determined by spin and orbital degrees of freedom, increases with increasing covalent bond length. We find separation-tunable Hubbard interaction strengths that are suitable for simulating strongly correlated phenomena in larger arrays of dopants, establishing dopants as a platform for quantum simulation of the Hubbard model.