Quantum simulations of a Fermi-Hubbard model using a semiconductor quantum dot array

Quantum dots hold a promise for quantum simulations of highly-correlated electronic phases as they readily adhere to a Fermi-Hubbard model in the elusive strong-interaction, low-temperature regime, where quantum correlations can span many sites. Working in solid-state inevitably entails disorder, however, which makes reaching homogeneity, even for small systems, rather difficult, and as such attempts at simulating Fermi-Hubbard physics in solid state have been few and far between. We describe a toolbox for semiconductor quantum dots based on interpreting well-known features in charge stability that allows for the independent tuning of site-specific energy offsets and tunnel couplings, and use this to map out the accessible parameter space of a triple quantum dot device up to a total of 12 electrons and from $t/U=0.01$ to $t/U=0.12$. As tunnel couplings are homogeneously increased, we witness the delocalization transition from Coulomb blockade to collective Coulomb blockade, a finite-size analogue of the Mott metal-to-insulator transition. A further automated application of these ideas, on larger and more homogeneous samples, will make the synthesis of tailor-made correlated-electronic phases possible in the near future.