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

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Abstract

A quantum simulation platform based on quantum dots is reported that can operate at relatively low temperatures, and its utility is shown by simulating a Fermi-Hubbard model.

Interacting fermions on a lattice can develop strong quantum correlations, which are the cause of the classical intractability of many exotic phases of matter1,2,3. Current efforts are directed towards the control of artificial quantum systems that can be made to emulate the underlying Fermi-Hubbard models4,5,6. Electrostatically confined conduction-band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical initialization of low-entropy states and readily adhere to the Fermi-Hubbard Hamiltonian7,8,9,10,11,12,13,14,15,16,17. Until now, however, the substantial electrostatic disorder of the solid state has meant that only a few attempts at emulating Fermi-Hubbard physics on solid-state platforms have been made18,19. Here we show that for gate-defined quantum dots this disorder can be suppressed in a controlled manner. Using a semi-automated and scalable set of experimental tools, we homogeneously and independently set up the electron filling and nearest-neighbour tunnel coupling in a semiconductor quantum dot array so as to simulate a Fermi-Hubbard system. With this set-up, we realize a detailed characterization of the collective Coulomb blockade transition20, which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition1. As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here will enable the investigation of the physics of ever more complex many-body states using quantum dots.

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