Analogue Quantum Simulation with Dopant Atoms in Silicon

Abstract

Strongly correlated materials can display exotic quantum phenomena relevant to the emergence of quantum technologies. Yet, many questions have remained open because of the difficulty in modelling the underlying physics beyond a few lattice sizes. Therefore, a continuing effort has been made to develop quantum simulation platforms, where these many-body states can be artificially emulated with a great degree of control in bespoke hardware implementations. This thesis focuses on the use of dopant-based atomic-scale devices in silicon to build artificial quantum matter probed by a low-temperature scanning tunnelling microscope (STM). We combine STM hydrogen lithography with phosphine doping for the placement of phosphorus donors in our silicon devices with atomic precision and perform spatially resolved measurements using the STM tip. We first establish the experimental platform by characterising strongly correlated states found in single and pairs of quantum dots made of a few donors each. Using these building blocks, we create devices based on dimerised chains to perform an analogue quantum simulation of the Su-Schrieffer-Hegger model, a topological quantum system that classical computers cannot solve effectively. As a preliminary result, we demonstrate the formation of 25 nm-long electronic bands in chains of 5 and 7 sites. These results demonstrate the viability of using silicon as a base for the realisation of Fermi-Hubbard analogue quantum simulators inside a low-temperature STM, with the tip as a tuneable local probe.