Understanding transport through many-body states of dopant arrays and jelly-bean quantum dots

Understanding many-body states in silicon quantum devices is essential for exploiting dopant arrays as analog quantum simulators and using jelly-bean quantum dots as charge pumps for long-range quantum information transfer. We investigate theoretically how transport reveals information about these many-body states. An extended Hubbard model is used to model many-body states in square, 3x3 dopant arrays. Each array is tunnel-coupled to a source and drain which can be an extended reservoirs or single-qubit charge emitters and collectors. Resonant tunneling into an empty array proceeds with an initial build-up of local charge near the source and quickly changes to tunnelling into extended array-modes. Even if the array is initially empty, tunneling into the array is quickly suppressed by Coulomb repulsion between tunneling electrons of opposite spin. When charge transfers from source to drain through the array only a fraction of one charge per spin transfers into the array. Symmetry-breaking ensures that a full charge can be transferred into the array. This understanding establishes the basis for extracting information from transport through many-body states of dopant arrays designed to be electronic, topological and magnetic quantum systems and simulators.