Title: Incorporation of random alloy GaBi$_{x}$As$_{1-x}$ barriers in InAs quantum dot molecules: alloy strain and orbital effects towards enhanced tunneling

Abstract: Self-assembled InAs quantum dots (QDs), which have long hole-spin coherence times and are amenable to optical control schemes, have long been explored as building blocks for qubit architectures. One such design consists of vertically stacking two QDs to create a quantum dot molecule (QDM). The two dots can be resonantly tuned to form "molecule-like" coupled hole states from the hybridization of hole states otherwise localized in each respective dot. Furthermore, spin-mixing of the hybridized states in dots offset along their stacking direction enables qubit rotation to be driven optically, allowing for an all-optical qubit control scheme. Increasing the magnitude of this spin mixing is important for optical quantum control protocols. To enhance the tunnel coupling and spin-mixing across the dots, we introduce Bi in the GaAs inter-dot barrier. Previously, we showed how to model InAs/GaBiAs in an atomistic tight-binding formalism, and how the dot energy levels are affected by the alloy. In this paper, we discuss the lowering of the tunnel barrier, which results in a three fold increase of hole tunnel coupling strength in the presence of a 7% alloy. Additionally, we show how an asymmetric strain between the two dots caused by the alloy shifts the resonance. Finally, we discuss device geometries for which the introduction of Bi is most advantageous.