UC Santa Barbara

Engineered quantum systems are a powerful tool for quantum sensing and simulating otherwise intractable many-body quantum systems. Defects in the solid-state have emerged as one particularly useful class of platforms for tackling these goals, and the nitrogen-vacancy (NV) center in diamond is an especially noteworthy example owing to its ease of addressability and functionality across a broad range of conditions. However, engineering the system dimensionality and the underlying Hamiltonian is required to achieve good sensitivity and effective simulation. In this thesis, we will discuss systems of disordered interacting spins across three, two, and one dimensions. A special focus will be on methods for engineering these systems, and, especially in Chapters 3 and 4, we will discuss some of the interesting physics one can probe using confinement (in 1 and 2D) and periodic drive (in 3D). The methods of engineering we will explore are primarily chemical vapor deposition (CVD)-based, and we will also discuss the primal role of miscut in determining the quality of CVD growth. For three-dimensional ensembles, we will highlight a new sequence, $\epsilon$-CPMG, and discuss the way in which this sequence can be used to characterize competing interactions in disordered dipolar ensembles. For two-dimensional systems, we will discuss how to generate 2D confinement and the many-body physics one can study using a careful analysis of decoherence profiles. Step bunches and hillocks will be considered as two possible methods for patterning low-dimensional geometries of spins, and, in the case of the step bunch, we will highlight some interesting physics that arises from the patterned one-dimensional structure.