  Trapped ion systems are a leading platform for quantum information
processing, but they are currently limited to 1D and 2D arrays, which imposes
restrictions on both their scalability and their range of applications. Here,
we propose a path to overcome this limitation by demonstrating that Penning
traps can be used to realize remarkably clean bilayer crystals, wherein
hundreds of ions self-organize into two well-defined layers. These bilayer
crystals are made possible by the inclusion of an anharmonic trapping
potential, which is readily implementable with current technology. We study the
normal modes of this system and discover salient differences compared to the
modes of single-plane crystals. The bilayer geometry and the unique properties
of the normal modes open new opportunities, in particular in quantum sensing
and quantum simulation, that are not straightforward in single-plane crystals.
Furthermore, we illustrate that it may be possible to extend the ideas
presented here to realize multilayer crystals with more than two layers. Our
work increases the dimensionality of trapped ion systems by efficiently
utilizing all three spatial dimensions and lays the foundation for a new
generation of quantum information processing experiments with multilayer 3D
crystals of trapped ions.
