Prediction of exotic ion-crystal structures in a Paul trap

Trapped Coulomb crystals are of prime importance for the fields of one-component plasmas, quantum computing, quantum simulations, artificial atoms, nonlinear spectroscopy, and structural phase transitions. In all these applications it is essential to be able to accurately predict the structure of the crystals given the trapping parameters. For the Paul trap, one of the most promising platforms for quantum computing, this is nontrivial, since the confining radio-frequency fields are time-dependent. The pseudopotential approach eliminates this time-dependence. However, the standard pseudopotential, commonly used in atomic physics and quantum computing applications, is not even powerful enough to predict all stable two-ion crystal configurations. In this paper, we develop an improved pseudopotential, applicable to few-ion Coulomb crystals. Our potential is vastly more accurate than the standard version, and is powerful enough to predict analytically the existence and structural phase boundaries of new three- and four-ion configurations that are completely missed by the standard pseudopotential. In particular, we make quantitative predictions of the border lines between different crystal configurations in the Paul trap's (q, a) stability diagram, which can be used to accurately switch between configurations. In addition, our improved pseudopotential accurately predicts the tilt angles of two-ion crystals. We also delineate the regions in (q, a) control parameter space where no two-, three-, and four-ion crystals exist. While this region is known for two-ion crystals, the regions for three- and four-ion crystals are new. Graphical abstract: .