The asymmetric rotating saddle potential as a mechanical analog to the RF Paul trap

Under specific conditions, a rotating saddle potential can confine the motion of a particle on its surface. This time-varying hyperbolic potential shares key characteristics with the RF-electric-quadrupole ion trap (RF Paul trap), making it a valuable mechanical analog. Previous work has primarily focused on symmetric saddles, characterized by equal curvatures along the trapping and anti-trapping directions. RF Paul traps, however, are asymmetric, because the degeneracy of the transverse motional modes must be lifted for laser cooling and other quantum control. In this paper, we investigate the motion of trapped particles in asymmetric rotating saddles. We demonstrate that even minor asymmetries, including those arising from manufacturing imperfections, can significantly affect particle trajectories and stability. Our analysis includes both theoretical modeling and experimental measurements. We derive the equations of motion for asymmetric saddles and solve them to explore stability and precession effects. Additionally, we present lifetime measurements of particles in saddles with varying degrees of asymmetry to map key features of the a–q stability diagram. This study underscores the importance of incorporating asymmetry into mechanical models of ion traps to better reflect real-world implementations.