Stability of two-ion crystals in the Paul trap: A comparison of exact and pseudopotential calculations

The stability of two-ion crystals in a Paul trap with a dc component in the quadrupole potential has been studied with the use of the monodromy matrix. The pseudopotential model predicts crystals with the ions at rest either along the trap axis or in the radial plane. The solutions of the full equations of motion disagree with the predictions of the pseudopotential model when the radial and axial secular frequencies are nearly degenerate: the crystal is either unstable (as first noted by Emmertet al.) or exists in a previously unanticipated configuration in which the ions lie at an angle to the trap axes. A bifurcation diagram near the edge of the crystalline stability range does not support a frequency-doubling route to chaos.Dedicated to H. Walther on the occasion of his 60th birthday