Quantum manifestations of order and chaos in the Paul trap

In the pseudopotential approximation the type of dynamics of two charged particles confined in a Paul trap depends on the ratio λ=${\mathrm{\omega }}_{\mathit{z}}$/${\mathrm{\omega }}_{\mathrm{\rho }}$ of the frequencies of the axial and the radial pseudo-oscillators, respectively. For λ=1/2,1,2 the classical dynamics is integrable. The classical dynamics appears to be nonintegrable for λ≠1/2,1,2 and shows a mixed phase space with interspersed regular and chaotic regions. The type of classical dynamics manifests itself in the statistics of the quasienergy spectrum of the Paul trap. In the integrable case (λ=1/2,2) we find level clustering, whereas level repulsion is obtained in the chaotic regime.