Quasienergy states of trapped ions
Institut für Physik, Johannes-Gutenberg-Universität, 55099 Mainz, Germany
Revised: 18 September 1999
Published online: 15 May 2000
The quantum models for a single trapped ion are extended to the description of the collective dynamics for systems of ions confined in quadrupole electromagnetic traps with cylindrical symmetry. A class of quantum Hamiltonians with suitable axial and radial interaction potentials given by homogeneous functions of degree and invariant under translations and axial rotations are introduced. The considered axial and radial quantum Hamiltonians for the center-of-mass and relative motions are described by collective dynamical systems associated to the symplectic group . Discrete quasienergy spectra are obtained and the corresponding quasienergy states are explicitly realized as coherent states parameterized by the stable solutions of the corresponding classical motion equations. Consequently, a correspondence between quantum and classical stability domains is established.
PACS: 32.80.Pj – Optical cooling of atoms; trapping / 03.65.Ge – Solutions of wave equations: bound states
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000