https://doi.org/10.1007/s100530050541
Quasienergy states of trapped ions
Institut für Physik, Johannes-Gutenberg-Universität, 55099 Mainz, Germany
Received:
24
June
1999
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
