Berlin 2001 – wissenschaftliches Programm
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Q: Quantenoptik
Q 17: Poster: Cooling and Trapping
Q 17.2: Poster
Mittwoch, 4. April 2001, 12:30–15:00, AT2
GEOMETRIC PHASES FOR TRAPPED ION STATES — •Viorica Gheorghe1,2, A. Gheorghe3, and G. Werth1 — 1Institut für Physik, Johannes-Gutenberg-Universität, D-55099, Mainz, Germany — 2National Institute for Laser, Plasma and Radiation, Bucharest, Romania — 3National Institute of Physics and Nuclear Engineering, Bucharest, Romania
Using the method developed in [1], the Berry phases corresponding to the solutions of the Schrödinger equation for systems of ions confined in electromagnetic quadrupole traps with cylindrical symmetry [2] have been obtained. The evolution operator can be written as the product of two unitary operators such that one of them is a time-periodic displacement operator for symplectic coherent states and the other gives the Berry phases corresponding to classical motion Hill equations. The decompositions of the total phase into dynami cal and geometrical phases for a single ion, for the center of mass collective motion and for the relative motion of stored ions are given. A scheme for measuring the Berry phases by using geometric transformations in the parameter space and the Jaynes-C ummings interaction is also discussed.
[1] Viorica N. Gheorghe and F. Vedel, Phys. Rev. A45, 4828-4832 (1992)
[2] V. N. Gheorghe and G. Werth, EPJD 10, 197 (2000)