Quantum dynamics of cold trapped ions, with application to quantum computation

The theory of interactions between lasers and cold trapped ions as it pertains to the design of Cirac-Zoller quantum computers is discussed. The mean positions of the trapped ions, the eigenvalues and eigenmodes of the ions' oscillations, the magnitude of the Rabi frequencies for both allowed and forbidden internal transitions of the ions and the validity criterion for the required Hamiltonian are calculated. Energy level data for a variety of ion species is also presented.Comment: 20 pages, 7 figures, 3 table

Majorization and Measures of Classical Polarization in Three Dimensions

There has been much discussion in the literature about rival measures of classical polarization in three dimensions. We gather and compare the various proposed measures of polarization, creating a geometric representation of the polarization state space in the process. We use majorization, previously used in quantum information, as a criterion to establish a partial ordering on the polarization state space. Using this criterion and other considerations, the most useful polarization measure in three dimensions is found to be one dependent on the Bloch vector decomposition of the polarization matrix.Comment: 8 page

Average quantum dynamics of closed systems over stochastic Hamiltonians

We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in closed system dynamics, in addition to the usual unitary evolution. We then show that, for an important class of problems in which the Hamiltonian is proportional to a Gaussian random process, the 2nd-order master equation yields exact dynamics. The general formalism is applied to study the examples of a two-level system, two atoms in a stochastic magnetic field and the heating of a trapped ion.Comment: 17 pages, 1 figure, submitted to Physical Review