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

Triplet superconductivity and proximity effect induced by Bloch and N\'{e}el domain walls

Noncollinear magnetic interfaces introduced in superconductor (SC)/ferromagnet/SC heterostructures allow for spin-flipping processes and are able to generate equal-spin spin-triplet pairing correlations within the ferromagnetic region. This leads to the occurrence of the so-called long-range proximity effect. Particular examples of noncollinear magnetic interfaces include Bloch and N\'{e}el domain walls. Here, we present results for heterostructures containing Bloch and N\'{e}el domain walls based on self-consistent solutions of the spin-dependent Bogoliubov$-$de Gennes equations in the clean limit. In particular, we investigate the thickness dependence of Bloch and N\'{e}el domain walls on induced spin-triplet pairing correlations and compare with other experimental and theoretical results, including conical magnetic layers as noncollinear magnetic interfaces. It is shown that both, Bloch and N\'{e}el domain walls lead to the generation of unequal-spin spin-triplet pairing correlations of similar strength as for conical magnetic layers. However, for the particular heterostructure geometries investigated, only Bloch domain walls lead to the generation of equal-spin spin-triplet pairing correlations. They are stronger than those generated by an equivalent thickness of conical magnetic layers. In order for N\'{e}el domain walls to induce equal-spin spin-triplet pairing correlations, they have to be oriented such that the noncollinearity appears within the plane parallel to the interface region.Comment: 11 pages, 4 figure

Spin-flipping with Holmium: Case study of proximity effect in superconductor/ferromagnet/superconductor heterostructures

Superconductor/ferromagnet/superconductor heterostructures exhibit a so-called long-range proximity effect provided some layers of conical magnet Holmium are included in the respective interface regions. The Ho layers lead to a spin-flip process at the interface generating equal-spin spin-triplet pairing correlations in the ferromagnet. These equal-spin spin-triplet pairing correlations penetrate much further into the heterostructure compared to the spin-singlet and unequal-spin spin-triplet correlations which occur in the absence of Ho. Here we present calculations of this effect based on the spin-dependent microscopic Bogoliubov-de Gennes equations solved within a tight-binding model in the clean limit. The influence of the ferromagnet and conical magnet layer thickness on the induced equal-spin spin-triplet pairing correlations is obtained and compared to available experimental data. It is shown that, in agreement with experiment, a critical minimum thickness of conical magnet layers has to be present in order to observe a sizeable amount of equal-spin spin-triplet pairing correlations.Comment: 8 pages, 6 figure

Proximity effect in superconductor/conical magnet/ferromagnet heterostructures

At the interface between a superconductor and a ferromagnetic metal spin-singlet Cooper pairs can penetrate into the ferromagnetic part of the heterostructure with an oscillating and decaying spin-singlet Cooper pair density. However, if the interface allows for a spin-mixing effect, equal-spin spin-triplet Cooper pairs can be generated that can penetrate much further into the ferromagnetic part of the heterostructure, known as the long-range proximity effect. Here, we present results of spin-mixing based on self-consistent solutions of the microscopic Bogoliubov-de Gennes equations incorporating a tight-binding model. In particular, we include a conical magnet into our model heterostructure to generate the spin-triplet Cooper pairs and analyse the influence of conical and ferromagnetic layer thickness on the unequal-spin and equal-spin spin-triplet pairing correlations. It will be show that, in agreement with experimental observations, a minimum thickness of the conical magnet is necessary to generate a sufficient amount of equal-spin spin-triplet Cooper pairs allowing for the long-range proximity effect.Comment: 14 pages, 7 figures, 1 tabl

Proximity effect in superconductor/conical magnet heterostructures

The presence of a spin-flip potential at the interface between a superconductor and a ferromagnetic metal allows for the generation of equal-spin spin-triplet Cooper pairs. These Cooper pairs are compatible with the exchange interaction within the ferromagnetic region and hence allow for the long-range proximity effect through a ferromagnet or half-metal. One suitable spin-flip potential is provided by incorporating the conical magnet Holmium (Ho) into the interface. The conical magnetic structure is characterised by an opening angle $\alpha$ with respect to the crystal $c$-axis and a turning (or pitch) angle $\beta$ measuring the rotation of magnetisation with respect to the adjacent layers. Here, we present results showing the influence of conical magnet interface layers with varying $\alpha$ and $\beta$ on the efficiency of the generation of equal-spin spin-triplet pairing. The results are obtained by self-consistent solutions of the microscopic Bogoliubov$-$de Gennes equations in the clean limit within a tight-binding model of the heterostructure. In particular, the dependence of unequal-spin and equal-spin spin-triplet pairing correlations on the conical magnetic angles $\alpha$ and $\beta$ are discussed in detail.Comment: 12 pages, 6 figure

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