Implementation of Grover's Quantum Search Algorithm in a Scalable System

We report the implementation of Grover's quantum search algorithm in the scalable system of trapped atomic ion quantum bits. Any one of four possible states of a two-qubit memory is marked, and following a single query of the search space, the marked element is successfully recovered with an average probability of 60(2)%. This exceeds the performance of any possible classical search algorithm, which can only succeed with a maximum average probability of 50%.Comment: 4 pages, 3 figures, updated error discussio

Phase Control of Trapped Ion Quantum Gates

There are several known schemes for entangling trapped ion quantum bits for large-scale quantum computation. Most are based on an interaction between the ions and external optical fields, coupling internal qubit states of trapped-ions to their Coulomb-coupled motion. In this paper, we examine the sensitivity of these motional gate schemes to phase fluctuations introduced through noisy external control fields, and suggest techniques to suppress the resulting phase decoherence.Comment: 21 pages 12 figure

Entanglement of Trapped-Ion Clock States

A M{\o}lmer-S{\o}rensen entangling gate is realized for pairs of trapped $^{111}$Cd$^+$ ions using magnetic-field insensitive "clock" states and an implementation offering reduced sensitivity to optical phase drifts. The gate is used to generate the complete set of four entangled states, which are reconstructed and evaluated with quantum-state tomography. An average target-state fidelity of 0.79 is achieved, limited by available laser power and technical noise. The tomographic reconstruction of entangled states demonstrates universal quantum control of two ion-qubits, which through multiplexing can provide a route to scalable architectures for trapped-ion quantum computing.Comment: 6 pages, 5 figure

Oscillations of a rapidly rotating annular Bose-Einstein condensate

A time-dependent variational Lagrangian analysis based on the Gross-Pitaevskii energy functional serves to study the dynamics of a metastable giant vortex in a rapidly rotating Bose-Einstein condensate. The resulting oscillation frequencies of the core radius reproduce the trends seen in recent experiments [Engels et al., Phys. Rev. Lett. 90, 170405 (2003)], but the theoretical values are smaller by a factor approximately 0.6-0.8.Comment: 7 pages, revtex

Rapidly rotating Bose-Einstein condensates in anharmonic potentials

Rapidly rotating Bose-Einstein condensates confined in anharmonic traps can exhibit a rich variety of vortex phases, including a vortex lattice, a vortex lattice with a hole, and a giant vortex. Using an augmented Thomas-Fermi variational approach to determine the ground state of the condensate in the rotating frame -- valid for sufficiently strongly interacting condensates -- we determine the transitions between these three phases for a quadratic-plus-quartic confining potential. Combining the present results with previous numerical simulations of small rotating condensates in such anharmonic potentials, we delineate the general structure of the zero temperature phase diagram.Comment: 5 pages, 5 figure

Diffused vorticity approach to the oscillations of a rotating Bose-Einstein condensate confined in a harmonic plus quartic trap

The collective modes of a rotating Bose-Einstein condensate confined in an attractive quadratic plus quartic trap are investigated. Assuming the presence of a large number of vortices we apply the diffused vorticity approach to the system. We then use the sum rule technique for the calculation of collective frequencies, comparing the results with the numerical solution of the linearized hydrodynamic equations. Numerical solutions also show the existence of low-frequency multipole modes which are interpreted as vortex oscillations.Comment: 10 pages, 4 figure

Vortex precession in Bose-Einstein condensates: observations with filled and empty cores

We have observed and characterized the dynamics of singly quantized vortices in dilute-gas Bose-Einstein condensates. Our condensates are produced in a superposition of two internal states of 87Rb, with one state supporting a vortex and the other filling the vortex core. Subsequently, the state filling the core can be partially or completely removed, reducing the radius of the core by as much as a factor of 13, all the way down to its bare value. The corresponding superfluid rotation rates, evaluated at the core radius, vary by a factor of 150, but the precession frequency of the vortex core about the condensate axis changes by only a factor of two.Comment: 4 pages, 3 figure

Efficient Photoionization-Loading of Trapped Cadmium Ions with Ultrafast Pulses

Atomic cadmium ions are loaded into radiofrequency ion traps by photoionization of atoms in a cadmium vapor with ultrafast laser pulses. The photoionization is driven through an intermediate atomic resonance with a frequency-quadrupled mode-locked Ti:Sapphire laser that produces pulses of either 100 fsec or 1 psec duration at a central wavelength of 229 nm. The large bandwidth of the pulses photoionizes all velocity classes of the Cd vapor, resulting in high loading efficiencies compared to previous ion trap loading techniques. Measured loading rates are compared with a simple theoretical model, and we conclude that this technique can potentially ionize every atom traversing the laser beam within the trapping volume. This may allow the operation of ion traps with lower levels of background pressures and less trap electrode surface contamination. The technique and laser system reported here should be applicable to loading most laser-cooled ion species.Comment: 11 pages, 12 figure

Kelvin Modes of a fast rotating Bose-Einstein Condensate

Using the concept of diffused vorticity and the formalism of rotational hydrodynamics we calculate the eigenmodes of a harmonically trapped Bose-Einstein condensate containing an array of quantized vortices. We predict the occurrence of a new branch of anomalous excitations, analogous to the Kelvin modes of the single vortex dynamics. Special attention is devoted to the excitation of the anomalous scissors mode.Comment: 7 pages, 3 figures, submitted to Phys. Rev.

Stability of rotating states in a weakly-interacting Bose-Einstein condensate

We investigate the lowest state of a rotating, weakly-interacting Bose-Einstein condensate trapped in a harmonic confining potential that is driven by an infinitesimally asymmetric perturbation. Although in an axially-symmetric confining potential the gas has an axially-symmetric single-particle density distribution, we show that in the presence of the small asymmetric perturbation its lowest state is the one given by the mean-field approximation, which is a broken-symmetric state. We also estimate the rate of relaxation of angular momentum when the gas is no longer driven by the asymmetric perturbation and identify two regimes of "slow" and "fast" relaxation. States of certain symmetry are found to be more robust.Comment: 6 pages, RevTe