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

Detecting unambiguously non-Abelian geometric phases with trapped ions

We propose for the first time an experimentally feasible scheme to disclose the noncommutative effects induced by a light-induced non-Abelian gauge structure with trapped ions. Under an appropriate configuration, a true non-Abelian gauge potential naturally arises in connection with the geometric phase associated with two degenerated dark states in a four-state atomic system interacting with three pulsed laser fields. We show that the population in atomic state at the end of a composed path formed by two closed loops $C_1$ and $C_2$ in the parameter space can be significantly different from the composed counter-ordered path. This population difference is directly induced by the noncommutative feature of non-Abelian geometric phases and can be detected unambiguously with current technology.Comment: 6 page

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

Magneto-optical Trapping of Cadmium

We report the laser-cooling and confinement of Cd atoms in a magneto-optical trap, and characterize the loading process from the background Cd vapor. The trapping laser drives the 1S0-1P1 transition at 229 nm in this two-electron atom and also photoionizes atoms directly from the 1P1 state. This photoionization overwhelms the other loss mechanisms and allows a direct measurement of the photoionization cross section, which we measure to be 2(1)x10^(-16)cm^(2) from the 1P1 state. When combined with nearby laser-cooled and trapped Cd^(+) ions, this apparatus could facilitate studies in ultracold interactions between atoms and ions.Comment: 8 pages, 11 figure

Relativity, rank and the utility of income

This is the accepted version of the following article: Rablen, M. D. (2008), Relativity, Rank and the Utility of Income. The Economic Journal, 118: 801–821, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0297.2008.02143.x/abstract.Relative utility has become an important concept in several disjoint areas of economics. I present a cardinal model of income utility based on the supposition that agents care about their rank in the income distribution and that utility is subject to adaptation over time. Utility levels correspond to the Leyden Individual Welfare Function while utility differences yield a version of the prospect theory value function, thereby providing a new and shared derivation of each. I offer an explanation of some long-standing paradoxes in the wellbeing literature and an insight into the links between relative comparisons and loss aversion.ESR

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

The use of happiness research for public policy

Research on happiness tends to follow a "benevolent dictator" approach where politicians pursue people's happiness. This paper takes an antithetic approach based on the insights of public choice theory. First, we inquire how the results of happiness research may be used to improve the choice of institutions. Second, we show that the policy approach matters for the choice of research questions and the kind of knowledge happiness research aims to provide. Third, we emphasize that there is no shortcut to an optimal policy maximizing some happiness indicator or social welfare function since governments have an incentive to manipulate this indicator

Precautionary Regulation in Europe and the United States: A Quantitative Comparison

Much attention has been addressed to the question of whether Europe or the United States adopts a more precautionary stance to the regulation of potential environmental, health, and safety risks. Some commentators suggest that Europe is more risk-averse and precautionary, whereas the US is seen as more risk-taking and optimistic about the prospects for new technology. Others suggest that the US is more precautionary because its regulatory process is more legalistic and adversarial, while Europe is more lax and corporatist in its regulations. The flip-flop hypothesis claims that the US was more precautionary than Europe in the 1970s and early 1980s, and that Europe has become more precautionary since then. We examine the levels and trends in regulation of environmental, health, and safety risks since 1970. Unlike previous research, which has studied only a small set of prominent cases selected non-randomly, we develop a comprehensive list of almost 3,000 risks and code the relative stringency of regulation in Europe and the US for each of 100 risks randomly selected from that list for each year from 1970 through 2004. Our results suggest that: (a) averaging over risks, there is no significant difference in relative precaution over the period, (b) weakly consistent with the flip-flop hypothesis, there is some evidence of a modest shift toward greater relative precaution of European regulation since about 1990, although (c) there is a diversity of trends across risks, of which the most common is no change in relative precaution (including cases where Europe and the US are equally precautionary and where Europe or the US has been consistently more precautionary). The overall finding is of a mixed and diverse pattern of relative transatlantic precaution over the period