Single-photon, cavity-mediated gates: detuning, losses, and non-adiabatic effects

We study several extensions of the single-photon, cavity-mediated quantum logical gates recently proposed by Koshino, Ishizaka and Nakamura: to a double-sided cavity configuration, to the case where the two atomic ground states are nondegenerate, and to include nonadiabatic corrections. Our analysis can be used to estimate the effects of various imperfections, and to prepare the way for a proof-of-principle demonstration with present technology. An interesting result is that the leading correction to the adiabatic approximation can be made to vanish for a suitable choice of detunings, provided the cavity is "good enough" (high enough ratio of coupling to loss). This could significantly relax the need for long single-photon pulses.Comment: 11 pages, 9 figures; to appear in Physical Review

"Modes of the universe" study of two-photon deterministic, passive quantum logical gates

We use the "modes of the universe" approach to study a cavity-mediated two-photon logical gate recently proposed by Koshino, Ishizaka and Nakamura. We clarify the relationship between the more commonly used input-output formalism, and that of Koshino et al., and show that some elements of this gate had been anticipated by other authors. We conclude that their proposed gate can work both in the good and bad cavity limits, provided only that the pulses are long enough. Our formalism allows us to estimate analytically the size of the various error terms, and to follow the spectral evolution of the field + cavity system in the course of the interaction.Comment: 9 pages, 8 figure

Positive Psychology Within a Cultural Context

As our capacity for communication with nations across the globe increases through the advances of technology, our interactions with others with different worldviews also become more frequent. This exposure to diversity on so many levels requires a better understanding of the multiple contexts in which people from different cultural backgrounds live and the strengths they possess that help them experience well-being. In order to define the characteristics that my be viewed as strengths in different groups, we must make efforts to remember that cultural rules and norms often dictate what can be called a strength versus a weakness. It is imperative that we are able to recognize that strengths may look very different in different contexts and that these diverse manifestations may come from a variety of worldviews. More work must be done in order to develop a better understanding of the way that cultural context plays a role in the operationalization, manifestation, and measurement of strengths in diverse groups. The following chapter provides a history of the connections between culture and positive psychology and discusses current issues regarding the link between cultural context and various personal characteristics. Examples from culturally sensitive positive psychology theory and research are also given in order to illustrate how researchers are better exploring positive psychology within a cultural context

Theory of photon coincidence statistics in photon-correlated beams

The statistics of photon coincidence counting in photon-correlated beams is thoroughly investigated considering the effect of the finite coincidence resolving time. The correlated beams are assumed to be generated using parametric downconversion, and the photon streams in the correlated beams are modeled by two partially correlated Poisson point processes. An exact expression for the mean rate of coincidence registration is developed using techniques from renewal theory. It is shown that the use of the traditional approximate rate, in certain situations, leads to the overestimation of the actual rate. The error between the exact and approximate coincidence rates increases as the coincidence-noise parameter, defined as the mean number of uncorrelated photons detected per coincidence resolving time, increases. The use of the exact statistics of the coincidence becomes crucial when the background noise is high or in cases when high precision measurement of coincidence is required. Such cases arise whenever the coincidence-noise parameter is even slightly in excess of zero. It is also shown that the probability distribution function of the time between consecutive coincidence registration can be well approximated by an exponential distribution function. The well-known and experimentally verified Poissonian model of the coincidence registration process is therefore theoretically justified. The theory is applied to an on-off keying communication system proposed by Mandel which has been shown to perform well in extremely noisy conditions. It is shown that the bit-error rate (BER) predicted by the approximate coincidence-rate theory can be significantly lower than the actual BER obtained using the exact theory

Photon Statistics of a Single Atom Laser

We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as β, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for β are 0.01\u3cβ\u3c1.0. We find that for large enough β, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as β is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with β values in the range considered here. As β is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results

Conicoid Mirrors

The first order equation relating object and image location for a mirror of arbitrary conic-sectional shape is derived. It is also shown that the parabolic reflecting surface is the only one free of aberration and only in the limiting case of distant sources.Comment: 9 page

An analytical model for the control of silica grout penetration in natural groundwater systems

Over the last three decades, colloidal silica has been investigated and more recently adopted as a low viscosity grouting technology (e.g. for grouting rock fractures within geological disposal facilities nuclear waste). The potential of colloidal silica as a favourable grouting material exists due to: its initial low viscosity; its low hydraulic conductivity after gelling (of the order of 10-7 cm/s); the very low injection pressures required; its controllable set/gel times (from minutes to several days); the fact it is environmentally inert; its small particle size (less than hundreds of nanometres) and its cost-effectiveness. Despite the documented success of colloidal silica based grouts for hydraulic barrier formation, research has not translated into widespread industrial use. A key factor in this limited commercial uptake is the lack of a predictive model for grout gelling which controls grout penetration: whilst data are available to underpin design of a grouting campaign in laboratory conditions, little research has been done to underpin applications in natural environments. Here we develop and validate an analytical model of colloidal silica gelling in groundwaters with varying pH and background electrolyte concentrations. This paper presents an analytical model that accounts for changes in pH, electrolyte concentration, cation valency and molar mass, silica particle size and silica concentration giving predictive capability without the need for site-specific calibration. The model is validated against experimental observations for gel times of 32 minutes to 766 minutes, the model accurately predicts the log(gel time) with an average error of 4% which corresponds to an R2 value of 0.96 The model is then applied to a hypothetical case study to demonstrate its use in grout design, based on published in-situ groundwater data from the Olkiluoto area of Finland. The model successfully predicts the required accelerator concentration to achieve a grout gel time of approximately 50 minutes, taking into account the cations already present within the synthetic groundwater

Deterministic and Probabilistic Binary Search in Graphs

We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to querying a node $q$, the algorithm learns either that $q$ is the target, or is given an edge out of $q$ that lies on a shortest path from $q$ to the target. We study this problem in a general noisy model in which each query independently receives a correct answer with probability $p > \frac{1}{2}$ (a known constant), and an (adversarial) incorrect one with probability $1-p$. Our main positive result is that when $p = 1$ (i.e., all answers are correct), $\log_2 n$ queries are always sufficient. For general $p$, we give an (almost information-theoretically optimal) algorithm that uses, in expectation, no more than $(1 - \delta)\frac{\log_2 n}{1 - H(p)} + o(\log n) + O(\log^2 (1/\delta))$ queries, and identifies the target correctly with probability at leas $1-\delta$. Here, $H(p) = -(p \log p + (1-p) \log(1-p))$ denotes the entropy. The first bound is achieved by the algorithm that iteratively queries a 1-median of the nodes not ruled out yet; the second bound by careful repeated invocations of a multiplicative weights algorithm. Even for $p = 1$, we show several hardness results for the problem of determining whether a target can be found using $K$ queries. Our upper bound of $\log_2 n$ implies a quasipolynomial-time algorithm for undirected connected graphs; we show that this is best-possible under the Strong Exponential Time Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs with non-uniform node querying costs, the problem is PSPACE-complete. For a semi-adaptive version, in which one may query $r$ nodes each in $k$ rounds, we show membership in $\Sigma_{2k-1}$ in the polynomial hierarchy, and hardness for $\Sigma_{2k-5}$