Quantifying non-Markovianity of continuous-variable Gaussian dynamical maps

We introduce a non-Markovianity measure for continuous-variable open quantum systems based on the idea put forward in H.-P. Breuer, that is, by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow of information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit

Promoting Metacognition and Motivation of Exceptional Children

Metacognition fosters independent learning by providing personal insight into one's own thinking. Such awareness can lead to flexible and confident problem solving as well as feelings of self-efficacy and pride. This is especially important for students who encounter difficulty in school because they do not understand how to appraise and manage their own resources for learning. Too often, students develop debilitating expectations and behavior that undermine learning in school and inhibit transfer of effective learning strategies. We describe four general kinds of instruction that help students learn to think: metacognitive explanation, scaffolded instruction, cognitive coaching, and cooperative learning. Teachers can adapt and combine these methods to teach students how to think as they read, write, and compute in classrooms.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69089/2/10.1177_074193259001100604.pd

On the relationship of congruence closureand unification

Congruence closure is a fundamental operation for symbolic computation. Unification closureis defined as its directional dual, i.e., on the same inputs but top-down as opposed to bottom-up. Unifying terms is another fundamental operation for symbolic computation and is commonly computed using unification closure. We clarify the directional duality by reducing unification closure to a special form of congruence closure. This reduction reveals a correspondence between repeated variables in terms to be unified and equalities of monadic ground terms. We then show that: (1) single equality congruence closure on a directed acyclic graph, and (2) acyclic congruence closure of a fixed number of equalities, are in the parallel complexity class NC. The directional dual unification closures in these two cases are known to be log-space complete for PTIME. As a consequence of our reductions we show that if the number of repeated variables in the input terms is fixed, then term unification can be performed in NC; this extends the known parallelizable cases of term unification. Using parallel complexity we also clarify the relationship of unification closure and the testing of deterministic finite automata for equivalence

Free-Space Quantum Electrodynamics with a single Rydberg superatom

The interaction of a single photon with an individual two-level system is the textbook example of quantum electrodynamics. Achieving strong coupling in this system so far required confinement of the light field inside resonators or waveguides. Here, we demonstrate strong coherent coupling between a single Rydberg superatom, consisting of thousands of atoms behaving as a single two-level system due to the Rydberg blockade, and a propagating light pulse containing only a few photons. The strong light-matter coupling in combination with the direct access to the outgoing field allows us to observe for the first time the effect of the interactions on the driving field at the single photon level. We find that all our results are in quantitative agreement with the predictions of the theory of a single two-level system strongly coupled to a single quantized propagating light mode. The demonstrated coupling strength opens the way towards interfacing photonic and atomic qubits and preparation of propagating non-classical states of light, two crucial building blocks in future quantum networks

How to make Dupire's local volatility work with jumps

There are several (mathematical) reasons why Dupire's formula fails in the non-diffusion setting. And yet, in practice, ad-hoc preconditioning of the option data works reasonably well. In this note we attempt to explain why. In particular, we propose a regularization procedure of the option data so that Dupire's local vol diffusion process recreates the correct option prices, even in manifest presence of jumps

Optimal unambiguous comparison of two unknown squeezed vacua

We propose a scheme for unambiguous state comparison (USC) of two unknown squeezed vacuum states of an electromagnetic field. Our setup is based on linear optical elements and photon-number detectors, and achieves optimal USC in an ideal case of unit quantum efficiency. In realistic conditions, i.e., for non-unit quantum efficiency of photodetectors, we evaluate the probability of getting an ambiguous result as well as the reliability of the scheme, thus showing its robustness in comparison to previous proposals.Comment: 7 pages, 4 figures (revised version

Observation of three-body correlations for photons coupled to a Rydberg superatom

We report on the experimental observation of non-trivial three-photon correlations imprinted onto initially uncorrelated photons through interaction with a single Rydberg superatom. Exploiting the Rydberg blockade mechanism, we turn a cold atomic cloud into a single effective emitter with collectively enhanced coupling to a focused photonic mode which gives rise to clear signatures in the connected part of the three-body correlation function of the out-going photons. We show that our results are in good agreement with a quantitative model for a single, strongly coupled Rydberg superatom. Furthermore, we present an idealized but exactly solvable model of a single two-level system coupled to a photonic mode, which allows for an interpretation of our experimental observations in terms of bound states and scattering states

Carbon capture using wastes: A review

Potential key strategies for the management of anthropogenic CO2 emissions include mineral carbonation and storage in oil wells and in the oceans. In Europe, a large-scale demonstration of carbon capture and storage (CCS) has recently been given the go-ahead, and the application of mineral carbonation technology (MCT) to serpentine and olive-type minerals. Although less controversial in its approach, MCT involves intensive pre-treatment of the mineral feedstock, and a consequent high sequestration cost USD100-120/tonne CO2 treated. Mineralisation by carbonation is reliant upon the long-term storage of CO2 in thermodynamically stable and environmentally benign carbonate-based reaction products that are persistent over geological-timescales. The use of solid industrial process wastes for storing carbon (via waste carbonation technology, WCT) may provide a shorter-term gain, as the industrialisation of CO2 mitigation technologies takes place. With WCT, CO2 is reacted with alkaline waste residues, to both risk-manage a high pH, and utilise waste CO2 gas, can be used as a pre-treatment prior to landfilling, facilitate valorisation and production of new materials. The present work examines the current status of waste carbonation and investigates the utilisation of seven ‘common’ alkaline industrial residues showing that they have potential to sequestrate 1Gtonne of CO2 worldwide. The projected average cost of USD38-95/tonne of CO2, is competitive with landfill and projected carbon taxes. If WCT is more widely commercially developed an option for the management of significant amounts of carbon could become more quickly established