Measuring a coherent superposition

We propose a simple method for measuring the populations and the relative phase in a coherent superposition of two atomic states. The method is based on coupling the two states to a third common (excited) state by means of two laser pulses, and measuring the total fluorescence from the third state for several choices of the excitation pulses.Comment: 7 pages, 1 figure, twocolumn REVTe

The Gelfand map and symmetric products

If A is an algebra of functions on X, there are many cases when X can be regarded as included in Hom(A,C) as the set of ring homomorphisms. In this paper the corresponding results for the symmetric products of X are introduced. It is shown that the symmetric product Sym^n(X) is included in Hom(A,C) as the set of those functions that satisfy equations generalising f(xy)=f(x)f(y). These equations are related to formulae introduced by Frobenius and, for the relevant A, they characterise linear maps on A that are the sum of ring homomorphisms. The main theorem is proved using an identity satisfied by partitions of finite sets.Comment: 14 pages, Late

Six solutions for more reliable infant research

Infant research is often underpowered, undermining the robustness and replicability of our findings. Improving the reliability of infant studies offers a solution for increasing statistical power independent of sample size. Here, we discuss two senses of the term reliability in the context of infant research: reliable (large) effects and reliable measures. We examine the circumstances under which effects are strongest and measures are most reliable and use synthetic datasets to illustrate the relationship between effect size, measurement reliability, and statistical power. We then present six concrete solutions for more reliable infant research: (a) routinely estimating and reporting the effect size and measurement reliability of infant tasks, (b) selecting the best measurement tool, (c) developing better infant paradigms, (d) collecting more data points per infant, (e) excluding unreliable data from the analysis, and (f) conducting more sophisticated data analyses. Deeper consideration of measurement in infant research will improve our ability to study infant development

Embedding variables in finite dimensional models

Global problems associated with the transformation from the Arnowitt, Deser and Misner (ADM) to the Kucha\v{r} variables are studied. Two models are considered: The Friedmann cosmology with scalar matter and the torus sector of the 2+1 gravity. For the Friedmann model, the transformations to the Kucha\v{r} description corresponding to three different popular time coordinates are shown to exist on the whole ADM phase space, which becomes a proper subset of the Kucha\v{r} phase spaces. The 2+1 gravity model is shown to admit a description by embedding variables everywhere, even at the points with additional symmetry. The transformation from the Kucha\v{r} to the ADM description is, however, many-to-one there, and so the two descriptions are inequivalent for this model, too. The most interesting result is that the new constraint surface is free from the conical singularity and the new dynamical equations are linearization stable. However, some residual pathology persists in the Kucha\v{r} description.Comment: Latex 2e, 29 pages, no figure

Coherent properties of a tripod system coupled via a continuum

We present results from a study of the coherence properties of a system involving three discrete states coupled to each other by two-photon processes via a common continuum. This tripod linkage is an extension of the standard laser-induced continuum structure (LICS) which involves two discrete states and two lasers. We show that in the tripod scheme, there exist two population trapping conditions; in some cases these conditions are easier to satisfy than the single trapping condition in two-state LICS. Depending on the pulse timing, various effects can be observed. We derive some basic properties of the tripod scheme, such as the solution for coincident pulses, the behaviour of the system in the adiabatic limit for delayed pulses, the conditions for no ionization and for maximal ionization, and the optimal conditions for population transfer between the discrete states via the continuum. In the case when one of the discrete states is strongly coupled to the continuum, the population dynamics reduces to a standard two-state LICS problem (involving the other two states) with modified parameters; this provides the opportunity to customize the parameters of a given two-state LICS system

Crystallite size dependent cation distribution in nanostructured spinels studied by nmr, mössbauer spectroscopy and XPS

Owing to the structural flexibility of spinels, providing a wide range of physical and chemical behavior, these materials have been considered as a convenient model system for the investigation of the size dependent properties of complex ionic systems. In this work, quantitative formation is obtained on the crystallite size dependent ionic configuration in nanosized spinel oxides prepared by mechanochemical processing of the corresponding bulk materials. Experimentally determined values of the crystallite size and of the mean degree of inversion of nanostructured spinels are used to calculate the volume fraction of interfaces/surfaces and their thickness in the nanomaterials

Measuring the Density Matrix by Local Addressing

We introduce a procedure to measure the density matrix of a material system. The density matrix is addressed locally in this scheme by applying a sequence of delayed light pulses. The procedure is based on the stimulated Raman adiabatic passage (STIRAP) technique. It is shown that a series of population measurements on the target state of the population transfer process yields unambiguous information about the populations and coherences of the addressed states, which therefore can be determined.Comment: 4 pages, 1 figur

Molecular heat pump for rotational states

In this work we investigate the theory for three different uni-directional population transfer schemes in trapped multilevel systems which can be utilized to cool molecular ions. The approach we use exploits the laser-induced coupling between the internal and motional degrees of freedom so that the internal state of a molecule can be mapped onto the motion of that molecule in an external trapping potential. By sympathetically cooling the translational motion back into its ground state the mapping process can be employed as part of a cooling scheme for molecular rotational levels. This step is achieved through a common mode involving a laser-cooled atom trapped alongside the molecule. For the coherent mapping we will focus on adiabatic passage techniques which may be expected to provide robust and efficient population transfers. By applying far-detuned chirped adiabatic rapid passage pulses we are able to achieve an efficiency of better than 98% for realistic parameters and including spontaneous emission. Even though our main focus is on cooling molecular states, the analysis of the different adiabatic methods has general features which can be applied to atomic systems

Wormholes supported by chiral fields

We consider static, spherically symmetric solutions of general relativity with a nonlinear sigma model (NSM) as a source, i.e., a set of scalar fields $\Phi = (\Phi^1,...,\Phi^n)$ (so-called chiral fields) parametrizing a target space with a metric $h_{ab}(\Phi)$. For NSM with zero potential $V(\Phi)$, it is shown that the space-time geometry is the same as with a single scalar field but depends on $h_{ab}$. If the matrix $h_{ab}$ is positive-definite, we obtain the Fisher metric, originally found for a canonical scalar field with positive kinetic energy; otherwise we obtain metrics corresponding to a phantom scalar field, including singular and nonsingular horizons (of infinite area) and wormholes. In particular, the Schwarzschild metric can correspond to a nontrivial chiral field configuration, which in this case has zero stress-energy. Some explicit examples of chiral field configurations are considered. Some qualitative properties of NSM configurations with nonzero potentials are pointed out.Comment: 5 two-column pages, to appear in Grav. Cosmo

Covariant gauge fixing and Kuchar decomposition

The symplectic geometry of a broad class of generally covariant models is studied. The class is restricted so that the gauge group of the models coincides with the Bergmann-Komar group and the analysis can focus on the general covariance. A geometrical definition of gauge fixing at the constraint manifold is given; it is equivalent to a definition of a background (spacetime) manifold for each topological sector of a model. Every gauge fixing defines a decomposition of the constraint manifold into the physical phase space and the space of embeddings of the Cauchy manifold into the background manifold (Kuchar decomposition). Extensions of every gauge fixing and the associated Kuchar decomposition to a neighbourhood of the constraint manifold are shown to exist.Comment: Revtex, 35 pages, no figure