Many-body Rabi oscillations of Rydberg excitation in small mesoscopic samples

We investigate the collective aspects of Rydberg excitation in ultracold mesoscopic systems. Strong interactions between Rydberg atoms influence the excitation process and impose correlations between excited atoms. The manifestations of the collective behavior of Rydberg excitation are the many-body Rabi oscillations, spatial correlations between atoms as well as the fluctuations of the number of excited atoms. We study these phenomena in detail by numerically solving the many-body Schr\"edinger equation.Comment: 8 pages, 5 figure

Correlations of Rydberg excitations in an ultra-cold gas after an echo sequence

We show that Rydberg states in an ultra-cold gas can be excited with strongly preferred nearest-neighbor distance if densities are well below saturation. The scheme makes use of an echo sequence in which the first half of a laser pulse excites Rydberg states while the second half returns atoms to the ground state, as in the experiment of Raitzsch et al. [Phys. Rev. Lett. 100 (2008) 013002]. Near to the end of the echo sequence, almost any remaining Rydberg atom is separated from its next-neighbor Rydberg atom by a distance slightly larger than the instantaneous blockade radius half-way through the pulse. These correlations lead to large deviations of the atom counting statistics from a Poissonian distribution. Our results are based on the exact quantum evolution of samples with small numbers of atoms. We finally demonstrate the utility of the omega-expansion for the approximate description of correlation dynamics through an echo sequence.Comment: 8 pages, 6 figure

A Class Of Functional Equations And Mielnik Probability Spaces

Let S be the unit sphere of a normed real linear space N and let (S, p) be a Mielnik space of dimension two. For p(x, y) = f(‖x+y‖), x, yєS, where /is a continuous, strictly increasing function from [0, 2] onto [0, 1], it has been shown that (S, p) being two dimensional is equivalent to N being an inner product space. In some polarization problems modeled on the unit sphere of an inner product space, the transition probability p(x, y) may not be as well behaved as p(x, y) = f(‖x + y‖). In order to provide a more suitable setting, we have constructed wide classes of two-dimensional transitional probability spaces (S, p), all having the same set of bases ℬ with p=⌽ ° f where ⌽ is a solution of a certain functional equation. In particular, for p(x, y) = ‖x+y‖24, we answer a question due to B. Mielnik. © American Mathematical Society 1976

Controlling the quantum state of a single photon emitted from a single polariton

We investigate in detail the optimal conditions for a high fidelity transfer from a single-polariton state to a single-photon state and subsequent homodyne detection of the single photon. We assume that, using various possible techniques, the single polariton has initially been stored as a spin-wave grating in a cloud of cold atoms inside a low-finesse cavity. This state is then transferred to a single-photon optical pulse using an auxiliary beam. We optimize the retrieval efficiency and determine the mode of the local oscillator that maximizes the homodyne efficiency of such a photon. We find that both efficiencies can have values close to one in a large region of experimental parameters.Comment: 10 pages, 8 figure

Long-range potentials and (n−1)d+ns(n-1)d+ns molecular resonances in an ultracold rydberg gas

We have calculated long-range molecular potentials of the $0_g^{+}$, $0_u^{-}$ and $1_u$ symmetries between highly-excited rubidium atoms. Strong $np+np$ potentials characterized by these symmetries are important in describing interaction-induced phenomena in the excitation spectra of high $np$ Rydberg states. Long-range molecular resonances are such phenomena and they were first reported in S.M. Farooqi {\it et al.}, Phys. Rev. Lett. {\bf 91} 183002. One class of these resonances occurs at energies corresponding to excited atom pairs $(n-1)d+ns$. Such resonances are attributed to $\ell$-mixing due to Rydberg-Rydberg interactions so that otherwise forbidden molecular transitions become allowed. We calculate molecular potentials in Hund's case (c), use them to find the resonance lineshape and compare to experimental results.Comment: 11 pages, 7 figure

Rydberg trimers and excited dimers bound by internal quantum reflection

Quantum reflection is a pure wave phenomena that predicts reflection of a particle at a changing potential for cases where complete transmission occurs classically. For a chemical bond, we find that this effect can lead to non-classical vibrational turning points and bound states at extremely large interatomic distances. Only recently has the existence of such ultralong-range Rydberg molecules been demonstrated experimentally. Here, we identify a broad range of molecular lines, most of which are shown to originate from two different novel sources: a single-photon associated triatomic molecule formed by a Rydberg atom and two ground state atoms and a series of excited dimer states that are bound by a so far unexplored mechanism based on internal quantum reflection at a steep potential drop. The properties of the Rydberg molecules identified in this work qualify them as prototypes for a new type of chemistry at ultracold temperatures.Comment: 6 pages, 3 figures, 1 tabl

Trade-Offs in Relative Limb Length among Peruvian Children: Extending the Thrifty Phenotype Hypothesis to Limb Proportions

Background and Methods Both the concept of ‘brain-sparing’ growth and associations between relative lower limb length, childhood environment and adult disease risk are well established. Furthermore, tibia length is suggested to be particularly plastic under conditions of environmental stress. The mechanisms responsible are uncertain, but three hypotheses may be relevant. The ‘thrifty phenotype’ assumes that some components of growth are selectively sacrificed to preserve more critical outcomes, like the brain. The ‘distal blood flow’ hypothesis assumes that blood nutrients decline with distance from the heart, and hence may affect limbs in relation to basic body geometry. Temperature adaptation predicts a gradient of decreased size along the limbs reflecting decreasing tissue temperature/blood flow. We examined these questions by comparing the size of body segments among Peruvian children born and raised in differentially stressful environments. In a cross-sectional sample of children aged 6 months to 14 years (n = 447) we measured head circumference, head-trunk height, total upper and lower limb lengths, and zeugopod (ulna and tibia) and autopod (hand and foot) lengths. Results Highland children (exposed to greater stress) had significantly shorter limbs and zeugopod and autopod elements than lowland children, while differences in head-trunk height were smaller. Zeugopod elements appeared most sensitive to environmental conditions, as they were relatively shorter among highland children than their respective autopod elements. Discussion The results suggest that functional traits (hand, foot, and head) may be partially protected at the expense of the tibia and ulna. The results do not fit the predictions of the distal blood flow and temperature adaptation models as explanations for relative limb segment growth under stress conditions. Rather, our data support the extension of the thrifty phenotype hypothesis to limb growth, and suggest that certain elements of limb growth may be sacrificed under tough conditions to buffer more functional traits

Optimization of electricity trading using linear programming

In the last two decades, the liberalization of the electricity markets have been established in order to increase efficiency, harmonize and reduce electricity prices, make a better use of resources, give customers the right to choose their supplier and provide customers with a better service. This change made the electricity market competitive and introduced several new subjects. In this paper, we study one of these subjects: Electricity Trading Company (ETC) and its daily trading process. We present a linear mathematical model of total daily profit maximization subject to flow constraints. It is assumed that the demand and supply are known and some of them are arranged. Possible transmission capacities are known but also additional capacities can be purchased. All trading, transmission prices and amounts are subject of auctions. First, we present energy trading problem as directed multiple-source and multiple-sink network and then model it using linear programming. Also, we provide one realistic example which is slightly changed in order to save confidentiality of the given data