Dark-State Polaritons in Single- and Double-Λ\Lambda Media

We derive the properties of polaritons in single-$\Lambda$ and double-$\Lambda$ media using a microscopic equation-of-motion technique. In each case, the polaritonic dispersion relation and composition arise from a matrix eigenvalue problem for arbitrary control field strengths. We show that the double-$\Lambda$ medium can be used to up- or down-convert single photons while preserving quantum coherence. The existence of a dark-state polariton protects this single-photon four-wave mixing effect against incoherent decay of the excited atomic states. The efficiency of this conversion is limited mainly by the sample size and the lifetime of the metastable state.Comment: 7 pages, 6 figure

Corporate Hierarchies and the Size of Nations: Theory and Evidence

Corporate organization varies within a country and across countries with country size. The paper starts by establishing some facts about corporate organization based on unique data of 660 Austrian and German corporations. The larger country (Germany) has larger firms with flatter more decentral corporate hierarchies compared to the smaller country (Austria). Firms in the larger country change their organization less fast than firms in the smaller country. Over time firms have been introducing less hierarchical organizations by delegating power to lower levels of the corporation. We develop a theory which explains these facts and which links these features to the trade environment that countries and firms face. We introduce firms with internal hierarchies in a Krugman (1980) model of trade. We show that international trade and the toughness of competition in international markets induce a power struggle in firms which eventually leads to decentralized corporate hierarchies. We offer econometric evidence which is consistent with the models predictions

Power in the Multinational Corporation in Industry Equilibrium

Recent theories of the multinational corporation introduce the property rights model of the firm and examine whether to integrate our outsource firm activities locally or to a foreign country. This paper focus instead on the internal organization of the multinational corporation by examining the power allocation between headquarters and subsidiaries. We provide a framework to analyse the interaction between the decision to serve the local market by exporting or FDI, market acces and the optimal mode of organization of the multinational corporation. We find that subsidiary managers are given most autonomy in their decision how to run the firm at intermediate levels of local competition. We then provide comparative statics for changes in fixed FDI entry costs and trade costs, information technology, the number of local competitors, and in the size of the local market

Weyl points and line nodes in gapless gyroid photonic crystals

Weyl points and line nodes are three-dimensional linear point- and line-degeneracies between two bands. In contrast to Dirac points, which are their two-dimensional analogues, Weyl points are stable in the momentum space and the associated surface states are predicted to be topologically non-trivial. However, Weyl points are yet to be discovered in nature. Here, we report photonic crystals, based on the double-gyroid structures, exhibiting frequency-isolated Weyl points with intricate phase diagrams. The surface states associated with the non-zero Chern numbers are demonstrated. Line nodes are also found in similar geometries; the associated surface states are shown to be flat bands. Our results are readily experimentally realizable at both microwave and optical frequencies.Comment: 6 figures and 8 pages including the supplementary informatio

Reflection nebulae in the Galactic Center: the case for soft X-ray imaging polarimetry

The origin of irradiation and fluorescence of the 6.4 keV bright giant molecular clouds surrounding Sgr A*, the central supermassive black hole of our Galaxy, remains enigmatic. Testing the theory of a past active period of Sgr A* requires X-ray polarimetry. In this paper, we show how modern imaging polarimeters could revolutionize our understanding of the Galactic Center. Through Monte Carlo modeling, we produce a 4-8 keV polarization map of the Galactic Center, focusing on the polarimetric signature produced by Sgr B1, Sgr B2, G0.11-0.11, Bridge E, Bridge D, Bridge B2, MC2, MC1, Sgr C3, Sgr C2, and Sgr C1. We estimate the resulting polarization, include polarized flux dilution by the diffuse plasma emission detected toward the GC, and simulate the polarization map that modern polarimetric detectors would obtain assuming the performances of a mission prototype. The eleven reflection nebulae investigated in this paper present a variety of polarization signatures, ranging from nearly unpolarized to highly polarized (about 77%) fluxes. A major improvement in our simulation is the addition of a diffuse, unpolarized plasma emission that strongly impacts soft X-ray polarized fluxes. The dilution factor is in the range 50% - 70%, making the observation of the Bridge structure unlikely even in the context of modern polarimetry. The best targets are the Sgr B and Sgr C complexes, and the G0.11-0.11 cloud. An exploratory observation of a few hundred kilo-seconds of the Sgr B complex would allow a significant detection of the polarization and be sufficient to derive hints on the primary source of radiation. A more ambitious program (few Ms) of mapping the giant molecular clouds could then be carried out to probe with great precision the turbulent history of Sgr A*, and place important constraints on the composition and three-dimensional position of the surrounding gas.Comment: 7 pages, 3 figures, 2 tables, accepted for publication in A&