Entropy Distance: New Quantum Phenomena

We study a curve of Gibbsian families of complex 3x3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology and information geometry. This research is motivated by a theory of info-max principles, where we contribute by computing first order optimality conditions of the entropy distance.Comment: 34 pages, 5 figure

Strongly birefringent cut-wire pair structure as negative index wave plates at THz frequencies

We report a new approach for the design and fabrication of thin wave plates with high transmission in the terahertz (THz) regime. The wave plates are based on strongly birefringent cut-wire pair metamaterials that exhibit refractive indices of opposite signs for two orthogonal polarization components of an incident wave. As specific examples, we fabricated and investigated a quarter- and a half-wave plate that revealed a peak intensity transmittance of 74% and 58% at 1.34 THz and 1.3 THz, respectively. Furthermore, the half wave plate displayed a maximum figure of merit (FOM) of 23 at 1.3 THz where the refractive index was -1.7. This corresponds to one of the highest FOMs reported at THz frequencies so far. The presented results evidence that negative index materials enter an application stage in terms of optical components for the THz technology.Comment: 4 pages, 3 figures, submitted to Appl. Phys. Let

Optomechanically induced transparency

Coherent interaction of laser radiation with multilevel atoms and molecules can lead to quantum interference in the electronic excitation pathways. A prominent example observed in atomic three-level-systems is the phenomenon of electromagnetically induced transparency (EIT), in which a control laser induces a narrow spectral transparency window for a weak probe laser beam. The concomitant rapid variation of the refractive index in this spectral window can give rise to dramatic reduction of the group velocity of a propagating pulse of probe light. Dynamic control of EIT via the control laser enables even a complete stop, that is, storage, of probe light pulses in the atomic medium. Here, we demonstrate optomechanically induced transparency (OMIT)--formally equivalent to EIT--in a cavity optomechanical system operating in the resolved sideband regime. A control laser tuned to the lower motional sideband of the cavity resonance induces a dipole-like interaction of optical and mechanical degrees of freedom. Under these conditions, the destructive interference of excitation pathways for an intracavity probe field gives rise to a window of transparency when a two-photon resonance condition is met. As a salient feature of EIT, the power of the control laser determines the width and depth of the probe transparency window. OMIT could therefore provide a new approach for delaying, slowing and storing light pulses in long-lived mechanical excitations of optomechanical systems, whose optical and mechanical properties can be tailored in almost arbitrary ways in the micro- and nano-optomechanical platforms developed to date

Cubic Defects: Comparing the Eight-State-System with its Two-Level-Approximation

Substitutional defects in a cubic symmetry (such as a lithium defect in a KCl host crystal) can be modeled appropriately by an eight-state-system. Usually this tunneling degree of freedom is approximated by a two-level-system. We investigate the observable differences between the two models in three contexts. First we show that the two models predict different relations between the temperature dependence of specific heat and static susceptibility. Second we demonstrate that in the presence of external forces (pressure and electric field) the eight-state-system shows features that cannot be understood within the framework of the two-level-approximation. In this context we propose an experiment for measuring the parameter for tunneling along the face diagonal. Finally we discuss the differences between the models appearing for strongly coupled pairs. Geometric selection rules and particular forms of asymmetry lead to clear differences between the two models.Comment: 19 pages, Latex, submitted to J. of Phys., some small supplement

Eta Carinae across the 2003.5 Minimum: Analysis in the visible and near infrared spectral region

We present an analysis of the visible through near infrared spectrum of Eta Carinae and its ejecta obtained during the "Eta Carinae Campaign with the UVES at the ESO VLT". This is a part of larger effort to present a complete Eta Carinae spectrum, and extends the previously presented analyses with the HST/STIS in the UV (1240-3159 A) to 10,430 A. The spectrum in the mid and near UV is characterized by the ejecta absorption. At longer wavelengths, stellar wind features from the central source and narrow emission lines from the Weigelt condensations dominate the spectrum. However, narrow absorption lines from the circumstellar shells are present. This paper provides a description of the spectrum between 3060 and 10,430 A, including line identifications of the ejecta absorption spectrum, the emission spectrum from the Weigelt condensations and the P-Cygni stellar wind features. The high spectral resolving power of VLT/UVES enables equivalent width measurements of atomic and molecular absorption lines for elements with no transitions at the shorter wavelengths. However, the ground based seeing and contributions of nebular scattered radiation prevent direct comparison of measured equivalent widths in the VLT/UVES and HST/STIS spectra. Fortunately, HST/STIS and VLT/UVES have a small overlap in wavelength coverage which allows us to compare and adjust for the difference in scattered radiation entering the instruments' apertures. This paper provides a complete online VLT/UVES spectrum with line identifications and a spectral comparison between HST/STIS and VLT/UVES between 3060 and 3160 A.Comment: 13 pages, 11 figures + atlas. The paper accepted for the ApJS and is accompanied with an atlas in the online edition pape

Rotational levels in quantum dots

Low energy spectra of isotropic quantum dots are calculated in the regime of low electron densities where Coulomb interaction causes strong correlations. The earlier developed pocket state method is generalized to allow for continuous rotations. Detailed predictions are made for dots of shallow confinements and small particle numbers, including the occurance of spin blockades in transport.Comment: RevTeX, 10 pages, 2 figure

Petrology and Geochemistry of Volcanic Rocks from the South Kauaʻi Swell Volcano, Hawaiʻi: Implications for the Lithology and Composition of the Hawaiian Mantle Plume

The South Kauaʻi Swell (SKS) volcano was sampled during four JASON dives and three dredge hauls recovering rocks that range from fresh pillow lavas to altered volcanic breccias. Two geochemical groups were identified: shield-stage tholeiites (5·4–3·9 Ma) and rejuvenation-stage alkalic lavas (1·9–0·1 Ma). The young SKS ages and the coeval rejuvenated volcanism along a 400km segment of the Hawaiian Islands (Maui to Niʻihau) are inconsistent with the timing and duration predictions by the flexure and secondary plume melting models for renewed volcanism. The SKS tholeiites are geochemically heterogeneous but similar to lavas from nearby Kauaʻi, Niʻihau and Waiʻanae volcanoes, indicating that their source regions within the Hawaiian mantle plume sampled a well-mixed zone. Most SKS tholeiitic lavas exhibit radiogenic Pb isotope ratios (208Pb*/206Pb*) that are characteristic of Loa compositions (>0·9475), consistent with the volcano’s location on the west side of the Hawaiian Islands. These results document the existence of the Loa component within the Hawaiian mantle plume prior to 5 Ma. Loa trend volcanoes are thought to have a major pyroxenite component in their source. Calculations of the pyroxenitic component in the parental melts for SKS tholeiites using high-precision olivine analyses and modeling of trace element ratios indicate a large pyroxenite proportion (≥50%), which was predicted by recent numerical models. Rejuvenation-stage lavas were also found to have a significant pyroxenite component based on olivine analyses (40–60%). The abundance of pyroxenite in the source for SKS lavas may be the cause of this volcano’s extended period of magmatism (>5 Myr). The broad distribution of the Loa component in the northern Hawaiian Island lavas coincides with the start of a dramatic magma flux increase (300%) along the Hawaiian Chain, which may reflect a major structural change in the source of the Hawaiian mantle plume

Continuity of the Maximum-Entropy Inference

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur