Breached pairing in trapped three-color atomic Fermi gases

We introduce an exactly solvable model for trapped three-color atom gases. Applications to a cigar-shaped trapped cold fermions reveal a complex structure of breached pairing phases. We find two competing superfluid phases at weak and intermediate couplings, each one with two color pair condensates, that can be distinguished from density profile measurements.Comment: 4 pages, 5 figure

Two-Photon-Absorption Scheme for Optical Beam Tracking

A new optical beam tracking approach for free-space optical communication links using two-photon absorption (TPA) in a high-bandgap detector material was demonstrated. This tracking scheme is part of the canonical architecture described in the preceding article. TPA is used to track a long-wavelength transmit laser while direct absorption on the same sensor simultaneously tracks a shorter-wavelength beacon. The TPA responsivity was measured for silicon using a PIN photodiode at a laser beacon wavelength of 1,550 nm. As expected, the responsivity shows a linear dependence with incident power level. The responsivity slope is 4.5 x 10(exp -7) A/W2. Also, optical beam spots from the 1,550-nm laser beacon were characterized on commercial charge coupled device (CCD) and complementary metal-oxide semiconductor (CMOS) imagers with as little as 13.7 microWatts of optical power (see figure). This new tracker technology offers an innovative solution to reduce system complexity, improve transmit/receive isolation, improve optical efficiency, improve signal-to-noise ratio (SNR), and reduce cost for free-space optical communications transceivers

Optimal Quantum Measurements of Expectation Values of Observables

Experimental characterizations of a quantum system involve the measurement of expectation values of observables for a preparable state |psi> of the quantum system. Such expectation values can be measured by repeatedly preparing |psi> and coupling the system to an apparatus. For this method, the precision of the measured value scales as 1/sqrt(N) for N repetitions of the experiment. For the problem of estimating the parameter phi in an evolution exp(-i phi H), it is possible to achieve precision 1/N (the quantum metrology limit) provided that sufficient information about H and its spectrum is available. We consider the more general problem of estimating expectations of operators A with minimal prior knowledge of A. We give explicit algorithms that approach precision 1/N given a bound on the eigenvalues of A or on their tail distribution. These algorithms are particularly useful for simulating quantum systems on quantum computers because they enable efficient measurement of observables and correlation functions. Our algorithms are based on a method for efficiently measuring the complex overlap of |psi> and U|psi>, where U is an implementable unitary operator. We explicitly consider the issue of confidence levels in measuring observables and overlaps and show that, as expected, confidence levels can be improved exponentially with linear overhead. We further show that the algorithms given here can typically be parallelized with minimal increase in resource usage.Comment: 22 page

Influencia normativa de las Organizaciones Internacionales Económicas en los procesos de integración económica

Las Organizaciones internacionales económicas son un actor clave en la creación, implementación y desarrollo de la normativa multilateral que regula los procesos de integración económica, pero ¿en qué forma e intensidad influyen normativamente esta clase de Organizaciones en dichos procesos? La subjetividad internacional de la cual gozan y la soberanía cedida por parte de los Estados ¿han sido suficientes para cumplir con sus expectativas? Junto con lo anterior, es importante reconocer las principales vías de acción y analizar la situación actual, tanto de los procesos de integración económica como de las Organizaciones que los regulan, reconociendo sus características, principios, efectos y objetivos esperados por parte de la comunidad internacional, y en definitiva determinar cuánto hay de realidad y cuánto ha quedado solamente en expectativa.The international economic Organizations play a key role in the creation, implementation, and development of the multilateral normative that regulate the processes of economic integration. However, how much and what influence do these Organizations have in these processes? Has the international subjectivity, of which they enjoy, and the given sovereignty on the part of the States been sufficient to meet with their expectations? Along with the above, it is important to recognize the principal courses of action and the current situation of the processes of economic inte- gration as well as the regulating Organizations, taking into consideration their characteristics, principles, effects and goals that are expected from the international community. How much is real and how much are just expectations.Les Organisations internationales économiques sont un acteur clé dans la création, exécution, et développement de la règlementation multilatérale qui régule les processus d’intégration économique, mais; sous quelle forme et comment cette classe d’Organisations influence-t-elle, dans les normes, lesdits processus? La subjectivité internationale dont elles profitent, et la souveraineté de la part des Etats, ont elles été suffisantes pour atteindre ses attentes? Suite à ce qui a été énoncé précédemment, il est important de reconnaitre les principales voies d’actions et un panorama actuel, autant dans les processus d’intégration économique comme celles des Organisations qui les régulent, reconnaissant ces caractéristiques, principes, effets et objectifs attendus de la part de la communauté internationale. Combien est réel, que reste-t-il encore dans l’attente

Entre el libre comercio y el proteccionismo. Impacto de los obstáculos sobre la equidad en el comercio en el marco de la Agenda 2030

The objective of the present article, is to analyze the current situation of free trade, the imposition of barriers, both tariff and non-tariff, and its incidence for the equity of international trade. This analysis deals in particular with the evolution of free trade and the different restrictions and obstacles that countries have imposed, seeking, on the one hand, the protection of their national industry, the defense of their own interests and, on the other hand, the search for commercial opening and trade facilitation through the general liberalization of barriers. Together with the above, a review is made of the objectives set by the international community for the coming years, taking as reference the horizon of 2030, within the framework of the Sustainable Development Goals.El objeto del presente trabajo, es analizar el estado actual del libre comercio, la imposición de barreras, tanto arancelarias como no arancelarias, y su incidencia para la equidad del comercio internacional. Dicho análisis aborda de manera particular la evolución del libre comercio y las distintas restricciones y obstáculos que los países han impuesto, procurando por una parte, la protección de su industria nacional, la defensa de sus propios intereses y por otra parte, la búsqueda de la apertura comercial y la facilitación del comercio a través de la liberalización generalizada de barreras. Junto a lo anterior, se hace una revisión de los objetivos planteados por la comunidad internacional para los próximos años, tomando como referencia el horizonte del año 2030, en el marco de los Objetivos de Desarrollo Sostenible

Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities

We introduce an algebraic methodology for designing exactly-solvable Lie model Hamiltonians. The idea consists in looking at the algebra generated by bond operators. We illustrate how this method can be applied to solve numerous problems of current interest in the context of topological quantum order. These include Kitaev's toric code and honeycomb models, a vector exchange model, and a Clifford gamma model on a triangular lattice.Comment: 12 pages, 5 figure

A Sub-Hertz, Low-Frequency Vibration Isolation Platform

One of the major technical problems deep-space optical communication (DSOC) systems need to solve is the isolation of the optical terminal from vibrations produced by the spacecraft navigational control system and by the moving parts of onboard instruments. Even under these vibration perturbations, the DSOC transceivers (telescopes) need to be pointed l000 fs of times more accurately than an RF communication system (parabolic antennas). Mechanical resonators have been extensively used to provide vibration isolation for groundbased, airborne, and spaceborne payloads. The effectiveness of these isolation systems is determined mainly by the ability of designing a mechanical oscillator with the lowest possible resonant frequency. The Low-Frequency Vibration Isolation Platform (LFVIP), developed during this effort, aims to reduce the resonant frequency of the mechanical oscillators into the sub-Hertz region in order to maximize the passive isolation afforded by the 40 dB/decade roll-off response of the resonator. The LFVIP also provides tip/tilt functionality for acquisition and tracking of a beacon signal. An active control system is used for platform positioning and for dampening of the mechanical oscillator. The basic idea in the design of the isolation platform is to use a passive isolation strut with an approximately equal to 100-mHz resonance frequency. This will extend the isolation range to lower frequencies. The harmonic oscillator is a second-order lowpass filter for mechanical disturbances. The resonance quality depends on the dissipation mechanisms, which are mainly hysteretic because of the low resonant frequency and the absence of any viscous medium. The LFVIP system is configured using the well-established Stewart Platform, which consists of a top platform connected to a base with six extensible struts (see figure). The struts are attached to the base and to the platform via universal joints, which permit the extension and contraction of the struts. The struts ends are connected in pairs to the base and to the platform, forming an octahedron. The six struts provide the vibration isolation due to the properties of mechanical oscillators that behave as second-order lowpass filters for frequencies above the resonance. At high frequency, the ideal second-order low-pass filter response is spoiled by the distributed mass and the internal modes of membrane and of the platform with its payload

Quantum phase diagram of the integrable p_x+ip_y fermionic superfluid

We determine the zero temperature quantum phase diagram of a p_x+ip_y pairing model based on the exactly solvable hyperbolic Richardson-Gaudin model. We present analytical and large-scale numerical results for this model. In the continuum limit, the exact solution exhibits a third-order quantum phase transition, separating a strong-pairing from a weak-pairing phase. The mean field solution allows to connect these results to other models with p_x+ip_y pairing order. We define an experimentally accessible characteristic length scale, associated with the size of the Cooper pairs, that diverges at the transition point, indicating that the phase transition is of a confinement-deconfinement type without local order parameter. We show that this phase transition is not limited to the p_x+ip_y pairing model, but can be found in any representation of the hyperbolic Richardson-Gaudin model and is related to a symmetry that is absent in the rational Richardson-Gaudin model.Comment: 12 figure

Efficient solvability of Hamiltonians and limits on the power of some quantum computational models

We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end. We show that these models can be efficiently simulated on a classical computer in time polynomial in the dimension of the algebra, regardless of the dimension of the Hilbert space where the algebra acts. Similar results hold for the computation of the expectation value of operators implemented by a gate-sequence. We introduce a Lie-algebraic notion of generalized mean-field Hamiltonians and show that they are efficiently ("exactly") solvable by means of a Jacobi-like diagonalization method. Our results generalize earlier ones on fermionic linear optics computation and provide insight into the source of the power of the conventional model of quantum computation.Comment: 6 pages; no figure

Geometry of Discrete Quantum Computing

Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2^{n} infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields Fp^2 (based on primes p congruent to 3 mod{4}) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space CP{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p+1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to DCP{2^{n}-1}, the discrete analog of the complex projective space, which has p^{2^{n}-1} (p-1)\prod_{k=1}^{n-1} (p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field Fp^2 have p^{n} (p-1)^{n} unentangled states (the product of the tally for a single qubit) with purity 1, and they have p^{n+1}(p-1)(p+1)^{n-1} maximally entangled states with purity zero.Comment: 24 page