Publication: Estructura de la polarización en estados cuánticos
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2019-02-25
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Universidad Complutense de Madrid
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Abstract
Un buen número de experimentos recientes han demostrado que la luz presenta muchas propiedades que no se pueden explicar de acuerdo con la teoría clásica y deben tratarse en el contexto de la óptica cuántica. Este es el objetivo básico de la presente memoria. En el artículo 1, abogamos por una simple expansión multipolar de la matriz de densidad de polarización. Los multipolos resultantes se utilizan para construir distribuciones de cuasiprobabilidad con buenas propiedades, que aparecen como una suma de momentos sucesivos de las variables de Stokes. El primer orden corresponde a la imagen clásica enla esfera de Poincaré. La cuasidistribución que más utilizaremos a lo largo de esta tesis es la función Q que aparece como la proyección en los estados que tienen la polarización más definida de acuerdo a la teoría cuántica. Al observar sus contribuciones multipolares,formulamos una jerarquía completa de medidas que evalúan adecuadamente las correlaciones de polarización de orden superior.El artículo 2 está dedicado al análisis del momento angular orbital de un campo de radiación. Dicha variable se modeliza mediante la superposición de dos osciladores armónicos independientes a lo largo de dos ejes ortogonales. Derivamos, a través de un cambio de variables consistente, un imagen física completa del momento angular orbital.En el artículo 3 profundizamos en la caracterización de las correlaciones de polarización de orden superior. Los multipolos resultantes aparecen como momentos sucesivos de las variables de Stokes y se pueden obtener a partir de mediciones realistas. Como resultado,obtenemos una jerarquía de grados de polarización que miden la información de polarización hasta un orden dado. Dichos grados se caracteriza por una distribución acumulativa que definimos en este artículo...
As it has been recently demonstrated in a number of recent experiments, light has many properties that cannot be explained in any classical theory and should be treated in the realm of quantum optics. This is the inspiring thread of this Thesis. In paper 1, we advocate a simple multipole expansion of the polarization density matrix.The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables. The first order corresponds to the classical picture on the Poincaré sphere. The quasidistribution that we will use the most throughout this Thesis is the Q function. It appears as the projection on the states having the most definite polarization allowed by the quantum theory. Looking at its multipolar contributions, we formulate a whole hierarchy of measures that properly assess higher-order polarization correlations. Paper 2 is devoted to the analysis of the orbital angular momentum of a light field. We model this variable as a superposition of two independent harmonic oscillators along two orthogonal axes. We derive, via a consistent change of variables, a comprehensive picture of the orbital angular momentum. In paper 3, we delve into the characterization of higher-order polarization correlations.The resulting multipoles appear as successive moments of the Stokes variables and can be obtained from feasible measurements. As a result, we obtain a hierarchy of degrees of polarization that measure the polarization information up to a given order. Such degrees are characterized by a cumulative distribution we introduce in this paper...
As it has been recently demonstrated in a number of recent experiments, light has many properties that cannot be explained in any classical theory and should be treated in the realm of quantum optics. This is the inspiring thread of this Thesis. In paper 1, we advocate a simple multipole expansion of the polarization density matrix.The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables. The first order corresponds to the classical picture on the Poincaré sphere. The quasidistribution that we will use the most throughout this Thesis is the Q function. It appears as the projection on the states having the most definite polarization allowed by the quantum theory. Looking at its multipolar contributions, we formulate a whole hierarchy of measures that properly assess higher-order polarization correlations. Paper 2 is devoted to the analysis of the orbital angular momentum of a light field. We model this variable as a superposition of two independent harmonic oscillators along two orthogonal axes. We derive, via a consistent change of variables, a comprehensive picture of the orbital angular momentum. In paper 3, we delve into the characterization of higher-order polarization correlations.The resulting multipoles appear as successive moments of the Stokes variables and can be obtained from feasible measurements. As a result, we obtain a hierarchy of degrees of polarization that measure the polarization information up to a given order. Such degrees are characterized by a cumulative distribution we introduce in this paper...
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Tesis de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Óptica, leída el 06-11-2018.