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Interacción de emisores cuánticos inmersos en cristales fotónicos

dc.rights.licenseReconocimiento 4.0 Internacional
dc.contributor.advisorVinck Posada, Herbert
dc.contributor.advisorGonzález Tudela, Alejandro
dc.contributor.authorNavarro Barón, Erik Petrovish
dc.date.accessioned2024-02-02T19:25:39Z
dc.date.available2024-02-02T19:25:39Z
dc.date.issued2023
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/85606
dc.descriptionIlustraciones
dc.description.abstractPhotonic crystals are periodic arrays of materials with different refractive indices. This modulation of refractive indices allows controlling the flow of light, leading to the development of different technological applications, such as the design of lasers, waveguides, and optical sensors. In particular, these materials have been used to improve the radiation-matter interaction meaningful in applications of quantum mechanics in the transport, processing, and storage of information and development of light sources with quantum properties. All these developments are based on two essential factors, which are the manipulation of the dispersion relation of light, that is, the allowed and disallowed wave frequencies inside this type of structures, and the possibility of confining electromagnetic fields in tiny regions of the order of the wavelength, and of controlling the degrees of freedom of these fields. Recent advances in radiation-matter interaction in nanophotonic systems, such as photonic crystals, have led to the discovery of unconventional phenomena that may become an engine for new protocols in quantum information processing. It has opened the door to exploring new physics in these systems, making it a current topic of great scientific interest. This thesis studies the properties of electromagnetic fields inside photonic crystals. From the development of different numerical, semianalytical, and analytical methods, Maxwell’s equations in these materials are solved, with which the band structure (allowed and not allowed wave frequencies) and the distribution of electromagnetic fields of different photonic crystal systems with periodicity in one and two dimensions are obtained. Based on the characteristics of these fields, the emission and interaction properties of emitters inside these photonic crystal structures are studied. In 1D crystals, the guided mode expansion (GME) method is adapted for calculating photonic bands in micropillars; using this method, it is possible to consider the effects that the finite dimensions of the structure have on the allowed and disallowed frequencies. A transfer matrix formalism is also used to implement an analytical method that evaluates the single-point Green’s function; this allows calculating the local density of states (LDOS) for a structure of periodic multilayers (1D photonic crystal) finite with a localized defect. Through the LDOS, we identified the defective mode of the structure and calculated the decay rates of emitters within the structure. In the case of two-dimensional photonic crystal slabs, two studies were performed. First, a semianalytical method was developed that combines the k.p approximation and the GME method to obtain an analytical expression of the photonic crystal modes, which is used to evaluate the Green’s function at frequencies close to a Dirac cone-like dispersion relation. Employing the two-point Green’s function, the properties of the interaction between dipolar emitters mediated by photons are studied; it was found that the interactions in these frequency regions are of long-range (decay with the distance between emitters as 1/r^γ) and also identified a trade-off mechanism between the range and magnitude of the interaction according to the positions of the emitters. In turn, it was found that the polarization of the dipole moment of the emitters plays an essential role in the interaction nature, being coherent (conservative) if the dipoles have linear polarization and being incoherent (dissipative) in almost the whole unit cell if the emitters have circular polarization. Second, a region of frequencies within the frequency bands of a photonic crystal slab that allows directional emission was considered; this region of frequencies is associated with van Hove singularities. Through the GME method, a description of the band and mode structure that explains the directionality by means of what is known as self-collimation was carried out. The effects of the position and polarization of the emitter in the selection of the directionality were studied, finding that utilizing these two parameters makes it possible to control the emission directions and the polarization of the emitted fields.
dc.description.abstractPhotonic crystals are periodic arrays of materials with different refractive indices. This modulation of refractive indices allows controlling the flow of light, leading to the development of different technological applications, such as the design of lasers, waveguides, and optical sensors. In particular, these materials have been used to improve the radiation-matter interaction meaningful in applications of quantum mechanics in the transport, processing, and storage of information and development of light sources with quantum properties. All these developments are based on two essential factors, which are the manipulation of the dispersion relation of light, that is, the allowed and disallowed wave frequencies inside this type of structures, and the possibility of confining electromagnetic fields in tiny regions of the order of the wavelength, and of controlling the degrees of freedom of these fields. Recent advances in radiation-matter interaction in nanophotonic systems, such as photonic crystals, have led to the discovery of unconventional phenomena that may become an engine for new protocols in quantum information processing. It has opened the door to exploring new physics in these systems, making it a current topic of great scientific interest. This thesis studies the properties of electromagnetic fields inside photonic crystals. From the development of different numerical, semianalytical, and analytical methods, Maxwell’s equations in these materials are solved, with which the band structure (allowed and not allowed wave frequencies) and the distribution of electromagnetic fields of different photonic crystal systems with periodicity in one and two dimensions are obtained. Based on the characteristics of these fields, the emission and interaction properties of emitters inside these photonic crystal structures are studied. In 1D crystals, the guided mode expansion (GME) method is adapted for calculating photonic bands in micropillars; using this method, it is possible to consider the effects that the finite dimensions of the structure have on the allowed and disallowed frequencies. A transfer matrix formalism is also used to implement an analytical method that evaluates the single-point Green’s function; this allows calculating the local density of states (LDOS) for a structure of periodic multilayers (1D photonic crystal) finite with a localized defect. Through the LDOS, we identified the defective mode of the structure and calculated the decay rates of emitters within the structure. In the case of two-dimensional photonic crystal slabs, two studies were performed. First, a semianalytical method was developed that combines the k.p approximation and the GME method to obtain an analytical expression of the photonic crystal modes, which is used to evaluate the Green’s function at frequencies close to a Dirac cone-like dispersion relation. Employing the two-point Green’s function, the properties of the interaction between dipolar emitters mediated by photons are studied; it was found that the interactions in these frequency regions are of long-range (decay with the distance between emitters as 1/r^γ) and also identified a trade-off mechanism between the range and magnitude of the interaction according to the positions of the emitters. In turn, it was found that the polarization of the dipole moment of the emitters plays an essential role in the interaction nature, being coherent (conservative) if the dipoles have linear polarization and being incoherent (dissipative) in almost the whole unit cell if the emitters have circular polarization. Second, a region of frequencies within the frequency bands of a photonic crystal slab that allows directional emission was considered; this region of frequencies is associated with van Hove singularities. Through the GME method, a description of the band and mode structure that explains the directionality by means of what is known as self-collimation was carried out. The effects of the position and polarization of the emitter in the selection of the directionality were studied, finding that utilizing these two parameters makes it possible to control the emission directions and the polarization of the emitted fields.
dc.description.sponsorshipConsejo Superior de Investigaciones Científicas (CSIC) - España
dc.format.extent104 páginas
dc.format.mimetypeapplication/pdf
dc.language.isospa
dc.publisherUniversidad Nacional de Colombia
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subject.ddc530 - Física::535 - Luz y radiación relacionada
dc.subject.ddc530 - Física::537 - Electricidad y electrónica
dc.subject.ddc530 - Física::539 - Física moderna
dc.titleInteracción de emisores cuánticos inmersos en cristales fotónicos
dc.typeTrabajo de grado - Doctorado
dc.type.driverinfo:eu-repo/semantics/doctoralThesis
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.publisher.programBogotá - Ciencias - Doctorado en Ciencias - Física
dc.contributor.researchgroupGrupo de Superconductividad y Nuevos Materiales
dc.contributor.researchgroupGrupo de Óptica E Información Cuántica
dc.description.degreelevelDoctorado
dc.description.degreenameDoctor en Ciencias - Física
dc.description.methodsEl presente proyecto realiza un estudio teórico que considera tres etapas para alcanzar los objetivos propuestos: Descripción de los campos electromagnéticos en nanoestructuras: en esta etapa se hizo uso de las leyes de la electrodinámica clásica para dar lugar al estudio y diseño de estructuras fotónicas con relaciones de dispersión tipo conos de Dirac y singularidades de van Hove. Se estudiarón las propiedades electromagnéticas desde dos enfoques: uno basado en las relaciones de dispersión en sistemas periódicos para lo cual se usan métodos semianalíticos y numéricos como Expansión en Modos Guiados y Expansión en Ondas Planas, estos métodos son implementados usando lenguajes de programación como Mathematica, Python y C++, así mismo se hace uso del software libre MPB desarrollado para el cálculo de relaciones de dispersión. Por otro lado, se considera un enfoque de estructuras finitas por medio de algoritmos de diferencias fi nitas en el dominio del tiempo y en el dominio de la frecuencia para lo cual se cuenta con el software Meep del MIT y el software comercial Lumerical de Ansys, en este caso se estudia la respuesta que tengan las nanoestructuras a fuentes en su interior. Estos dos enfoques conllevan al cálculo de funciones de Green para los campos electromagnéticos, lo cual se usa como insumo básico en la descripción de la interacción radiación materia y la dinámica cuántica de emisores interaccionando por medio de la luz. Esto permite caracterizar el papel de los campos en la interacci on entre emisores, particularmente evidenciar el rol que juegan la polarización, el alcance y dirección de propagación de los campos; esto hace posible abordar desde un primer frente los objetivos 1-3. Dinámica cuántica de emisores interaccionando con fotones: esta etapa pretende caracterizar las interacciones emergentes de uno o varios emisores con la nanoestructura, permitiendo el desarrollo de los objetivos 1-3. Se prestó principal atención a sintonizar parámetros de los emisores como posición, polarización y frecuencia, que modi quen propiedades de la interacción emisor-emisor, como pueden ser: alcance de las interacciones, lo cual está relacionado al objetivo 1; distribución espacial de la emisión, relacionado al objetivo 2 y rol de la polarización de la luz, que daría cumplimiento al objetivo 3. Para esta caracterización se tiene en cuenta inicialmente técnicas perturbativas tradicionalmente usadas en óptica cuántica, como ecuaciones maestras; para después realizar un análisis no-perturbativo de la dinámica usando técnicas más avanzadas, como el uso de funciones de Green para el cálculo analítico de la dinámica. Diseño de aplicaciones: esta etapa final está enfocada a dar cumplimiento al objetivo 4, que pretende elucidar el desarrollo de aplicaciones para explotar las interacciones emergentes caracterizadas en las etapas anteriores. Algunas aplicaciones plausibles pueden ser el desarrollo de protocolos para generar entrelazamiento a larga distancia, control de la interacción entre emisores por medio de la polarización o dirección de la emisión de luz y la generación de transiciones de fase que permitan observar fenómenos no locales.
dc.description.researchareaMateria Condensada
dc.description.researchareaCristales Fotónicos
dc.description.researchareaInteracción radiación materia
dc.description.researchareaComputación y simulación cuántica
dc.identifier.instnameUniversidad Nacional de Colombia
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourlhttps://repositorio.unal.edu.co/
dc.publisher.facultyFacultad de Ciencias
dc.publisher.placeMedellín, Colombia
dc.publisher.branchUniversidad Nacional de Colombia - Nivel Nacional
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.subject.proposalCristal Fotónico
dc.subject.proposalPhotonic Crystal
dc.subject.proposaldiole-dipole interaction
dc.subject.proposalInteracción dipolo-dipolo
dc.subject.proposalFunciones de Green
dc.subject.proposalInteracción mediada por fotones
dc.subject.proposalPhoton-mediated interaction
dc.subject.proposalGreen's functions
dc.subject.proposalBand Structure
dc.subject.proposalEstructura de bandas
dc.subject.proposalEmisroes cuánticos
dc.subject.proposalQuantum emitters
dc.title.translatedInteraction of quantum emitters embedded in photonic crystals
dc.type.coarhttp://purl.org/coar/resource_type/c_db06
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.contentText
dc.type.redcolhttp://purl.org/redcol/resource_type/TM
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2
oaire.fundernameUniversidad Nacional de Colombia
oaire.fundernameMinisterio de Ciencias - Gobierno Nacinal de Colombia
dcterms.audience.professionaldevelopmentEstudiantes
dcterms.audience.professionaldevelopmentInvestigadores
dc.description.curricularareaÁrea Curricular en Física
dc.contributor.orcidNavarro-Baron, Erik Petrovish [0000-0002-9985-3841]
dc.contributor.cvlacNAVARRO BARÓN, ERIK PETROVISH [0001493647]
dc.contributor.scopusNavarro-Barón, Erik Petrovish [57189043120]
dc.contributor.researchgateNavarro Barón, Eerik Peetrovish [Erik-Petrovish-Navarro-Baron]
dc.contributor.googlescholarNavarro-Baron, Erik Petrovish [epnavarrob]
dc.subject.wikidataCristal fotónico
dc.subject.wikidataRefracción
dc.subject.wikidataEcuaciones de Maxwell


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