Simulação óptica de uma partícula livre quântica relativística

• Autor(a) principal: Silva, Thais de Lima
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/001300000dg1g
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/7068
• topic: Zitterbewegung; Óptica paraxial; Simulação clássica; Zitterbewegung; Paraxial optics; Classical simulation; CIENCIAS EXATAS E DA TERRA::FISICA

Among the first attempts towards the unification of quantum and special relativity theories that which more highlighted was the Dirac’s electron theory. Amongst its achievements is the accurated calculation of the hydrogen spectrum and the antiparticles prediction. Even though it provides good results, some difficulties arise in this theory such as the existence of negative energy states for free particles. At the same time that it allows for the antiparticle discovery, it leads to questions like the trembling motion of a free electron (zitterbewegung). It is not a consensus whether this motion is real or just a theoretical failure in describing the reality. In this work we present a proposal to simulate the Dirac electron dynamics and, therefore, zitterbewegung, by means of a transformation of a paraxial light beam. The same transformation as is carried out on the vector state by the Dirac’s evolution operator is implemented in the transverse beam profile using wave plates and spatial light modulator. The proposal includes the cases of one and two spatial dimensions by simulating the spatial degrees of freedom into the transverse coordinates of the light beam, which offers a difficulty in simulating the three dimensional dynamics in general case. However, we show that it is possible for particular initial states. Our simulation presents some advantages over previously ones, namely: it does not require the construction of specificaly designed devices; the adjustable parameters are present on phases printed by the modulator and can be arbitrarily changed; it permits the measurement of the mean as well as the standard position operators; it permits the simulation in two and three spatial dimensions.