Publicación: Application of spin echo technique to Bose-Einstein condensates: time evolution of the spins by simulating and computing the Gross-Pitaevskii equation
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2016-10-21
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Atribución-NoComercial-SinDerivadas 4.0 Internacional
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Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias.
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Los fundamentos de la Resonancia Magnetica Nuclear (RMN, o NMR por sus siglas en ingles) se basan en las propiedades magneticas de los nucleos atomicos, como el espn y el momento angular orbital, permitiendo un control preciso en la dinamica del sistema nuclear mediante pulsos de radio frecuencia (RF). La RMN ha revolucionado el campo de la imagen medica, siendo una de las pocas tecnicas que no implica radiaciones ionizantes, junto a la ecografa. Sin embargo, no solamente el campo de la medicina se benecia de las increibles aplicaciones de este fenomeno fsico. Tambien la informacion estructural y qumica de diversas especies atomicas pueden investigarse utilizando RMN. Ademas, en el innovador y puntero campo de la investigacion en computacion cuantica, la resonancia magnetica se presenta como una de las posibles alternativas para crear el primer ordenador cuantico. Por otra parte, la aplicacion de la resonancia magnetica en estados de la materia unicos que aparecen a temperaturas enormemente bajas, explora el comportamiento de los espines en diferentes elementos, revelando propiedades fsicas de importancia inigualable. En esta tesis se estudia la aplicacion de una precisa secuencia de pulsos, llamada eco de espn, a un especco condensado de Bose-Einstein, un espinor de espn-1. El interes de este trabajo se centra en el analisis de la evolucion de los espines con el tiempo, considerando solo las interacciones de corto alcance. Las simulaciones se han generado aplicando algoritmos numericos, utilizando una herramienta en MATLAB R llamada GPELab, desarrollada para representar ecuaciones de Schr odinger no lineales, denominadas ecuaciones de Gross-Pitaevskii. Las tecnicas empleadas se han descrito en detalle, analizando el tipo de algoritmo escogido para estudiar la dinamica del sistema. Estos estudios pueden implementarse en numerosas posibilidades experimentales, ofreciendo una nueva alternativa al uso de RMN en el estudios de sistemas a muy bajas temperaturas.
The principles of Nuclear Magnetic Resonance (NMR) can be understood thanks to the magnetic properties of the nuclei derived from the intrinsic spin and the orbital angular momentum, enabling a precise control on the dynamics of the nuclear spin system by means of radio-frequency (RF) pulses. NMR has revolutionised the eld of medical imaging, being one of the few techniques where no ionizing radiation is employed, besides ultrasound. However, not exclusively medicine benets from the outstanding applications of this physical phenomenon. Structural and chemical information of diverse atomic species can be likewise investigated through NMR. Furthermore, in the recent cutting-edge research in quantum computing, magnetic resonance is an alternative technique to create the rst quantum computer. Moreover, the application of NMR to unique states of matter at very low temperatures explores the behaviour of the spins in dierent elements, revealing very interesting physical properties. In this thesis, the application of an important and precise pulse sequence, spin echo, to a specic type of Bose-Einstein condensate, a spin-1 spinor, is studied. The interest of this work focusses on analysing the spin evolution when only the short range interaction constants are taking into account. The simulations are computed applying numerical algorithms, by making use of GPELab, a MATLAB R toolbox developed to model non linear Schr odinger equations, the so called Gross-Pitaevskii equations. The techniques are explored more in detail, analysing the type of algorithm to be applied to compute the dynamics of the system. These results can be implemented in numerous experimental possibilities, and open up a new alternative to apply NMR in systems at very cold temperatures.
The principles of Nuclear Magnetic Resonance (NMR) can be understood thanks to the magnetic properties of the nuclei derived from the intrinsic spin and the orbital angular momentum, enabling a precise control on the dynamics of the nuclear spin system by means of radio-frequency (RF) pulses. NMR has revolutionised the eld of medical imaging, being one of the few techniques where no ionizing radiation is employed, besides ultrasound. However, not exclusively medicine benets from the outstanding applications of this physical phenomenon. Structural and chemical information of diverse atomic species can be likewise investigated through NMR. Furthermore, in the recent cutting-edge research in quantum computing, magnetic resonance is an alternative technique to create the rst quantum computer. Moreover, the application of NMR to unique states of matter at very low temperatures explores the behaviour of the spins in dierent elements, revealing very interesting physical properties. In this thesis, the application of an important and precise pulse sequence, spin echo, to a specic type of Bose-Einstein condensate, a spin-1 spinor, is studied. The interest of this work focusses on analysing the spin evolution when only the short range interaction constants are taking into account. The simulations are computed applying numerical algorithms, by making use of GPELab, a MATLAB R toolbox developed to model non linear Schr odinger equations, the so called Gross-Pitaevskii equations. The techniques are explored more in detail, analysing the type of algorithm to be applied to compute the dynamics of the system. These results can be implemented in numerous experimental possibilities, and open up a new alternative to apply NMR in systems at very cold temperatures.
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Facultad de Ciencias
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Física Matemática y de Fluídos