Formalismo para el diseño y control de interferencias cuánticas en la dinámica de polarización en sistemas de espines nucleares.

Abstract

En este trabajo se han estudiado sistemas que presentan notables efectos de interferencias cuánticas en el dominio temporal. De interés, han sido los sistemas de espines de tamaños finitos (moleculares) en donde nos hemos interesado en la descripción de la dinámica de excitaciones locales de espín en el límite de altas temperaturas. El marco teórico, mediante la utilización de un formalismo que proviene del campo de la materia condensada de sólidos: el formalismo de funciones de Green de no-equilibrio dentro de la descripción de Keldysh. Los resultados analíticos obtenidos con este método están basados en el mapeo de espines a fermiones.

One of the main features of quantum mechanics is the particle description in terms of a wave function. This wavy nature is manifested through amazing quantum interference effects. In this work we will focus on the description of quantum interference effects in the time domain. Particular interest is put in spin systems of finite size (molecular size) where we study local spin excitation dynamics in the high temperature limit. The theoretical framework is a formalism that was born in the condense matter field of solids: The non-equilibrium Green function formalism within the Keldysh description. The analytical results obtained with this method are based in the spin-fermion mapping. In the first part of the work we study the quantum interferences in the time domain of closed one dimensional spin systems. The absence of external perturbation provides a high control degree of the quantum dynamics obtaining greater manifestation of the interferences. The application of the non-equilibrium formalism to these systems allows us to identify the objects or functions involved in the spin dynamics description. High spatial dimensions or complex interaction nets between spins, degrade the temporal interferences associated with the one dimensional dynamics. This leads us to define a temporal scale within which the interferences are lost. This degradation, that becomes evident in finite size systems, is confirmed analytically in an infinite size system. This is achieved by extending the application of the Keldysh formalism to a two interacting spin system coupled to an infinite set of spins representing the degrees of freedom of the environment. Assuming that the excitation dynamics inside the environment is much faster than that within the system, it is obtained analytical expressions for the local polarization correlation functions of the system. These results improve those obtained within the density matrix formalism under the same approximations. Besides, the fermionic view of spins allows us to identify some effects that were not evidenced with the density matrix description, such as the existence of a dynamical phase transition. Finally, we study the effects produced in the system observables under slow dynamics inside the environment. We observe the appearance of memory or non-Markovian effects that are manifested in a progressive grow of the oscillation frequency of the system.