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Aspectos cuánticos de la sincronización de osciladores armónicos acoplados en presencia de disipación (Quantum aspects of synchronization of harmonic coupled oscillators in presence of dissipation)

Manzano Paule, Gonzalo (2011) Aspectos cuánticos de la sincronización de osciladores armónicos acoplados en presencia de disipación (Quantum aspects of synchronization of harmonic coupled oscillators in presence of dissipation). [Trabajo Fin de Máster]

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Abstract

En este trabajo de Fin de Máster estudiamos el fenómeno de la sincronización en sistemas de osciladores armónicos cuánticos acoplados en presencia de disipación. Un primer estudio de dos osciladores con diferentes frecuencias enseña que, independientemente de la intensidad del acoplamiento,los osciladores no sincronizan en presencia de entornos independientes. La condición que posibilita
la emergencia de sincronización espontánea es la presencia de un entorno común. Asociada a este fenomeno se encuentra una mayor robustez de las correlaciones cuánticas entre osciladores,dependiendo de la relación entre sus diferentes frecuencias naturales y el valor de la constante de
acoplamiento entre ellos. Extendiendo el ánalisis al caso mas complejo de N osciladores, determinamos las condiciones más generales necesarias para la aparición de este fenómeno a través de la relacion entre las tasas de disipación de los automodos. Esta descripción nos permite establecer
una correspondencia clara con la conservación de las correlaciones, centrándonos en el análisis de la dinámica del entrelazamiento y discord. El estudio del caso de tres osciladores nos permite identicar la rica tipologia de comportamientos que pueden surgir y determinar la influencia de las condiciones de contorno (cadena abierta o cerrada). Demostramos además la existencia de regiones de parámetros (así como la manera de obtenerlas en cadenas genéricas) donde el sistema no termaliza, dando lugar a una conservación asintótica de las correlaciones. En este contexto calculamos analíticamente el entrelazamiento entre osciladores resonantes en los extremos de la cadena abierta, obteniendo un diagrama de fases para su existencia asintótica dependiendo de la temperatura y compresión del
estado inicial del sistema. Encontramos en este diagrama que el entrelazamiento se podrá mantener asintóticamente hasta altas temperaturas. [ABSTRACT] In this Master Thesis work we study the phenomenon of synchronization in coupled quantum harmonic oscillators systems in the presence of dissipation. A first study of two oscillators with diferent frequencies shows that independently on the coupling strength, the oscillators do not synchronize in the presence of independent environments. The enabling condition for the emergence of spontaneous synchronization is the presence of a common environment. Associated with this phenomenon there are more robust quantum correlations between oscillators, depending on the relationship between their natural frequencies and coupling strength. Extending the analysis to the more complex case of N oscillators, we determine the general conditions for the emergence of this phenomenon through the relationship among the eigenmodes rates of dissipation. This description makes it possible to
establish a clear correspondence with the preservation of the correlations, where we focus on the analysis of entanglement dynamics and discord. The study of the case of three oscillators allows us to identify a rich variety of properties and to determine the influence of different boundary conditions (open or closed chain). Furthermore we demonstrate the existence of parameters regions (also showing how to get them in generic chains) where the system does not thermalize, giving rise to an asymptotic conservation of correlations. In this context we analytically derive the entanglement between resonant oscillators at the ends of the open chain, obtaining a phase diagram for its asymptotic existence depending on the equilibrium temperature and squeezing of the initial state
of the system. We find in this diagram that asymptotic entanglement can be maintained up to high temperatures.


Item Type:Trabajo Fin de Máster
Additional Information:

Máster en Física Fundamental. Facultad de Ciencias Físicas
Curso 2010-2011

Directors:
DirectorsDirector email
Zambrini, Roberta roberta@ifisc.uib-csic.es
Uncontrolled Keywords:Sincronizacón, Discord, Entrelazamiento, Decoherencia, Baño Común, Disipación, Cadenas de Osciladores, Sistemas Abiertos, Información Cuántica, Synchronization, Discord, Entanglement, Decoherence, Common Bath, Dissipation, Harmonic Chains, Open Systems, Quantum Information
Subjects:Sciences > Physics > Quantum theory
ID Code:13436
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Deposited On:02 Nov 2011 11:48
Last Modified:01 Nov 2012 23:05

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