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Quantum aspects of synchronization of coupled harmonic oscillators in presence of dissipation

Manzano Paule, Gonzalo (Supervisor: Zambrini, Roberta)
Master Thesis UCM , (2011)

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 different 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.