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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)

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2011
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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.
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Máster en Física Fundamental. Facultad de Ciencias Físicas Curso 2010-2011
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[1] Gian Luca Giorgi, Fernando Galve, Gonzalo Manzano, Pere Colet and Roberta Zambrini, Quantum Correlations and mutual synchronization. arXiv:1105.4129v2 [quantph] (2011). [2] A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, 2001). [3] S. H. Strogatz, Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering, Westview Press (2001). [4] I. Goychuk, J. Casado-Pascual, M. Morillo, J. Lehmann and P. Hänggi, Quantum Stochastic Synchronization Phys. Rev. Lett. 97, 210601 (2006). [5] O. V. Zhirov and D. L. Shepelyansky, Quantum Synchronization, Phys. Rev. Lett. 100, 014101 (2008). [6] S-B. Shim, M. Imboden, P. Mohanty, Synchronized Oscillation in Coupled Nanomechanical Oscillators, Science, 316, 95 (2007). [7] G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, Collective Dynamics in Optomechanical Arrays, Phys. Rev. Lett. 107, 043603 (2011). [8] R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Quantum Entanglement, Rev. Mod. Phys. 81, 865 (2009). [9] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, )2000). [10] G. Vidal and R. F. Werner, Computable measure of entanglement, Phys. Rev. A 65, 032314 (2002). [11] G. Adesso, A. Serani, F. Illuminati, Quantication and Scaling of Multipartite Entanglement in Continuous Variable Systems, Phys. Rev. Lett. 93, 220504 (2004). [12] H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88, 017901 (2001). [13] L. Henderson and V. Vedral, Classical, quantum and total correlations, J. Phys. A 34, 6899 (2001). [14] A. Datta, A. Shaji and C. M. Caves , Quantum Discord and the Power of One Qubit, Phys. Rev. Lett. 100, 050502 (2008). [15] B. P. Lanyon, M. Barbieri, M. P. Almeida and A. G. White, Experimental quantum computing without entanglement, Phys. Rev. Lett. 101, 200501 (2008). [16] D. Girolami and G. Adesso, Quantum discord for general two-qubit states: Analytical progress, Phys. Rev. A 83, 052108 (2011). [17] F. Galve, G. L. Giorgi and R. Zambrini Maximally discordant mixed states of two qubits Phys. Rev. A 83, 012102 (2011). [18] P. Giorda and M. G. A. Paris, Gaussian Quantum Discord, Phys. Rev. Lett. 105, 020503 (2010). [19] G. Adesso and A. Datta, Quantum versus classical correlations in Gaussian states, Phys. Rev. Lett 105, 030501 (2010). [20] T. Rocheleau, T. Ndukum, C. Macklin, J. B. Hertzberg, A. A. Clerk and K. C. Schwab Preparation and detection of a mechanical resonator near the ground state of motion, Nature 463, 72 (2010). [21] F. Marquardt and S. M. Girvin, Optomechanics, Physics 2, 40 (2009). [22] D. Van Thourhout and J. Roels, Optomechanical device actuation through the optical gradient force, Nature Phot. 4 211, (2010). [23] F. Marino F. S. Cataliotti, A. Farsi1, M. S. de Cumis and F. Marin, Classical Signature of Ponderomotive Squeezing in a Suspended Mirror Resonator, Phys. Rev. Lett. 104, 073601 (2010). [24] P. Verlot, A. Tavernarakis, T. Briant, P.-F. Cohadon and A. Heidmann, Backaction Amplication and Quantum Limits in Optomechanical Measurements, Phys. Rev. Lett. 104, 133602 (2010). [25] K. R. Brown, C. Ospelkaus, Y. Colombe, A.C. Wilson, D. Leibfried, D. J. Wineland, Coupled quantized mechanical oscillators, Nature, 471, 196 (2011). [26] M. Harlander, R. Lechner, M. Brownnutt, R. Blatt, and W. Hänsel, Trapped-ion antennae for the transmission of quantum information, Nature 471, 200 (2011). [27] W. H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75, 715 (2003). [28] G. Auletta, M. Fortunato, G. Parisi, Quantum Mechanics (Cambridge University Press, New York 2009). [29] T. Brandes Chapter 7 of UMIST-Bradford Lectures on Background to Quantum Information Theory. [30] A. Rivas and S. F. Huelga, Introduction to the Time Evolution of Open Quantum Systems, arXiv:1104.5242v1 [quant-ph]. [31] B. L. Hu, J. P. Paz and Y. Zhang, Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise, Phys. Rev. D 45, 28432861 (1992). [32] H. P. Breuer and F. Petruccione, The theory of open quantum systems (Oxford University Press, Oxford, (2002). [33] D. A. Lidar, I. L. Chuang and K. B. Whaley, Decoherence-free subspaces for quantum computation, Phys. Rev. Lett. 81, 25942597 (1998). [34] F. Benatti, R. Floreanini, M. Piani, Environment Induced Entanglement in Markovian Dissipative Dynamics, Phys. Rev. Lett. 91, 070402 (2003). [35] D. Braun, Creation of Entanglement by Interaction with a Common Heat Bath Phys. Rev. Lett. 89, 277901 (2002). [36] C-H. Chou, T. Yu and B. L. Hu, Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment, Phys. Rev. E 77, 011112 (2008). [37] J. P. Paz and A. J. Roncaglia, Dynamics of the entanglement between two oscillators in the same environment, Phys. Rev. Lett. 100, 220401 (2008); Dynamical phases for the evolution of the entanglement between two oscillators coupled to the same environment, Phys. Rev. A 79, 032102 (2009). [38] T. Yu and J. H. Eberly, Sudden death of entanglement, Science 323, 598 (2009). [39] F. Galve, G. L. Giorgi and R. Zambrini, Entanglement dynamics of nonidentical oscillators under decohering environments, Phys. Rev. A 81, 062117 (2010)