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LA DINÁMICA DE CANALES DISIPATIVOS LORENTZIANOS ES NO MARKOVIANA

Karen Fonseca, R. R. Rey-González

Published Jul 1, 2013• 0 citations
OpenAlex

Abstract

We consider the dissipative dynamics of an exciton in a Lorentzian reservoir, relevant in the description of some photosynthetic complexes. Although this dynamics have been frequently described as non-Markovian, we show that this characterization may be misleading. We describe an approach within which it is possible to decide if thisdynamics is or not Markovian. We apply this approach to the Lorentzian reservoir.

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IS THE DYNAMICS OF DISSIPATIVE LORENTZIAN CHANNELS NON MARKOVIAN?

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ResumenConsideramos la dinámica disipativa de un excitón en un reservorio Lorentziano, relevante en la descripción de algunos complejos fotosintéticos.Aunque esta dinámica se ha descrito con frecuencia como no Markoviana, mostramos que esta puede ser una caracterización equivocada.Describimos un enfoque en el cual es posible decidir si la dinámica es o no Markoviana y lo aplicamos al reservorio Lorentziano.

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We consider the dissipative dynamics of an exciton in a Lorentzian reservoir, relevant in the description of some photosynthetic complexes. Although this dynamics have been frequently described as non-Markovian, we show that this characterization may be misleading. We describe an approach within which it is possible to decide if thisdynamics is or not Markovian. We apply this approach to the Lorentzian reservoir.
We provide a thorough analysis of the entanglement dynamics of an interacting two-qubit system in the non-Markovian regime. In such a regime, the time scale on which the reservoir degrees of freedom evolve is either of the same order of magnitude or less than that on which the system evolves. We used an exact numerical method; the Quasi-Adiabatic Path Integral (QUAPI) technique, to describe the corresponding qubit dissipative dynamics in such a non-Markovian regime. We computed the time evolution of the density operator for the quibits, from which we quantified the coherences and population dynamics, as well as the qubit-bath coupling effects. Using negativity as a metric, we calculated the dynamics of non-local quantum correlations (entanglement), and indentified a non-Markovian quantum phenomena in terms of early stage disentanglement, and the collapse and revival of entanglement.
Abstract Understanding the dynamical behavior of a qubit in a reservoir is critical to applications in quantum technological protocols, ranging from quantum computation to quantum metrology. The effect of the reservoir depends on reservoir’s spectral structure, as well as on the qubit-reservoir coupling strength. We here propose a measure for quantifying the non-Markovian effect of a reservoir with a Lorentzian spectrum, based on the maximum qubit-reservoir quantum entanglement that can be extracted. Numerical simulation shows this entanglement exhibits a monotonous behavior in response to the variation of the coupling strength. We confirm the validity of this measure with an experiment, where a superconducting qubit is controllably coupled to a lossy resonator, which acts as a reservoir for the qubit. The experimental results illustrate the maximal extractable entanglement is progressively increased with the strengthening of the non-Markovianity.
Understanding the dynamical behavior of a qubit in a reservoir is critical to applications in quantum technological protocols, ranging from quantum computation to quantum metrology. The effect of the reservoir depends on the reservoir's spectral structure as well as on the qubit-reservoir coupling strength. We here propose a measure for quantifying the non-Markovian effect of a reservoir with a Lorentzian spectrum, based on the maximum qubit-reservoir quantum entanglement that can be extracted. Numerical simulation shows that this entanglement exhibits a monotonous behavior in response to the variation of the coupling strength. We confirm the validity of this measure with an experiment where a superconducting qubit is controllably coupled to a lossy resonator, which acts as a reservoir for the qubit. The experimental results illustrate that the maximal extractable entanglement is progressively increased with the strengthening of non-Markovianity.
We extend the quantum Monte Carlo wave-function method of quantum optics to non-Markovian system-reservoir interactions. The finite correlation time of the reservoir and the associated memory effects are incorporated into the dynamics by expanding the initial system using fictitious harmonic-oscillator modes, which have Markovian dissipative interactions. The underlying principle is the fact that a class of reservoir spectral functions can be approximated by a finite superposition of Lorentzian functions with positive coefficients.
We consider two recently proposed measures of non-Markovianity applied to a particular quantum process describing the dynamics of a driven qubit in a structured reservoir. The motivation for this study is twofold: on one hand, we study the differences and analogies of the non-Markovianity measures, and on the other hand, we investigate the effect of the driving force on the dissipative dynamics of the qubit. In particular we ask if the driving force introduces new channels for energy and/or information transfer between the system and the environment or if it amplifies existing ones. We show under which conditions the presence of the driving force slows down the inevitable loss of quantum properties of the qubit.