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Simulation of a non-Markovian evolution using coherence

Marrou Osores, Jean Paúl

Published Jun 12, 2019• 0 citations
OpenAlex

Abstract

This thesis will be oriented in the study of open quantum systems. The transition of processes that go between the Markovian and non-Markovian regime will be studied. The diagnose of non-Markovianity will be made in terms of the variation of the coherence of the state. Accordingly, an optical setup will be implemented that allows us to manipulate certain degrees of freedom, like the polarization and the optical path. Theoretically, we have found that the coherence of the system is transferred to the environment and it decreases as we move a parameter that we will take as time. This situation has been confirmed in the experiment. Then, due to the second part of the setup, which produces a non-Markovian evolution by also changing one of its parameters, we have accomplished the goal of returning the information back into the system and to measure the non-Markovianity of the process.

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This thesis will be oriented in the study of open quantum systems. The transition of processes that go between the Markovian and non-Markovian regime will be studied. The diagnose of non-Markovianity will be made in terms of the variation of the coherence of the state. Accordingly, an optical setup will be implemented that allows us to manipulate certain degrees of freedom, like the polarization and the optical path. Theoretically, we have found that the coherence of the system is transferred to the environment and it decreases as we move a parameter that we will take as time. This situation has been confirmed in the experiment. Then, due to the second part of the setup, which produces a non-Markovian evolution by also changing one of its parameters, we have accomplished the goal of returning the information back into the system and to measure the non-Markovianity of the process.
The present manuscript represents the completion of a research path carried forward during my doctoral studies in the University of Turku. It contains information regarding my scientific contribution to the field of open quantum systems, accomplished in collaboration with other scientists. \n \nThe main subject investigated in the thesis is the non-Markovian dynamics of open quantum systems with focus on continuous variable quantum channels, e.g. quantum Brownian motion models. Non-Markovianity is here interpreted as a manifestation of the existence of a flow of information exchanged by the system and environment during the dynamical evolution. While in Markovian systems the flow is unidirectional, i.e. from the system to the environment, in non-Markovian systems there are time windows in which the flow is reversed and the quantum state of the system may regain coherence and correlations previously lost. \n \nSignatures of a non-Markovian behavior have been studied in connection with the dynamics of quantum correlations like entanglement or quantum discord. Moreover, in the attempt to recognisee non-Markovianity as a resource for quantum technologies, it is proposed, for the first time, to consider its effects in practical quantum key distribution protocols. It has been proven that security of coherent state protocols can be enhanced using non-Markovian properties of the transmission channels. \n \nThe thesis is divided in two parts: in the first part I introduce the reader to the world of continuous variable open quantum systems and non-Markovian dynamics. The second part instead consists of a collection of five publications inherent to the topic.
This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.
The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behavior. Here, we review recent ideas developing a general mathematical definition for non-Markoviantiy in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system-environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system.
In this Thesis various aspects of memory effects in the dynamics of open quantum systems are studied. We develop a general theoretical framework for open quantum systems beyond the Markov approximation which allows us to investigate different sources of memory effects and to develop methods for harnessing them in order to realise controllable open quantum systems. \n \nIn the first part of the Thesis a characterisation of non-Markovian dynamics in terms of information flow is developed and applied to study different sources of memory effects. Namely, we study nonlocal memory effects which arise due to initial correlations between two local environments and further the memory effects induced by initial correlations between the open system and the environment. \n \nThe last part focuses on describing two all-optical experiment in which through selective preparation of the initial environment states the information flow between the system and the environment can be controlled. In the first experiment the system is driven from the Markovian to the non- Markovian regime and the degree of non-Markovianity is determined. In the second experiment we observe the nonlocal nature of the memory effects and provide a novel method to experimentally quantify frequency correlations in photonic environments via polarisation measurements.
In this thesis, we discuss aspects of the simulation, characterisation, and control of the dynamics of open quantum systems. The latter are systems governed by quantum mechanical laws and interacting with an environment, which is typically much larger than the system itself. According to the standard approach, one is usually able to perform a suitable average over the environmental degrees of freedom, resulting in an effective description of the main system dynamics, which accounts for the effects of the interaction with the surroundings. In standard scenarios, usually studied within the so-called Born-Markov approximation, the system-environment coupling is weak and such that we can perform a neat separation of timescales: the environmental dynamics is assumed to be fast compared to the typical evolution timescale of the system of interest. However, nowadays we are able to inspect physical scenarios where the usual Born-Markov approximation breaks down: the interaction between system and environment can be strong, likely leading to non-negligible memory (non-Markovian) effects. In this work, we discuss some instances in which we cannot work in the standard Born-Markov regime. We introduce and analyse some numerical and analytical techniques to characterise and simulate non-standard scenarios. We show that, even in the Markovian regime, the traditional formulation of thermodynamic irreversibility shows flaws and inconsistencies. We thus use phase-space methods to assess the role of initial correlations shared by the two parties of a bipartite harmonic system in the entropy production rate, including non-Markovian effects. Furthermore, we show that certain interactions enable to redraw the boundaries between the system and the environment in an effective manner, resulting in a new picture where the system degrees of freedom are augmented, while the residual environment is rearranged in such a way that the Born-Markov approximation is recovered. This analytical technique, known as reaction coordinate mapping approach, is employed in this work to show that, upon an accurate choice of the parameter regime, a spin-boson model can serve as a quantum analogue simulator of non-Markovian multiphoton Jaynes-Cummings models. These systematic studies shed light on the thermodynamic characterisation of open quantum systems, as well as on their numerical simulation.