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arXiv:1911.07958 · Physical Review A

Quantum Darwinism and non-Markovianity in a model of quantum harmonic oscillators

S. M. Oliveira, A. L. de Paula, Raphael C. Drumond

Published Nov 18, 2019• 20 citations
arXivHTMLPDF

Abstract

To explain aspects of the quantum-to-classical transition, quantum Darwinism explores the fact that, due to interactions between a quantum open system and its surrounding environment, information about the system can be spread redundantly to the environment. Here we recall that there are in the literature two distinct and nonequivalent ways to make this statement precise and quantitative. We first point out the difference with some simple but illustrative examples. We then consider a model where Darwinism can be seen from both perspectives. Moreover, the non-Markovianity of our model can be varied with a parameter. In a recent work [F. Galve et al., Sci. Rep. 6, 19607 (2016)], the authors concluded that quantum Darwinism can be hindered by non-Markovianity. We depart from their analysis and argue that, from both perspectives to quantum Darwinism, there is no clear relationship between non-Markovianity and quantum Darwinism in our model.

DOI
10.1103/physreva.100.052110

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To explain aspects of the quantum-to-classical transition, quantum Darwinism explores the fact that, due to interactions between a quantum open system and its surrounding environment, information about the system can be spread redundantly to the environment. Here we recall that there are in the literature two distinct and nonequivalent ways to make this statement precise and quantitative. We first point out the difference with some simple but illustrative examples. We then consider a model where Darwinism can be seen from both perspectives. Moreover, the non-Markovianity of our model can be varied with a parameter. In a recent work [F. Galve et al., Sci. Rep. 6, 19607 (2016)], the authors concluded that quantum Darwinism can be hindered by non-Markovianity. We depart from their analysis and argue that, from both perspectives to quantum Darwinism, there is no clear relationship between non-Markovianity and quantum Darwinism in our model.
Quantum Darwinism attempts to explain the emergence of objective reality of the state of a quantum system in terms of redundant information about the system acquired by independent noninteracting fragments of the environment. The consideration of interacting environmental elements gives rise to a rich phenomenology, including the occurrence of non-Markovian features, whose effects on objectification in the manner of quantum Darwinism needs to be fully understood. We study a model of local interaction between a simple quantum system and a multimode environment that allows for a clear investigation of the interplay between information trapping and propagation in the environment and the emergence of quantum Darwinism. We provide strong evidence of the correlation between non-Markovianity and quantum Darwinism in such a model, thus providing strong evidence of a potential link between such fundamental phenomena.
In this thesis, I present my work during my Ph.D. in quantum Darwinism. It is a original project, which has been peer-reviewed and accepted for publication in a respected international journal. In the first chapters, I recalled the essential concepts to understand quantum Darwinism, and in the two last, I present my works. The quantum Darwinism concept was constructed to explain a possible quantum-to-classical transition. My main interests are to find the quantum Darwinism implications in the system’s dynamics and to find more realistic models where it applies. The first work was finished and published while the second is still in progress. In the first model I studied quantum Darwinism in a many-body system of quantum harmonic oscillators where the subenvironments neither interact nor correlate between themselves. Through analytical and numerical calculations, we observed quantum Darwinism from two different approaches. We show quantum Darwinism through the BPH approach in a model for the first time. In contrast with a recently published work, we also show that quantum Darwinism can be observed even in a system with a high degree of non-Markovianity, and proposed a more suitable way to quantify it. In the second work, we investigate quantum Darwinism in a more realistic model where the subenvironments can become strongly correlated. The model consists of a two-level atom interacting with a fermionic environment and was used to study orthogonality catastrophe. As both orthogonality catastrophe and quantum Darwinism comes with decoherence, we are investigating if these two concepts are correlated. Beyond that, we chose this model because it can be mapped in a bosonic model of the Tonks-Girardeau gas enabling an experimental implementation with cold atoms. We are performing numerical and analytical calculations in this work. In the sixth chapter, I present the first result and describe what is missing.
Quantum Darwinism explains the emergence of a classical description of objects in terms of the creation of many redundant registers in an environment containing their classical information. This amplification phenomenon, where only classical information reaches the macroscopic observer and through which different observers can agree on the objective existence of such object, has been revived lately for several types of situations, successfully explaining classicality. We explore quantum Darwinism in the setting of an environment made of two level systems which are initially prepared in the ground state of the XX\mathit{XX}XX model, which exhibits different phases; we find that the different phases have different abilities to redundantly acquire classical information about the system, the ``ferromagnetic phase'' being the only one able to complete quantum Darwinism. At the same time we relate this ability to how non-Markovian the system dynamics is, based on the interpretation that non-Markovian dynamics is associated with backflow of information from environment to system, thus spoiling the information transfer needed for Darwinism. Finally, we explore mixing of bath registers by allowing a small interaction among them, finding that this spoils the stored information as previously found in the literature.
An explanation for the quantum-to-classical transition has long been sought after since the haydays of the field. Decoherence theory and open quantum system dynamics have paved the way, showing how a system can become correlated with, and so lose information into the environment. Quantum Darwinism, and its more stringent cousins Strong Quantum Darwinism and Spectrum Broadcast Structures, seek to explain how this information loss is achieved in such a way as to be objective, classical and redundant. However there remains questions as to how the structure of the environment, states and types of interactions can give rise to this redundant encoding. In this thesis, we collect the work of 3 of our papers, exploring these questions. First, we show how information from one environment can spread to another. Then we show how commutativity can play a role in the emergence of objectivity. Lastly, we move beyond a single, pure system to a more realistic bipartite one, with both classical and quantum correlations between the subsystems. We shall show how interactions between only these subsystems can mediate the redundancy of others, and how these can lower bound and upper bound other forms of interactions between said subsystems and the environment.
We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors.
We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors.