Łamanie nierówności Leggetta-Garga w otwartych układach kwantowych

Abstract

This dissertation concerns an analysis of obtained theoretical values of temporal correlation functions in open quantum systems in the context of Leggett-Garg inequalities. The violation of these inequalities indicates that a system reveals non-classical correlations. A special case of the temporal correlations, analysed in this work, are used to tests of macrorealism, likewise as an indicator of the “quantumness” of a system or in order to perform the quantum information protocols. Despite of the well grounded results on the temporal quantum correlations in isolated systems, the open systems are still barely explored. The main motivation to study this subject is a possibility to obtain better models of real physical systems and to develop new methods to control the amount of the non-classical correlations. The main research objective is to establish an influence on the amount of the non-classical correlations in the measured subsystem by a coupling with the environment. In this work, four distinct physical models of open quantum systems are presented. In the first one there is revealed a violation of Leggett-Garg inequality in the system weakly coupled to thermal environment where especially is discussed the process of decoherence and dissipation. The main result is an observation that, under some conditions, the violation of the inequality is independent of environment properties like temperature. The second model concerns an analysis of temporal quantum correlations in the systems that dynamics is governed by the angular momentum operators and driven by classical white noise. In this case strict analytical results reveal an exponential dumping of the non-classical correlations as well as a property that such dumping can be less effective for systems with larger state space. The last but not least two models for which is calculated the Leggett-Garg correlator are the systems which interact with the environment due to the spin-spin coupling. In this context, a physical model of atoms from the first group of the periodic table and a model of quantum-classical hybrids, for which is discussed the semi-classical approach, is proposed. In both examples it is proven that for “more macroscopic” systems as well as for “classical environments”, it is possible to observe higher violation of the Leggett-Garg inequality.