1,721,034 research outputs found
NON-MARKOVIANITY AND INITIAL CORRELATIONS IN THE DYNAMICS OF OPEN QUANTUM SYSTEMS
Full text linkIn the present thesis we investigate two basic issues in the dynamics of open quantum systems, namely, the concept of non-Markovianity and the effects of initial system-environment correlations in the subsequent reduced dynamics.
In recent research, a great effort has been put into the study and understanding of non-Markovian features within the dynamics of open quantum systems. At the same time, quantum non-Markovianity has been defined and quantified in terms of quantum dynamical maps, using either a divisibility property or the behavior of the trace distance between pairs of reduced states evolved from different initial states. We investigate these approaches by means of several examples, focusing in particular on their relation with the very definition of non-Markov process used in classical probability theory. Indeed, the notion of non-Markovian behavior in the dynamics of the state of a physical system and the notion of non-Markov process are quite different and it will appear how the former represents sufficient, but not necessary condition with respect to the latter. In particular, we explicitly show that the above-mentioned divisibility property in the classical case is not, in general, equivalent to the Chapman-Kolmogorov equation, proper to Markov stochastic processes. Furthermore, by taking into account a bipartite open system, we emphasize how the presence of non-Markovian effects strongly depends on where the border between open system and environment is set.
A second relevant topic investigated in this thesis concerns the dynamics of open quantum system in the presence of initial system-environment correlations. By means of the approach based on trace distance, we go beyond the usual assumption that the open system and the environment are initially uncorrelated. The trace-distance analysis provides a characterization of open-system dynamics relying on measurements on the open system only, without the need for any extra information about the total system or system-environment interaction. After an introduction to the general theoretical scheme, we report an all-optical experimental realization, in which the total system under investigation consists of a couple of entangled photons generated by spontaneous parametric down conversion and initial correlations are introduced in a general fashion by means of a spatial light modulator. Finally, we take into account the Jaynes-Cummings model, showing how trace distance establishes general connections between correlation properties of initial total states and dynamical quantities that characterize the evolution of the open system
Quantum regression theorem and non-Markovianity of quantum dynamics
Full text linkWe explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation
Quantum master equation for collisional dynamics of massive particles with internal degrees of freedom
Full text linkWe address the microscopic derivation of a quantum master equation in Lindblad form for the dynamics of a massive test particle with internal degrees of freedom, interacting through collisions with a background ideal gas. When either internal or center-of-mass degrees of freedom can be treated classically, previously established equations are obtained as special cases. If in an interferometric setup the internal degrees of freedom are not detected at the output, the equation can be recast in the form of a generalized Lindblad structure, which describes non-Markovian effects. The effect of internal degrees of freedom on center-of-mass decoherence is considered in this framework
Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system
Full text linkWe consider the exact reduced dynamics of a two-level system coupled to a bosonic reservoir, further obtaining the exact time-convolutionless and Nakajima-Zwanzig non-Markovian equations of motion. The system considered includes the damped and undamped Jaynes- Cummings model. The result is obtained by exploiting an expression of quantum maps in terms of matrices and a simple relation between the time evolution map and the time-convolutionless generator as well as the Nakajima Zwanzig memory kernel. This nonperturbative treatment shows that each operator contribution in Lindblad form appearing in the exact time-convolutionless master equation is multiplied by a different time-dependent function. Similarly, in the Nakajima-Zwanzig master equation each such contribution is convoluted with a different memory kernel. It appears that, depending on the state of the environment, the operator structures of the two sets of equations of motion can exhibit important
differences
Signatures of non-Markovianity in classical single-time probability distributions
No full textWe show that the Kolmogorov distance allows to quantify memory effects in classical stochastic processes by studying the evolution of the singletime probability distribution. We further investigate the relation between the Kolmogorov distance and other sufficient but not necessary signatures of non- Markovianity within the classical setting
Two-step procedure to discriminate discordant from classical correlated or factorized states
Full text linkWe devise and experimentally realize a procedure capable of detecting and distinguishing quantum discord and classical correlations as well the presence of factorized states in a joint system-environment setting. Our scheme builds on recent theoretical results showing how the distinguishability between two reduced states of a quantum system in a bipartite setting can convey important information about the correlations present in the bipartite state and the interaction between the subsystems. The two addressed subsystems are the polarization and spatial degrees of freedom of the signal beam generated by parametric down-conversion, which are suitably prepared by the idler beam. Different global and local operations allow for the detection of different correlations by studying via state tomography the trace distance behavior between suitable polarization subsystem states
Quantum probes to experimentally assess correlations in a composite system
Full text linkWe suggest and demonstrate a technique to obtain relevant information about a composite system by performing measurements on only a small and easily accessible part of it, which we call a quantum probe. We show in particular how quantitative information about the angular correlations of pairs of entangled photons generated by spontaneous parametric down-conversion may be accessed through the study of the trace distance between two polarization states evolved from different initial conditions. After estimating the optimal polarization states to be used as the quantum probe, we provide a detailed analysis of the connections between the increase of the trace distance above its initial value and the amount of angular correlation
Quantum interference induced by initial system–environment correlations
Full text linkWe investigate the quantum interference induced by a relative phase in the correlated initial state of a system which consists in a two-level atom interacting with a damped mode of the radiation field. We show that the initial relative phase has significant effects on both the evolution of the atomic excited-state population and the information flow between the atom and the reservoir, as quantified by the trace distance. Furthermore, by considering two two-level atoms interacting with a common damped mode of the radiation field, we highlight how initial relative phases can affect the subsequent entanglement dynamics
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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