Non-Markovian Dynamics in Continuous Variable Quantum Systems

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. The 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. Signatures 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. The 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.

Non-Markovian Dynamics and the Quantum-To-Classical Transition for Quantum Brownian Motion

In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.

Quantum Tomography with Phase Space Measurements

This thesis addresses the use of covariant phase space observables in quantum tomography. Necessary and sufficient conditions for the informational completeness of covariant phase space observables are proved, and some state reconstruction formulae are derived. Different measurement schemes for measuring phase space observables are considered. Special emphasis is given to the quantum optical eight-port homodyne detection scheme and, in particular, on the effect of non-unit detector efficiencies on the measured observable. It is shown that the informational completeness of the observable does not depend on the efficiencies. As a related problem, the possibility of reconstructing the position and momentum distributions from the marginal statistics of a phase space observable is considered. It is shown that informational completeness for the phase space observable is neither necessary nor sufficient for this procedure. Two methods for determining the distributions from the marginal statistics are presented. Finally, two alternative methods for determining the state are considered. Some of their shortcomings when compared to the phase space method are discussed.

Quantum Hall effect in 2 dimensional GaInAs structure

Transport properties of GaAs / δ – Mn / GaAs / InxGa1-xAs / GaAs structure with Mn δ – layer, which is separated from InxGa1-xAs quantum well (QW) by 3 nm thick GaAs spacer was investigated. This structure with high mobility was characterized by X-ray difractometry and reflectometry. Transport and electrical properties of the structure were measured by using Pulsed Magnetic Field System (PMFS). During investigation of the Shubnikov – de Haas and the Hall effects the main parameters of QW structure such as cyclotron mass, Fermi level, g – factor, Dingle temperature and concentration of holes were estimated. Obtained results show high quality of the prepared structure. However, anomalous Hall effect at temperatures 2.09 K, 3 K, 4.2 K is not clearly observed. Attempts to identify magnetic moment were made. For this purpose the polarity of the filed was changed to the opposite at each shot. As a result hysteresis loop was not observed in the magnetic field dependences of the anomalous Hall resistivity.This can be attributed to the imperfection of the experimental setup.

Non-Markovian dynamics and quantum information probes

This Thesis discusses the phenomenology of the dynamics of open quantum systems marked by non-Markovian memory effects. Non-Markovian open quantum systems are the focal point of a flurry of recent research aiming to answer, e.g., the following questions: What is the characteristic trait of non-Markovian dynamical processes that discriminates it from forgetful Markovian dynamics? What is the microscopic origin of memory in quantum dynamics, and how can it be controlled? Does the existence of memory effects open new avenues and enable accomplishments that cannot be achieved with Markovian processes? These questions are addressed in the publications forming the core of this Thesis with case studies of both prototypical and more exotic models of open quantum systems. In the first part of the Thesis several ways of characterizing and quantifying non-Markovian phenomena are introduced. Their differences are then explored using a driven, dissipative qubit model. The second part of the Thesis focuses on the dynamics of a purely dephasing qubit model, which is used to unveil the origin of non-Markovianity for a wide class of dynamical models. The emergence of memory is shown to be strongly intertwined with the structure of the spectral density function, as further demonstrated in a physical realization of the dephasing model using ultracold quantum gases. Finally, as an application of memory effects, it is shown that non- Markovian dynamical processes facilitate a novel phenomenon of timeinvariant discord, where the total quantum correlations of a system are frozen to their initial value. Non-Markovianity can also be exploited in the detection of phase transitions using quantum information probes, as shown using the physically interesting models of the Ising chain in a transverse field and a Coulomb chain undergoing a structural phase transition.

Memory Effects in the Dynamics of Open Quantum Systems

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. In 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. The 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.

Instability of a square sheet under symmetric biaxial loading

An early experiment found that a square rubber sheet under symmetric biaxial loading may not remain square. This curious result has been one of the most instructive examples in finite elasticity. Here thermodynamic considerations are used to analyze this instability.

Universal Quantum Cloning

After introducing the no-cloning theorem and the most common forms of approximate quantum cloning, universal quantum cloning is considered in detail. The connections it has with universal NOT-gate, quantum cryptography and state estimation are presented and briefly discussed. The state estimation connection is used to show that the amount of extractable classical information and total Bloch vector length are conserved in universal quantum cloning. The 1  2 qubit cloner is also shown to obey a complementarity relation between local and nonlocal information. These are interpreted to be a consequence of the conservation of total information in cloning. Finally, the performance of the 1  M cloning network discovered by Bužek, Hillery and Knight is studied in the presence of decoherence using the Barenco et al. approach where random phase fluctuations are attached to 2-qubit gates. The expression for average fidelity is calculated for three cases and it is found to depend on the optimal fidelity and the average of the phase fluctuations in a specific way. It is conjectured to be the form of the average fidelity in the general case. While the cloning network is found to be rather robust, it is nevertheless argued that the scalability of the quantum network implementation is poor by studying the effect of decoherence during the preparation of the initial state of the cloning machine in the 1 ! 2 case and observing that the loss in average fidelity can be large. This affirms the result by Maruyama and Knight, who reached the same conclusion in a slightly different manner.

Lung tissue mechanics in the early stages of induced paracoccidioidomycosis in rats

Pulmonary dysfunction represents the most important cause of death in patients with paracoccidioidomycosis (PBM). In order to investigate the functional changes of the lungs in the early stages of PBM, a model of benign disease was developed by intratracheal challenge of 12-week old isogenic Wistar rats with 1 x 106 yeast forms of Paracoccidioides brasiliensis. Animals were studied 30 and 60 days after infection, when fully developed granulomas were demonstrable in the lungs. Measurements of airway resistance, lung elastance and tissue hysteresis were made during sinusoidal deformations (100 breaths/min, tidal volume = 2 ml) with direct measurement of alveolar pressure using the alveolar capsule technique. Infection caused a significant increase in hysteresis (infected: 1.69, N = 13; control: 1.13, N = 12, P = 0.024, ANOVA), with no alterations in airway resistance or lung elastance. Histopathological analysis revealed the presence of fully developed granulomas located in the axial compartment of the lung interstitial space. These results suggest that alterations of tissue mechanics represent an early event in experimental PBM

The effects of positive end-expiratory pressure on respiratory system mechanics and hemodynamics in postoperative cardiac surgery patients

We prospectively evaluated the effects of positive end-expiratory pressure (PEEP) on the respiratory mechanical properties and hemodynamics of 10 postoperative adult cardiac patients undergoing mechanical ventilation while still anesthetized and paralyzed. The respiratory mechanics was evaluated by the inflation inspiratory occlusion method and hemodynamics by conventional methods. Each patient was randomized to a different level of PEEP (5, 10 and 15 cmH2O), while zero end-expiratory pressure (ZEEP) was established as control. PEEP of 15-min duration was applied at 20-min intervals. The frequency dependence of resistance and the viscoelastic properties and elastance of the respiratory system were evaluated together with hemodynamic and respiratory indexes. We observed a significant decrease in total airway resistance (13.12 ± 0.79 cmH2O l-1 s-1 at ZEEP, 11.94 ± 0.55 cmH2O l-1 s-1 (P<0.0197) at 5 cmH2O of PEEP, 11.42 ± 0.71 cmH2O l-1 s-1 (P<0.0255) at 10 cmH2O of PEEP, and 10.32 ± 0.57 cmH2O l-1 s-1 (P<0.0002) at 15 cmH2O of PEEP). The elastance (Ers; cmH2O/l) was not significantly modified by PEEP from zero (23.49 ± 1.21) to 5 cmH2O (21.89 ± 0.70). However, a significant decrease (P<0.0003) at 10 cmH2O PEEP (18.86 ± 1.13), as well as (P<0.0001) at 15 cmH2O (18.41 ± 0.82) was observed after PEEP application. Volume dependence of viscoelastic properties showed a slight but not significant tendency to increase with PEEP. The significant decreases in cardiac index (l min-1 m-2) due to PEEP increments (3.90 ± 0.22 at ZEEP, 3.43 ± 0.17 (P<0.0260) at 5 cmH2O of PEEP, 3.31 ± 0.22 (P<0.0260) at 10 cmH2O of PEEP, and 3.10 ± 0.22 (P<0.0113) at 15 cmH2O of PEEP) were compensated for by an increase in arterial oxygen content owing to shunt fraction reduction (%) from 22.26 ± 2.28 at ZEEP to 11.66 ± 1.24 at PEEP of 15 cmH2O (P<0.0007). We conclude that increments in PEEP resulted in a reduction of both airway resistance and respiratory elastance. These results could reflect improvement in respiratory mechanics. However, due to possible hemodynamic instability, PEEP should be carefully applied to postoperative cardiac patients.

Respiratory mechanics and morphometric changes during anesthesia with ketamine in normal rats

Ketamine is believed to reduce airway and pulmonary tissue resistance. The aim of the present study was to determine the effects of ketamine on the resistive, elastic and viscoelastic/inhomogeneous mechanical properties of the respiratory system, lungs and chest wall, and to relate the mechanical data to findings from histological lung analysis in normal animals. Fifteen adult male Wistar rats were assigned randomly to two groups: control (N = 7) and ketamine (N = 8). All animals were sedated (diazepam, 5 mg, ip) and anesthetized with pentobarbital sodium (20 mg/kg, ip) or ketamine (30 mg/kg, ip). The rats were paralyzed and ventilated mechanically. Ketamine increased lung viscoelastic/inhomogeneous pressure (26%) compared to the control group. Dynamic and static elastances were similar in both groups, but the difference was greater in the ketamine than in the control group. Lung morphometry demonstrated dilation of alveolar ducts and increased areas of alveolar collapse in the ketamine group. In conclusion, ketamine did not act at the airway level but acted at the lung periphery increasing mechanical inhomogeneities possibly resulting from dilation of distal airways and alveolar collapse.

Symmetric pollen mitosis I and suppression of pollen mitosis II prevent pollen development in Brachiaria jubata (Gramineae)

Microsporogenesis and pollen development were analyzed in a tetraploid (2n = 4x = 36) accession of the forage grass Brachiaria jubata (BRA 007820) from the Embrapa Beef Cattle Brachiaria collection that showed partial male sterility. Microsporocytes and pollen grains were prepared by squashing and staining with 0.5% propionic carmine. The meiotic process was typical of polyploids, with precocious chromosome migration to the poles and laggards in both meiosis I and II, resulting in tetrads with micronuclei in some microspores. After callose dissolution, microspores were released into the anther locule and appeared to be normal. Although each microspore initiated its differentiation into a pollen grain, in 11.1% of them nucleus polarization was not observed, i.e., pollen mitosis I was symmetric and the typical hemispherical cell plate was not detected. After a central cytokinesis, two equal-sized cells showing equal chromatin condensation and the same nuclear shape and size were formed. Generative cells and vegetative cells could not be distinguished. These cells did not undergo the second pollen mitosis and after completion of pollen wall synthesis each gave rise to a sterile and uninucleate pollen grain. The frequency of abnormal pollen mitosis varied among flowers and also among inflorescences. All plants were equally affected. The absence of fertile sperm cells in a considerable amount of pollen grains in this accession of B. jubata may compromise its use in breeding and could explain, at least in part, why seed production is low when compared with the amount of flowers per raceme.

Distortion and internal warping torsion of a double symmetric hollow section

This thesis is made in cooperation with Laboratory of Steel Structures and the steel company SSAB. Maximization of the benefits of high-strength steel usually requires the usage of thin wall thicknesses. This means the failures related to buckling, distortion and warping stand out. One must be aware of these phenomena to design thin-walled structures stressed with forces such as torsional loading. It is also important to take into account small stress ranges when evaluating the accurate fatigue strength of structures. The objective of this thesis is to clarify the theory of the uniform and non-uniform torsion. This paper focuses on warping due to the non-uniform torsion in double symmetric box girder and structural hollow section. The arisen stress states are explained and researched using the finite element method. Another research target is the distortion in double symmetric box girder due to torsion, and the restraining effect of transverse diaphragms at the load end. Multiple transverse diaphragms are used to study more efficient restraining against warping and distortion than a common one end plate structure.

Comorbidity of psychiatric disorders and symmetric distal polyneuropathy among type II diabetic outpatients

The objective of the present study was to establish the frequency of psychiatric comorbidity in a sample of diabetic patients with symmetric distal polyneuropathy (SDPN). Sixty-five patients with type 2 diabetes mellitus were selected consecutively to participate in the study at Instituto Estadual de Diabetes e Endocrinologia. All patients were submitted to a complete clinical and psychiatric evaluation, including the Portuguese version of the structured clinical interview for DSM-IV, the Beck Depression Inventory, the Neuropathy Symptom Score, and Neuropathy Disability Score. SDPN was identified in 22 subjects (33.8%). Patients with and without SDPN did not differ significantly regarding sociodemographic characteristics. However, a trend toward a worse glycemic control was found in patients with SDPN in comparison to patients without SDPN (HbA1c = 8.43 ± 1.97 vs 7.48 ± 1.95; P = 0.08). Patients with SDPN exhibited axis I psychiatric disorders significantly more often than those without SDPN (especially anxiety disorders, in general (81.8 vs 60.0%; P = 0.01), and major depression - current episode, in particular (18.2 vs 7.7%; P = 0.04)). The severity of the depressive symptoms correlated positively with the severity of SDPN symptoms (r = 0.38; P = 0.006), but not with the severity of SDPN signs (r = 0.07; P = 0.56). In conclusion, the presence of SDPN seems to be associated with a trend toward glycemic control. The diagnosis of SDPN in diabetic subjects seems also to be associated with relevant psychiatric comorbidity, including anxiety and current mood disorders.

Tabvla Rvssiae ex autographo, quod delineandum curavit Foedor filius tzaris Boris desumta; et ad fluvios Dwinam, Zuchanam, aliaque loca, quantum ex tabulis et notitiis ad nos delatis fieri potuit, amplificata: ac magno domino, tzari , et magno duci Michäeli Foedorowits omnium Russorum, autcratori Wolodimeriae, Moscoviae et Novogardia. Tzari Cazaniae, tzari Astracaniae, tzari Siberiae, domino Plescoviae magno duci Smolenscoviae, Otweriae, Iugoriae, Permiae, Wiatkiae, Bulgariae etc: domino regionum Iveriae Kartalinie et Groesiniae tzari etc: dedicata ab Hesselo Gerardo M.DC.XIIII.

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