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.

Be-Fe coupled method for the analysis of 3D elastodynamic problems in the time domain

By coupling the Boundary Element Method (BEM) and the Finite Element Method (FEM) an algorithm that combines the advantages of both numerical processes is developed. The main aim of the work concerns the time domain analysis of general three-dimensional wave propagation problems in elastic media. In addition, mathematical and numerical aspects of the related BE-, FE- and BE/FE-formulations are discussed. The coupling algorithm allows investigations of elastodynamic problems with a BE- and a FE-subdomain. In order to observe the performance of the coupling algorithm two problems are solved and their results compared to other numerical solutions.

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.

Using green fluorescent protein to understand the mechanisms of G-protein-coupled receptor regulation

G protein-coupled receptor (GPCR) activation is followed rapidly by adaptive changes that serve to diminish the responsiveness of a cell to further stimulation. This process, termed desensitization, is the consequence of receptor phosphorylation, arrestin binding, sequestration and down-regulation. GPCR phosphorylation is initiated within seconds to minutes of receptor activation and is mediated by both second messenger-dependent protein kinases and receptor-specific G protein-coupled receptor kinases (GRKs). Desensitization in response to GRK-mediated phosphorylation involves the binding of arrestin proteins that serve to sterically uncouple the receptor from its G protein. GPCR sequestration, the endocytosis of receptors to endosomes, not only contributes to the temporal desensitization of GPCRs, but plays a critical role in GPCR resensitization. GPCR down-regulation, a loss of the total cellular complement of receptors, is the consequence of both increased lysosomal degradation and decreased mRNA synthesis of GPCRs. While each of these agonist-mediated desensitization processes are initiated within a temporally dissociable time frame, recent data suggest that they are intimately related to one another. The use of green fluorescent protein from the jellyfish Aqueora victoria as an epitope tag with intrinsic fluorescence has facilitated our understanding of the relative relationship between GRK phosphorylation, arrestin binding, receptor sequestration and down-regulation.

Immunization by subcutaneous implants of polyester-polyurethane sponges coupled with antigen

A new protocol is described for immunization of outbred Swiss mice. The procedure is based on subcutaneous implantation of antigen-coupled polyester-polyurethane sponges cut into disks of 10 mm in diameter vs 2 mm in thickness. Antigen coupling was performed by overnight incubation of the sponge with a solution of ovalbumin (Ova) (2 mg/ml) diluted in sodium carbonate buffer, pH 9.6. The amount of ovalbumin that was taken up by the sponge was between 71.4 to 82.5 µg. This was estimated by comparing the Ova absorbance at 280 nm in coating buffer solutions before and after incubation. To compare the efficiency of the proposed method, experimental groups immunized with the antigen in the presence of adjuvants (10 µg in Al(OH)3 or 100 µg in complete Freund's adjuvant (CFA)) were run in parallel. The data obtained after the 3rd week of immunization indicate that both cellular and humoral immune responses were achieved. These were assayed by antigen-induced footpad swelling and ELISA (specific antibodies), respectively. The levels of both immune responses elicited were similar to the responses observed in mice immunized with ovalbumin in the presence of Al(OH)3. The method might represent an advantage when immunizing with pathogenic antigens. Preliminary experiments have suggested that the antigen remains immobilized or bound to the sponge for a long period of time, since there is an increment on the cell population inside the sponges after boosting the animals. If so, the undesirable effects of immunization would be reduced.

An optically coupled power stimulus isolation unit with high voltage and fast rise time output

Recent technological developments have created new devices that could improve and simplify the construction of stimulus isolators. HEXFET transistors can switch large currents and hundreds of volts in nanoseconds. The newer opto-isolators can give a pulse rise time of a few nanoseconds, with output compatible with MOSFET devices, in which delays are reduced to nanoseconds. Integrated DC/DC converters are now available. Using these new resources we developed a new electrical stimulus isolator circuit with selectable constant-current and constant-voltage modes, which are precise and easy to construct. The circuit works like a regulated power supply in both modes with output switched to zero or to free mode through an opto-isolator device. The isolator analyses showed good practical performance. The output to ground resistance was 1011 ohms and capacitance 35 picofarads. The rise time and fall time were identical (5 µs) and constant. The selectable voltage or current output mode made it very convenient to use. The current mode, with higher output resistance values in low current ranges, permits intracellular stimulation even with tip resistances close to 100 megaohms. The high compliance of 200 V guarantees the value of the current stimulus. The very low output resistance in the voltage mode made the device highly suitable for extracellular stimulation with low impedance electrodes. Most importantly, these characteristics were achieved with a circuit that was easy to build and modify and assembled with components available in Brazil.

Disintegrins: integrin selective ligands which activate integrin-coupled signaling and modulate leukocyte functions

Extracellular matrix proteins and cell adhesion receptors (integrins) play essential roles in the regulation of cell adhesion and migration. Interactions of integrins with the extracellular matrix proteins lead to phosphorylation of several intracellular proteins such as focal adhesion kinase, activating different signaling pathways responsible for the regulation of a variety of cell functions, including cytoskeleton mobilization. Once leukocytes are guided to sites of infection, inflammation, or antigen presentation, integrins can participate in the initiation, maintenance, or termination of the immune and inflammatory responses. The modulation of neutrophil activation through integrin-mediated pathways is important in the homeostatic control of the resolution of inflammatory states. In addition, during recirculation, T lymphocyte movement through distinct microenvironments is mediated by integrins, which are critical for cell cycle, differentiation and gene expression. Disintegrins are a family of low-molecular weight, cysteine-rich peptides first identified in snake venom, usually containing an RGD (Arg-Gly-Asp) motif, which confers the ability to selectively bind to integrins, inhibiting integrin-related functions in different cell systems. In this review we show that, depending on the cell type and the microenvironment, disintegrins are able to antagonize the effects of integrins or to act agonistically by activating integrin-mediated signaling. Disintegrins have proven useful as tools to improve the understanding of the molecular events regulated by integrin signaling in leukocytes and prototypes in order to design therapies able to interfere with integrin-mediated effects.

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.

[N. 1:9000000].

De lapsu generis humani in quantum ex lumine naturae constat

Invokaatio: D.F.G.

De usuris, in quantum sunt concessae?

Dedikaatio: Henricus Florinus, Jonas Petrejus, Jacobus Lvnd, Jsaacus Piilman, Ericus Ehrling, Nicolaus Procopaeus.