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.

Hitsausvirtalähteen ohjaus lämmöntuonnin ja jatkuvan jäähtymisen S-käyrän perusteella

Lämmöntuonnilla on oleellinen vaikutus hitsausliitoksen ominaisuuksiin, koska se vaikuttaa liitoksen jäähtymisnopeuteen, jolla on puolestaan suuri vaikutus jäähtymisessä syntyviin mikrorakenteisiin. Jatkuvan jäähtymisen S-käyrältä voidaan ennustaa hitsausliitokseen syntyvät mikrorakenteet. S-käyrät voidaan laatia hitsausolosuhteiden mukaisesti, jolloin faasimuutoskäyttäytyminen sularajalla saadaan selvitettyä. Tämän diplomityön tavoitteena oli kehittää hitsausvirtalähteen ohjaustapaa lämmöntuontiin ja jatkuvan jäähtymisen S-käyriin perustuen. Jatkuvan jäähtymisen S-käyrillä ja lämmöntuontiin perustuvalla hitsausparametrien säädöllä on yhteys. Työssä tutkittiin, miten haluttuun jäähtymisnopeuteen johtava lämmöntuonti voidaan määrittää S-käyrälle luotettavasti. Työssä perehdyttiin jatkuvan jäähtymisen S-käyriin ja eri jäähtymisnopeuksilla hitsausliitokseen syntyviin mikrorakenteisiin sekä hitsaus-inverttereiden ohjaus- ja säätötekniikkaan. Teoriaosuuden jälkeen tarkasteltiin eri vaihtoehtoja, miten hitsattavan materiaalin koostumusvaihtelut sekä lämmöntuontiin vaikuttavat tekijät voidaan ottaa huomioon virtalähteen ohjauksessa lämmöntuonnin perusteella. S-käyrältä määritettyjen lämmöntuonnin arvojen perusteella tehtiin kahdet koehitsaukset, joissa käytettiin kolmea eri aineenpaksuutta. Tulosten perusteella arvioitiin lämmöntuonnin arvojen toimivuutta käytännössä ja tutkittiin liitokseen syntyviä mikrorakenteita. Tutkimuksen pohjalta esitettiin jatkokehitystoimenpiteitä, joiden mukaan voidaan edetä lämmöntuontiin perustuvan säätöjärjestelmän kehitysprojektissa.

Hydrogen Sensor Application of Anodic Titanium Oxide Nanostructures

Hydrogen (H2) fuel cells have been considered a promising renewable energy source. The recent growth of H2 economy has required highly sensitive, micro-sized and cost-effective H2 sensor for monitoring concentrations and alerting to leakages due to the flammability and explosiveness of H2 Titanium dioxide (TiO2) made by electrochemical anodic oxidation has shown great potential as a H2 sensing material. The aim of this thesis is to develop highly sensitive H2 sensor using anodized TiO2. The sensor enables mass production and integration with microelectronics by preparing the oxide layer on suitable substrate. Morphology, elemental composition, crystal phase, electrical properties and H2 sensing properties of TiO2 nanostructures prepared on Ti foil, Si and SiO2/Si substrates were characterized. Initially, vertically oriented TiO2 nanotubes as the sensing material were obtained by anodizing Ti foil. The morphological properties of tubes could be tailored by varying the applied voltages of the anodization. The transparent oxide layer creates an interference color phenomena with white light illumination on the oxide surface. This coloration effect can be used to predict the morphological properties of the TiO2 nanostructures. The crystal phase transition from amorphous to anatase or rutile, or the mixture of anatase and rutile was observed with varying heat treatment temperatures. However, the H2 sensing properties of TiO2 nanotubes at room temperature were insufficient. H2 sensors using TiO2 nanostructures formed on Si and SiO2/Si substrates were demonstrated. In both cases, a Ti layer deposited on the substrates by a DC magnetron sputtering method was successfully anodized. A mesoporous TiO2 layer obtained on Si by anodization in an aqueous electrolyte at 5°C showed diode behavior, which was influenced by the work function difference of Pt metal electrodes and the oxide layer. The sensor enabled the detection of H2 (20-1000 ppm) at low operating temperatures (50–140°C) in ambient air. A Pd decorated tubular TiO2 layer was prepared on metal electrodes patterned SiO2/Si wafer by anodization in an organic electrolyte at 5°C. The sensor showed significantly enhanced H2 sensing properties, and detected hydrogen in the range of a few ppm with fast response/recovery time. The metal electrodes placed under the oxide layer also enhanced the mechanical tolerance of the sensor. The concept of TiO2 nanostructures on alternative substrates could be a prospect for microelectronic applications and mass production of gas sensors. The gas sensor properties can be further improved by modifying material morphologies and decorating it with catalytic materials.

Magnetophotoresistance in Pr 1–x CaxMnO3 Thin Films

In this work, a colossal magnetoresistive (CMR) Pr1−xCaxMnO3 (PCMO) man- ganite thin films and polycrystalline samples were studied with the main focus on the properties of the insulator to metal Mott phase transition. The polycrystalline PCMO samples were fabricated with the solid state reaction method. The polycrystalline sam- ples were further processed into the epitaxial thin films with the pulsed laser deposition method (PLD). The structural and magnetic properties of the samples were systemat- ically investigated and the thin films samples were further investigated with magneto- transport measurement where the thin films response to illumination was also studied. After the successful synthesis of polycrystalline PCMO samples with varying x = between 0.0 - 0.5, the magnetic characterization of the samples showed rich magnetic properties having the signatures of the magnetic phase coexistence of antiferromag- netic (AFM) and ferromagnetic (FM) ordering and cluster glass behaviour. With the increased doping concentration from x = 0.3 to 0.5, the AFM charge-order (CO) phase started to form up being strongest on the sample x = 0.5. This AFM CO phase could be melted with the high external magnetic field at temperatures below Neel’s tempera- ture TN inducing an irreversible first order metamagnetic AFM to FM phase transition. The strength of the AFM CO phase decreased with decreasing Ca concentration and increasing temperature. The polycrystalline PCMO samples with Ca concentrations of 0.3 - 0.5, showing metamagnetic behaviour, were selected for the fabrication of the thin film samples. The films were grown using two different in situ oxygen treatment temperatures at 500 ◦C and 700 ◦C in the PLD system. The films with x = 0.4 and 0.5 showed weaker AFM CO phase with greatly reduced melting fields when compared to polycrystalline samples. Also, the robustness of the AFM CO phase was further decreased in thin films with the lower oxygen treatment temperature of 500 ◦C. The magneto-transport measurements made on the thin films showed that the melting of AFM CO phase was connected to CMR effect where the increasing magnetic field induced an insulator to metal phase transition, which reduces the resistivity of the film around nine orders of magnitude. The use of illumination during the magneto-transport measurements showed a vari- ety of intriguing phenomena including magnetophotoresistance. The illumination had a huge effect to the insulator to metal transition (IMT) reducing the transition magnetic field significantly. Moreover, by magnetically biasing the thin films with the constant external magnetic field, the IMT could be induced by switching on the illumination.

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.

Covariant Phase Observables in Quantum Mechanics

The aim of this thesis is to present a solution to the quantum phase problem of the single-mode optical field. The solution is based on the use of phase shift covariant normalized positive operator measures. These measures describe realistic direct coherent state phase measurements such as the phase measurement schemes based on eight-port homodyne detection or heterodyne detection. The structure of covariant operator measures and, more generally, covariant sesquilinear form measures is analyzed in this work. Four different characterizations for phase shift covariant normalized positive operator measures are presented. The canonical covariant operator measure is definded and its properties are studied. Finally, some other suggested phase theories are introduced to investigate their connections to the covariant sesquilinear form measures.

Quantum transport phenomena and shallow impurity states in CdSb

This work is dedicated to investigation of the energy spectrum of one of the most anisotropic narrow-gap semiconductors, CdSb. At the beginning of the present studies even the model of its energy band structure was not clear. Measurements of galvanomagnetic effects in wide temperature range (1.6 - 300 K) and in magnetic fields up to 30 T were chosen for clarifying of the energy spectrum in the intentionally undoped CdSb single crystals and doped with shallow impurities (In, Ag). Detection of the Shubnikov - de Haas oscillations allowed estimating the fundamental energy spectrum parameters. The shapes of the Fermi surfaces of electrons (sphere) and holes (ellipsoid), the number of the equivalent extremums for valence band (2) and their positions in the Brillouin zone were determined for the first time in this work. Also anisotropy coefficients, components of the tensor of effective masses of carriers, effective masses of density of states, nonparabolicity of the conduction and valence bands, g-factor and its anisotropy for n- and p-CdSb were estimated for the first time during these studies. All the results obtained are compared with the cyclotron resonance data and the corresponding theoretical calculations for p-CdSb. This is basic information for the analyses of the complex transport properties of CdSb and for working out the energy spectrum model of the shallow energy levels of defects and impurities in this semiconductor. It was found out existence of different mechanisms of hopping conductivity in the presence of metal - insulator transition induced by magnetic field in n- and p-CdSb. Quite unusual feature opened in CdSb is that different types of hopping conductivity may take place in the same crystal depending on temperature, magnetic field or even orientation of crystal in magnetic field. Transport properties of undoped p-CdSb samples show that the anisotropy of the resistivity in weak and strong magnetic fields is determined completely by the anisotropy of the effective mass of the holes. Temperature and magnetic field dependence of the Hall coefficient and magnetoresistance is attributed to presence of two groups of holes with different concentrations and mobilities. The analysis demonstrates that below Tcr ~ 20 K and down to ~ 6 - 7 K the low-mobile carriers are itinerant holes with energy E2 ≈ 6 meV. The high-mobile carriers, at all temperatures T < Tcr, are holes activated thermally from a deeper acceptor band to itinerant states of a shallower acceptor band with energy E1 ≈ 3 meV. Analysis of temperature dependences of mobilities confirms the existence of the heavy-hole band or a non-equivalent maximum and two equivalent maxima of the light-hole valence band. Galvanomagnetic effects in n-CdSb reveal the existence of two groups of carriers. These are the electrons of a single minimum in isotropic conduction band and the itinerant electrons of the narrow impurity band, having at low temperatures the energies above the bottom of the conduction band. It is found that above this impurity band exists second impurity band of only localized states and the energy of both impurity bands depend on temperature so that they sink into the band gap when temperature is increased. The bands are splitted by the spin, and in strong magnetic fields the energy difference between them decreases and redistribution of the electrons between the two impurity bands takes place. Mobility of the conduction band carriers demonstrates that scattering in n-CdSb at low temperatures is strongly anisotropic. This is because of domination from scattering on the neutral impurity centers and increasing of the contribution to mobility from scattering by acoustic phonons when temperature increases. Metallic conductivity in zero or weak magnetic field is changed to activated conductivity with increasing of magnetic field. This exhibits a metal-insulator transition (MIT) induced by the magnetic field due to shift of the Fermi level from the interval of extended states to that of the localized states of the electron spectrum near the edge of the conduction band. The Mott variablerange hopping conductivity is observed in the low- and high-field intervals on the insulating side of the MIT. The results yield information about the density of states, the localization radius of the resonant impurity band with completely localized states and about the donor band. In high magnetic fields this band is separated from the conduction band and lies below the resonant impurity bands.

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.