Ring Dark Solitons in Toroidal Bose-Einstein Condensates

In this Thesis, we study various aspects of ring dark solitons (RDSs) in quasi-two-dimensional toroidally trapped Bose-Einstein condensates, focussing on atomic realisations thereof. Unlike the well-known planar dark solitons, exact analytic expressions for RDSs are not known. We address this problem by presenting exact localized soliton-like solutions to the radial Gross-Pitaevskii equation. To date, RDSs have not been experimentally observed in cold atomic gases, either. To this end, we propose two protocols for their creation in experiments. It is also currently well known that in dimensions higher than one, (ring) dark solitons are susceptible, in general, to an irreversible decay into vortex-antivortex pairs through the snake instability. We show that the snake instability is caused by an unbalanced quantum pressure across the soliton's notch, linking the instability to the Bogoliubov-de Gennes spectrum. In particular, if the angular symmetry is maintained (or the toroidal trapping is restrictive enough), we show that the RDS is stable (long-lived with a lifetime of order seconds) in two dimensions. Furthermore, when the decay does take place, we show that the snake instability can in fact be reversible, and predict a previously unknown revival phenomenon for the original (many-)RDS system: the soliton structure is recovered and all the point-phase singularities (i.e. vortices) disappear. Eventually, however, the decay leads to an example of quantum turbulence; a quantum example of the laminar-to-turbulent type of transition.

Yang-Tse-Kiang : from the sea to Nanking

Kartta kuuluu A. E. Nordenskiöldin kokoelmaan

Spin Polarization and Normal Reflection at Nanoscale Point Contacts

This thesis presents point-contact measurements between superconductors (Nb, Ta, Sn,Al, Zn) and ferromagnets (Co, Fe, Ni) as well as non-magnetic metals (Ag, Au, Cu, Pt).The point contacts were fabricated using the shear method. The differential resistanceof the contacts was measured either in liquid He at 4.2 K or in vacuum in a dilutionrefrigerator at varying temperature down to 0.1 K. The contact properties were investigatedas function of size and temperature. The measured Andreev-reflection spectrawere analysed in the framework of the BTK model – a three parameter model that describescurrent transport across a superconductor - normal conductor interface. Theoriginal BTK model was modified to include the effects of spin polarization or finitelifetime of the Cooper pairs. Our polarization values for the ferromagnets at 4.2 K agree with the literature data, but the analysis was ambiguous because the experimental spectra both with ferromagnets and non-magnets could be described equally well either with spin polarization or finite lifetime effects in the BTK model. With the polarization model the Z parametervaries from almost 0 to 0.8 while the lifetime model produces Z values close to 0.5. Measurements at lower temperatures partly lift this ambiguity because the magnitude of thermal broadening is small enough to separate lifetime broadening from the polarization. The reduced magnitude of the superconducting anomalies for Zn-Fe contacts required an additional modification of the BTK model which was implemented as a scaling factor. Adding this parameter led to reduced polarization values. However, reliable data is difficult to obtain because different parameter sets produce almost identical spectra.

Comparison of sweat rate during graded exercise and the local rate induced by pilocarpine

Centrally stimulated sweat rate produced by graded exercise until exhaustion was compared to the local sweat rate induced by pilocarpine, often used as a sweating index for healthy individuals. Nine young male volunteers (22 ± 4 years) were studied in temperate environment in two situations: at rest and during progressive exercise with 25 W increases every 2 min until exhaustion, on a cycle ergometer. In both situations, sweating was induced on the right forearm with 5 ml 0.5% pilocarpine hydrochloride applied by iontophoresis (1.5 mA, 5 min), with left forearm used as control. Local sweat rate was measured for 15 min at rest. During exercise, whole-body sweat rate was calculated from the body weight variation. Local sweat rate was measured from the time when heart rate reached 150 bpm until exhaustion and was collected using absorbent filter paper. Pharmacologically induced local sweat rate at rest (0.4 ± 0.2 mg cm-2 min-1) and mean exercise-induced whole-body sweat rate (0.4 ± 0.1 mg cm-2 min-1) were the same (P > 0.05) but were about five times smaller than local exercise-induced sweat rate (control = 2.1 ± 1.4; pilocarpine = 2.7 ± 1.2 mg cm-2 min-1), indicating different sudorific mechanisms. Both exercise-induced whole-body sweat rate (P < 0.05) and local sweat rate (P < 0.05) on control forearm correlated positively with pilocarpine-induced local sweat rate at rest. Assuming that exercise-induced sweating was a result of integrated physiological mechanisms, we suggest that local and whole-body sweat rate measured during graded exercise could be a better sweating index than pilocarpine.

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.

Lunae, Veneris, Mercurii, exteriora & interiora quantum scire datum est exhibens

Variantti A.

Use of the Wasserman equation in optimization of the duration of the power ramp in a cardiopulmonary exercise test: a study of Brazilian men

This study aimed to analyze the agreement between measurements of unloaded oxygen uptake and peak oxygen uptake based on equations proposed by Wasserman and on real measurements directly obtained with the ergospirometry system. We performed an incremental cardiopulmonary exercise test (CPET), which was applied to two groups of sedentary male subjects: one apparently healthy group (HG, n=12) and the other had stable coronary artery disease (n=16). The mean age in the HG was 47±4 years and that in the coronary artery disease group (CG) was 57±8 years. Both groups performed CPET on a cycle ergometer with a ramp-type protocol at an intensity that was calculated according to the Wasserman equation. In the HG, there was no significant difference between measurements predicted by the formula and real measurements obtained in CPET in the unloaded condition. However, at peak effort, a significant difference was observed between oxygen uptake (V˙O2)peak(predicted)and V˙O2peak(real)(nonparametric Wilcoxon test). In the CG, there was a significant difference of 116.26 mL/min between the predicted values by the formula and the real values obtained in the unloaded condition. A significant difference in peak effort was found, where V˙O2peak(real)was 40% lower than V˙O2peak(predicted)(nonparametric Wilcoxon test). There was no agreement between the real and predicted measurements as analyzed by Lin’s coefficient or the Bland and Altman model. The Wasserman formula does not appear to be appropriate for prediction of functional capacity of volunteers. Therefore, this formula cannot precisely predict the increase in power in incremental CPET on a cycle ergometer.

Modification of a quantum efficiency measurement system for multi-junction solar cells

In this thesis the basic structure and operational principals of single- and multi-junction solar cells are considered and discussed. Main properties and characteristics of solar cells are briefly described. Modified equipment for measuring the quantum efficiency for multi-junction solar cell is presented. Results of experimental research single- and multi-junction solar cells are described.

Non-Markovian dynamics in quantum optical dephasing channels

Quantum computation and quantum communication are two of the most promising future applications of quantum mechanics. Since the information carriers used in both of them are essentially open quantum systems it is necessary to understand both quantum information theory and the theory of open quantum systems in order to investigate realistic implementations of such quantum technologies. In this thesis we consider the theory of open quantum systems from a quantum information theory perspective. The thesis is divided into two parts: review of the literature and original research. In the review of literature we present some important definitions and known results of open quantum systems and quantum information theory. We present the definitions of trace distance, two channel capacities and superdense coding capacity and give a reasoning why they can be used to represent the transmission efficiency of a communication channel. We also show derivations of some properties useful to link completely positive and trace preserving maps to trace distance and channel capacities. With the help of these properties we construct three measures of non-Markovianity and explain why they detect non-Markovianity. In the original research part of the thesis we study the non-Markovian dynamics in an experimentally realized quantum optical set-up. For general one-qubit dephasing channels we calculate the explicit forms of the two channel capacities and the superdense coding capacity. For the general two-qubit dephasing channel with uncorrelated local noises we calculate the explicit forms of the quantum capacity and the mutual information of a four-letter encoding. By using the dynamics in the experimental implementation as a set of specific dephasing channels we also calculate and compare the measures in one- and two-qubit dephasing channels and study the options of manipulating the environment to achieve revivals and higher transmission rates in superdense coding protocol with dephasing noise. Kvanttilaskenta ja kvanttikommunikaatio ovat kaksi puhutuimmista tulevaisuuden kvanttimekaniikan käytännön sovelluksista. Koska molemmissa näistä informaatio koodataan systeemeihin, jotka ovat oleellisesti avoimia kvanttisysteemejä, sekä kvantti-informaatioteorian, että avointen kvanttisysteemien tuntemus on välttämätöntä. Tässä tutkielmassa käsittelemme avointen kvanttisysteemien teoriaa kvantti-informaatioteorian näkökulmasta. Tutkielma on jaettu kahteen osioon: kirjallisuuskatsaukseen ja omaan tutkimukseen. Kirjallisuuskatsauksessa esitämme joitakin avointen kvanttisysteemien ja kvantti-informaatioteorian tärkeitä määritelmiä ja tunnettuja tuloksia. Esitämme jälkietäisyyden, kahden kanavakapasiteetin ja superdense coding -kapasiteetin määritelmät ja esitämme perustelun sille, miksi niitä voidaan käyttää kuvaamaan kommunikointikanavan lähetystehokkuutta. Näytämme myös todistukset kahdelle ominaisuudelle, jotka liittävät täyspositiiviset ja jäljensäilyttävät kuvaukset jälkietäisyyteen ja kanavakapasiteetteihin. Näiden ominaisuuksien avulla konstruoimme kolme epä-Markovisuusmittaa ja perustelemme, miksi ne havaitsevat dynamiikan epä-Markovisuutta. Oman tutkimuksen osiossa tutkimme epä-Markovista dynamiikkaa kokeellisesti toteutetussa kvanttioptisessa mittausjärjestelyssä. Yleisen yhden qubitin dephasing-kanavan tapauksessa laskemme molempien kanavakapasiteettien ja superdense coding -kapasiteetin eksplisiittiset muodot. Yleisen kahden qubitin korreloimattomien ympäristöjen dephasing-kanavan tapauksessa laskemme yhteisen informaation lausekkeen nelikirjaimisessa koodauksessa ja kvanttikanavakapasiteetin. Käyttämällä kokeellisen mittajärjestelyn dynamiikkoja esimerkki dephasing-kanavina me myös laskemme konstruoitujen epä-Markovisuusmittojen arvot ja vertailemme niitä yksi- ja kaksi-qubitti-dephasing-kanavissa. Lisäksi käyttäen kokeellisia esimerkkikanavia tutkimme, kuinka ympäristöä manipuloimalla superdense coding –skeemassa voidaan saada yhteinen informaatio ajoittain kasvamaan tai saavuttaa kaikenkaikkiaan korkeampi lähetystehokkuus.

Extreme Observables and Optimal Measurements in Quantum Theory

Optimization of quantum measurement processes has a pivotal role in carrying out better, more accurate or less disrupting, measurements and experiments on a quantum system. Especially, convex optimization, i.e., identifying the extreme points of the convex sets and subsets of quantum measuring devices plays an important part in quantum optimization since the typical figures of merit for measuring processes are affine functionals. In this thesis, we discuss results determining the extreme quantum devices and their relevance, e.g., in quantum-compatibility-related questions. Especially, we see that a compatible device pair where one device is extreme can be joined into a single apparatus essentially in a unique way. Moreover, we show that the question whether a pair of quantum observables can be measured jointly can often be formulated in a weaker form when some of the observables involved are extreme. Another major line of research treated in this thesis deals with convex analysis of special restricted quantum device sets, covariance structures or, in particular, generalized imprimitivity systems. Some results on the structure ofcovariant observables and instruments are listed as well as results identifying the extreme points of covariance structures in quantum theory. As a special case study, not published anywhere before, we study the structure of Euclidean-covariant localization observables for spin-0-particles. We also discuss the general form of Weyl-covariant phase-space instruments. Finally, certain optimality measures originating from convex geometry are introduced for quantum devices, namely, boundariness measuring how ‘close’ to the algebraic boundary of the device set a quantum apparatus is and the robustness of incompatibility quantifying the level of incompatibility for a quantum device pair by measuring the highest amount of noise the pair tolerates without becoming compatible. Boundariness is further associated to minimum-error discrimination of quantum devices, and robustness of incompatibility is shown to behave monotonically under certain compatibility-non-decreasing operations. Moreover, the value of robustness of incompatibility is given for a few special device pairs.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.