This report describes a project performed at Linnaeus University with the task of solving the Schrodinger equation for electrons in homonuclear diatomic molecules, using the finite element method in Python. The Schrodinger equation is solved for the hydrogen atom, nitrogen atom, hydrogen molecule and nitrogen molecule using a finite element method. The results of the hydrogen atom showed a high accuracy compared to the analytical solution, given that the domain had high enough resolution. The solutions of the hydrogen molecule, nitrogen atom and nitrogen molecule showed reasonable accuracy although the resolution appeared sufficient. This foundation of Python code can be further built upon to explore more molecules and more properties, such as total energies and vibrational energies.

In this project we simulate explosions of nano water droplets using molecular dynamics. The water droplets are put under the exposure of a high-energy X-ray laser, which induces a quick Coulomb explosion. The explosion patterns, reporting the resulting position of the atoms, are then analyzed in different ways. Methods to deduce the initial shape of an ellipsoidal water droplet based on its explosion pattern are developed.

We constructed a standalone optical trapping system that was steerable in three dimensions and allowed for sufficient imaging of one цm particles with a CCD camera. The motion of the trapped particles was monitored by both a position sensitive detector as well with the CCD camera. The trap stiffness was evaluated by the power spectrum method and the equipartition theorem. For calibration of the stiffness of the trap, we found that the power spectrum method with data assessed by the PSD was most straightforward and accurate. The equipartition method was compromised by noise, low resolution and the bandwidth of the detector. With a HeNe laser run at 10 mW output power the trap strength of our system reached ~2 pN/um. The results also showed a decrease in the trap stiffness and particle's position variance when the size of trapped particles increased.

No description available.

Assessing the mixing of two liquids is a critical task in the biotechnical industry. At Cytiva, affinity chromatography columns depend on a well-mixed aqueous salt solution to release the target from the affinity resin. A mixer is often incorporated into the flow path to ensure effective mixing of the liquids.These mixers generate complex three-dimensional flowfields, and existing measurement techniques frequently average the flow depth, thereby losing essential spatial information. This project introduces and implements a novel method for assessing mixing in four dimensions, requiring simultaneous imaging of the flow from multiple view points. The flowfield is reconstructed from the image data using a least squares tomographic reconstruction technique. Additionally, a methodwas developed to reconstruct the same flowfield numerous times using different underlying section meshes. These results are then interpolated on a common grid and averaged. The findings demonstrate that this method accurately resolves the flowfield qualitatively and quantitatively. The averaging method enables lower downsampling factors and higher overall accuracy. However, challenges such as achieving uniform pipe illumination and enhancing data acquisition rates remain. Addressing these issues is essential for fully resolving three-dimensional flowfields over time. Future work will improve lighting and data acquisition to enhance the method’s applicability for higher Reynolds number applications.

In this thesis we study device-independent quantum key distribution based on energy-time entanglement. This is a method for cryptography that promises not only perfect secrecy, but also to be a practical method for quantum key distribution thanks to the reduced complexity when compared to other quantum key distribution protocols. However, there still exist a number of loopholes that must be understood and eliminated in order to rule out eavesdroppers. We study several relevant loopholes and show how they can be used to break the security of energy-time entangled systems. Attack strategies are reviewed as well as their countermeasures, and we show how full security can be re-established. Quantum key distribution is in part based on the profound no-cloning theorem, which prevents physical states to be copied at a microscopic level. This important property of quantum mechanics can be seen as Nature's own copy-protection, and can also be used to create a currency based on quantummechanics, i.e., quantum money. Here, the traditional copy-protection mechanisms of traditional coins and banknotes can be abandoned in favor of the laws of quantum physics. Previously, quantum money assumes a traditional hierarchy where a central, trusted bank controls the economy. We show how quantum money together with a blockchain allows for Quantum Bitcoin, a novel hybrid currency that promises fast transactions, extensive scalability, and full anonymity. / En viktig konsekvens av kvantmekaniken är att okända kvanttillstånd inte kan klonas. Denna insikt har gett upphov till kvantkryptering, en metod för två parter att med perfekt säkerhet kommunicera hemligheter. Ett komplett bevis för denna säkerhet har dock låtit vänta på sig eftersom en attackerare i hemlighet kan manipulera utrustningen så att den läcker information. Som ett svar på detta utvecklades apparatsoberoende kvantkryptering som i teorin är immun mot sådana attacker. Apparatsoberoende kvantkryptering har en mycket högre grad av säkerhet än vanlig kvantkryptering, men det finns fortfarande ett par luckor som en attackerare kan utnyttja. Dessa kryphål har tidigare inte tagits på allvar, men denna avhandling visar hur även små svagheter i säkerhetsmodellen läcker information till en attackerare. Vi demonstrerar en praktisk attack där attackeraren aldrig upptäcks trots att denne helt kontrollerar systemet. Vi visar också hur kryphålen kan förhindras med starkare säkerhetsbevis. En annan tillämpning av kvantmekanikens förbud mot kloning är pengar som använder detta naturens egna kopieringsskydd. Dessa kvantpengar har helt andra egenskaper än vanliga mynt, sedlar eller digitala banköverföringar. Vi visar hur man kan kombinera kvantpengar med en blockkedja, och man får då man en slags "kvant-Bitcoin". Detta nya betalningsmedel har fördelar över alla andra betalsystem, men nackdelen är att det krävs en kvantdator.

This thesis describes the work performed at the Quantum Optics lab at UNAM,Mexico City. Third order spontaneous parametric down conversion (TOSPDC) isa quantum optical process where an incoming photon is annihilated and generatesthree quantum entangled photons, so called photon triplets, under energy and mo-mentum conservation. This TOSPDC process was experimentally realized using afused silica optical fiber as nonlinear source. The spectra of the emitted signal weremeasured and coincidence counts measurements were performed in order to verifythe generation of these triplets. An average of 0.8 triplets per second were detected,which is the first sign of a realized TOSPDC process to our knowledge. At thispoint, the signal was too low for any spectra to be recorded. There is a lot of roomfor improvements, especially regarding the equipment used due to the heavy signalloss throughout the experimental setup, and more experiments will be performed toproperly verify the production and entanglement of the triplet photons.

Quantification of spectral data is of great interest in many fields of science, since it can provide further insight into other properties of an object. However, traditional cameras are usually made to image the world in a similar fashion as to how we see it, wherefore they are usually not fit to record nor measure further spectral information. To get a better insight into the spectral properties of an object, a hyperspectral camera might be of use, since those can often identify and measure hundreds of different spectral bands. In this study we look at the construction and further development of an existing design of a push broom hyperspectral imaging system, built with optics for a fraction of the cost of commercial ones. With developed software and objects at hand a spectral calibration was performed, showing a possible spectral range of 184(2)-918(11) nm, but the use of the whole spectral range was however not possible due to limitations in the transmissivity of the lenses below 350 nm. A shift of the spectral range towards longer wavelengths is proposed, which would give further insight into the near infrared spectrum without any information losses. It was found that the spectral calibration of the imager was the main limiting factor of the system, since inaccuracies up to ±11 nm were identified, while the resolution has been found to be 1.4 nm in previous studies, proving that better calibrations are of essence. In good operating conditions, the resolution in the angle of view of the imager was found to be 0.55 mdeg. If the measurement conditions are not as good, or if such kind of spatial resolution is not required, a camera with a smaller detector size and larger pixels could be used to lower the cost of the system without a deterioration in image quality, since the uncertainties in the calibrations and measurement conditions were found to be the limiting factor.

In this thesis, periodic structures with higher symmetries symmetries are discussed. The main focus of the thesis is on twist symmetries. Importantly, the attractive properties of twist symmetries for the control of electromagnetic wave propagation are demonstrated. Furthermore, the additional degree of freedom offered by twist symmetries is used to design two microwave devices. A structure is twist-symmetric if its periodicity can be described by the geometrical operation consisting of a translation and a rotation around an axis. In this thesis, it is demonstrated that there are no stop-bands between the first q modes in the Brillouin diagram of a twist-symmetric structure, where q is the symmetry order. The importance of the symmetry to the absence or presence of stop-bands is illustrated by studying structures where the symmetry is gradually broken. Furthermore, it is demonstrated that a twist-symmetric structure can produce a higher and less dispersive effective refractive index, compared to a conventional periodic structure. These characteristics are attractive for the design of microwave devices. To provide insight into the physics of twist symmetry, a mode matching formulation is derived to analyze twist-symmetric coaxial transmission lines. The formulation is used to highlight the importance of higher order coupling on the response in structures with varying order of the twist symmetry.  In this thesis, we also discuss another type of symmetry; polar glide symmetry. A periodic structure possesses a polar glide symmetry if its periodicity can be described by the geometrical operation consisting of a translation and a reflection in a cylindrical surface. It is demonstrated that there is no stop-band between the first two modes in a polar glide structure, which is similar to what has been reported for Cartesian glide symmetry previously. Furthermore, twist symmetry and polar glide symmetry is combined into twisted polar glide symmetry. The effect of this combination on the stop-band between the second and third modes is demonstrated. It is concluded that this type of symmetry finds application in filter design. Finally, the additional design freedom offered by twist symmetry is used to produce two microwave components. A reconfigurable phase shifter is designed, where the phase delay in the phase shifter depends on the order of the twist symmetry. Furthermore, a flat lens is designed to transform a spherical wave into a quasi-planar wave. The focusing properties of the lens is obtained by locally varying the order of the symmetry throughout the lens aperture. / I denna avhandling diskuteras periodiska strukturer med högre symmetrier. Huvudfokus av avhandlingen är skruvsymmetrier. Vi visar de attraktiva egenskaperna av skruvsymmetrier för kontrollen av elektromagnetiska vågor. Dessutom används den extra designfriheten från skruvsymmetrier för att designa två mikrovågskomponenter. En struktur är skruvsymmetrisk om dess period kan beskrivas av en geometriska operation bestående av en translation och en rotation runt en axel. I denna avhandling visar vi att det inte finns några bandgap mellan de första q moderna i Brillouindiagrammet för en skruvsymmetrisk struktur, där q är symmetriordningern. Betydelsen av symmetri för frånvaron och närvaron av bandgap illustreras genom att studera strukturer där symmetrin gradvis bryts. Vidare visar vi att en skruvsymmetrisk struktur kan producera ett högre och mindre dispersivt effektivt refraktivt index jämfört med en vanlig periodisk struktur. Dessa egenskaper är attraktiva i designen av mikrovågskomponenter. För att ge insikt i fysiken bakom skruvsymmetrier tas en modmatchningsformulering fram för att studera skruvsymmetriska koaxiala transmissionsledare. Formuleringen används för att belysa vikten av högre ordnings vågkoppling för egenskaperena i strukturer med olika ordnings skruvsymmetri.  I denna avhandling diskuteras ytterliage en typ av högre symmetri; polär glidsymmetri. En struktur har en polär glidsymmetri om dess period kan beskrivas av en geometriska operation bestående av en translation och en spegling i en cylindrisk yta. Vi visar att det inte finns något bandgap mellan de två första moderna i en struktur med polär glidsymmetri, vilket också tidigare visats för Cartesisk glidsymmetri. Vidare kombinerar vi skruv- och polär glidsymmetri. Implikationerna av denna kombination på bandgapet mellan högre moder diskuteras. Vi kommer fram till att denna typ av kombinerad symmetri finner tillämpningar i filterdesign.  Slutligen används den extra designfriheten från skruvsymmetri för att designa två mikrovågskomponenter. En konfigurerbar fasskiftare designas, där fasskiftningen beror på symmetriordningen. Vidare designas en platt lins som omvandlar en sfärisk våg till en kvasiplan våg. Fokuseringsegenskaperna i linsen uppnås genom att lokalt variera symmetriordningen i linsens apertur. / <p>QC 20211103</p>

Calculation of number of photon pairs produced by type-I degenerate Spontaneous Parametric Down-Conversion inside a BBO crystal.