Large scattering lengths and long-range interactions in ultracold atomic gases

This thesis studies bosonic and fermionic quantum gases. In the first part, a variational many-body theory is used to explain a Bragg scattering experiment carried out on a bosonic quantum gas [S.B. Papp et al. Bragg Spectroscopy of a Strongly Interacting 85Rb Bose-Einstein Condensate. Phys. Rev. Lett. 101, 135301 (2008)]. A key feature in the experiment was the use of a Feshbach resonance, which made large values of the scattering length accessible. Due to the large values of the scattering length, existing models such as the Beliaev model could not be used to explain the observations, and therefore the experiment was a particularly interesting one to analyze. In our first approach, we constructed ad hoc potentials that fitted the observed excitation spectrum, and later we improved our approach by using T-matrix formalism to describe the Feshbach resonant system. All in all, the phenomenological model we developed fits the observed excitation spectrum and yields correct molecular Feshbach resonance state energies in certain cases. The second part of this thesis studies fermionic quantum gases. We focus on studying a gas of spin-1/2 particles confined to a spin-dependent optical lattice. The lattice geometry is such that the up-spin component is loaded in a honeycomb lattice, and the down-spin component is confined to the underlying triangular lattice. We considered attractive on-site and nearest-neighbor interactions, and formulated the nearest-neighbor interaction term in such a way that it takes into account the possibility of spontaneous time-reversal symmetry breaking. Furthermore, we took into account the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which breaks spatial symmetry. Within a mean-field approximation, we showed that the FFLO state is the ground state of the system in many instances. In addition, we found out that the system spontaneously breaks time-reversal symmetry if the nearest-neighbor interaction strength is large. Due to the time-reversal symmetry breaking, the system has topologically non-trivial phases characterized by nonzero Chern numbers. Finally, there were also cases where the time-reversal symmetry was broken in the FFLO phase, and thus we found a phase where spatial and time-reversal symmetries are simultaneously broken.Tässä väitöskirjassa käsitellään bosonisia ja fermionisia kvanttikaasuja. Työn ensimmäisessä osassa mallinnetaan eräässä Bose-kaasussa tehdyn Braggin sirontakokeen tulokset variaatiolaskentaan perustuvan monen kappaleen teorian avulla. Kokeessa sirontapituus pystyttiin säätämään suureksi Feshbach-resonanssin avulla ja tämän takia olemassa olevia malleja ei voitu käyttää tulosten selittämiseen. Tämä teki kokeesta erityisen kiinnostavan tutkimuskohteen. Ensin kehitimme joukon ad hoc -potentiaaleja, joilla sovitimme havaitun eksitaatiospektrin. Myöhemmin hyödynsimme T-matriisiformalismia Feshbach-resonanssin kuvaamisessa ja tällöin pystyimme mallintamaan myös sidottujen tilojen energioita. Yhteenvetona mallista voidaan todeta, että se mallintaa havaitun eksitaatiospektrin ja antaa oikean sidotun tilan energian joissain tapauksissa. Tämän työn toisessa osassa tutkitaan fermionisia kvanttikaasuja. Erityisesti tutkimme spin-riippuvaan optiseen hilaan vangittuja spin-1/2 hiukkasia. Hilageometriassa ylös-spin komponentti liikkuu hunajakennohilassa, mutta alas-spin komponentti on rajoitettu hunajakennohilan alihilaan, nimittäin kolmiohilaan. Sisällytimme malliimme attraktiivisen kontaktivuorovaikutuksen ja lähinaapurivuorovaikutuksen ja muotoilimme lähinaapurivuorovaikutusta kuvaavan termin siten, että se ottaa huomioon spontaanin ajankääntösymmetrian rikkoutumisen mahdollisuuden. Lisäksi otimme huomioon Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) faasin mahdollisuuden. Keskiarvotetun kentän approksimaation puitteissa osoitimme, että FFLO tila on systeemin perustila useissa tapauksissa. Lisäksi osoitimme, että ajankääntösymmetria rikkoutuu spontaanisti, jos lähinaapurivuorovaikutus on riittävän voimakas. Lopuksi näytimme myös, että ajankääntösymmetria rikkoutuu joissain tapauksissa myös FFLO faasissa. Toisin sanoen löysimme faasin, jossa ajankääntösymmetria ja spatiaalinen symmetria rikkoutuvat yhtä aikaa

A New Elbow Estimation Method for Selecting the Best Solution in Sparse Unmixing

The goal of hyperspectral image analysis is often to determine which materials, out of a given set of possibilities, are present in each pixel. As hyperspectral data are being gathered in rapidly increasing amounts, automatic image analysis is becoming progressively more important. Automatic identification of materials from a mixed pixel is possible with 1) Bayesian unmixing algorithms and 2) multiobjective sparse unmixing algorithms when a method such as elbow estimation is used to select the best solution from the set of Pareto-optimal solutions. We develop a new elbow estimation method called termination condition adaptive elbow (TCAE) for selecting the best solution from the set of Pareto-optimal solutions to a biobjective unmixing problem. Specifically, the two objectives are assumed to be the sparsity level of the fractional abundance vector and the reconstruction error. We conduct experiments with real-world unmixing applications in mind, and TCAE performs significantly better than a state-of-the-art elbow estimation method when they are both used to select the best solution from the sequence of fractional abundance vectors generated by iterative spectral mixture analysis (ISMA). Furthermore, the combination of ISMA and TCAE is able to identify endmembers from mixed pixels several times faster and with higher F1-score than the two Bayesian unmixing algorithms used as a reference. We conclude that the combination of ISMA and TCAE facilitates automatic, reliable, and rapid identification of endmembers from mixed pixels

A versatile capacitive sensing platform for the assessment of the composition in gas mixtures

The energy market is facing a major transition, in which natural gas and renewable gasses will play an important role. However, changing gas sources and compositions will force the gas transporters, gas engine manufacturers, and gas grid operators to monitor the gas quality in a more intensive way. This leads to the need for lower cost, smaller, and easy to install gas quality sensors. A new approach is proposed in this study that is based on the chemical interactions of the various gas components and responsive layers applied to an array of capacitive interdigitated electrodes. For Liquid Natural Gas (LNG), containing a relative high concentration of higher hydrocarbons, an array of ten capacitive chips is proposed, that is sufficient to calculate the full composition, and can be used to calculate energy parameters, such as Wobbe Index, Calorific Value, and Methane Number. A first prototype was realized that was small enough to be inserted in low and medium pressure gas pipes and LNG engine fuel lines. Adding the pressure and temperature data to the chip readings enables the determination of the concentrations of the various alkanes, hydrogen, nitrogen, and carbon dioxide, including small fluctuations in water vapor pressure. The sensitivity and selectivity of the new sensor is compared to a compact analyzer employing tunable filter infrared spectrometry