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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 nearestneighbor 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. Tiivistelmä 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 spinriippuvaan optiseen hilaan vangittuja spin-1/2 hiukkasia. Hilageometriassa ylös-spin komponentti liikkuu hunaja...

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“…Therefore, by employing the Stokes' theorem, we obtain c n = 1 2πi 56) where ∂R 2 means the boundary of region R 2 . Since it can be shown that…”

Section: Let Us Definementioning

confidence: 99%

Elementary excitations and universal interaction in Bose-Einstein condensates at large scattering lengths

2011

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“…If the collision event is fast enough the single particle of the scatterer recoils like a free particle and this is incorporated into (42) with the delta function giving energy conservation. The different recoil processes are determined by the probability that a particle has a momentum p, i.e.…”

Section: Momentum Distributionmentioning

confidence: 99%

Many-body theories of condensed phases of 4He and normal 3He

Reatto

1992

J Low Temp Phys

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“…Vo(r) = V(r) -(h2/4m) V2uo(r) (5) V(r) is the 4He-4He interaction potential and m is the mass of the 4He atom.…”

Section: Self-consistent Paired-phonon Analysismentioning

confidence: 99%

“…The method of calculation is the same as the recent ground-state calculation on threedimensional liquid 4He. 5 The optimum Jastrow wave function with longrange correlation and structure in the intermediate range is first obtained by carrying out a self-consistent paired-phonon calculation i.n conjunction with the HNC approximation. Then the effect of the three-body extended Jastrow correction is calculated.…”

Section: Introductionmentioning

confidence: 99%

Ground state of two-dimensional liquid 4He

Chang

1980

J Low Temp Phys

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The ground-state energy and liquid structure function of two-dimensional liquid 4He are calculated in the density range 0.028-0.075 ~-e, using the Lennard-Jones 6-12 potential. The optimal Jastrow function is first determined by a self-consistent paired-phonon calculation and then the contributions of three-body factors the wave function are calculated. Tables of values are given at several densities for the radial distribution function, Jastrow function, and liquid structure function.

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Energy and structure of the ground state of liquidHe4

Cited by 143 publications

References 27 publications

Elementary excitations and universal interaction in Bose-Einstein condensates at large scattering lengths

Elementary excitations and universal interaction in Bose-Einstein condensates at large scattering lengths

Many-body theories of condensed phases of 4He and normal 3He

Ground state of two-dimensional liquid 4He

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