School of Physics - Theses
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ItemBound states and structural properties of trap-imbalanced fermions( 2016)Ultracold quantum gases, which were only recently realised experimentally, have become one of the most active fields of modern research. This is due to the precision and power of the experiments, as well as the great variety of physical phenomena that they exhibit. In this thesis, the physics of few-body scattering in the strongly-interacting regime is studied. The study of few-body physics allows a better understanding of many-body systems, particularly with strong interactions, which make the usual many-body theoretical techniques untenable. The particular topic of this thesis is few-body scattering in heteronuclear systems, which contain two species of atom with different masses and/or harmonic trapping frequencies. These mass and trap imbalances lead to a variety of interesting physics that is not present in homonuclear systems. Deeply-bound Efimov states with unusual properties appear in systems containing two species of fermions when the ratio of the two species' masses becomes sufficiently large. Other types of deeply bound states also appear above a lower critical mass ratio. We use an implementation of a stochastic variational method to study states of this type under a trap imbalance i.e.\ with two species of fermion with different harmonic trapping frequencies. The stochastic variational method works by randomly generating trial functions, then using a competitive selection scheme to select the best contributions to the approximate variational solution. Using this method, it is shown that the introduction of a trap imbalance has no effect ont the physics of these bound states. Also using this variational method, the effect of trap imbalances on two- and three-body systems, with and without mass imbalances, is studied in detail. It is found that the trap imbalance has the immediate effect of lifting structural and energetic degeneracies between different total angular momentum states of the few-body system. Furthermore, trap imbalances significantly alter the usual physics of the three-fermion system, in which two atoms form a deeply-bound dimer while the third remains unbound. The trap imbalance changes this picture and causes all three atoms to overlap considerably in the ground state, forming a loosely-bound trimer state. Such alterations to the few-body collision properties can have significant effects on the many-body physics of an atomic gas. Thus these results indicate the possibility of additional methods of tuning and control for heteronuclear many-body systems. These results may also be of interest in explicitly few-body experiments, which remain largely unexplored at this time.