Many- and few-body physics in low-dimensional resonantly-interacting Fermi quantum gases

This thesis deals with theoretical investigations of atomic Fermi quantum gases in reduced dimensionalities. The principal focus is on the role of resonant interparticle interactions.
We discuss the issue of inelastic pair collisions in a spin-polarized Fermi gas. We develop a theory for describing two-body relaxation of single-component fermions near a p-wave Feshbach resonance. It is shown that in reduced dimensionalities the enhancement of the inelastic rate constant on approach to the resonance is much weaker compared to the three dimensional case. It opens prospects for realizing novel and exotic many-body phases of strongly interacting fermions.
We then illustrate this with the elusive itinerant ferromagnetic state in a one-dimensional two-component Fermi gas. We first consider the regime of an infinitely strong contact intercomponent repulsion and show that including a near-resonant attraction in the odd-wave interaction channel makes the energy of the ferromagnetic state lower than those of non-ferromagnetic states.
We then study the same system in the case of weak or intermediate contact repulsion strength. We find that the resonantly-enhanced attractive interaction in the odd-wave channel leads to the first-order phase transition to the so-called spin segregated state. In this state the gas separates into domains with non-zero local magnetization.