ULTRACOLD FERMIONIC FEW-BODY SYSTEMS IN REDUCED DIMENSIONS: STATIC AND DYNAMIC PROPERTIES
Gharashi, Seyed Ebrahim
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Much progress has been made in the preparation and manipulation of tunable ultracold atomic samples over the last three decades.Small samples of ultracold $^6$Li atoms, e.g., have beenprepared experimentally in effectively one-dimensional geometries.The study of few-atom samples is particularly interestingsince they serve as building blocks ofmany-body systems.This thesis studies static and dynamic properties of ultracold fermionic few-body systems.A Lippmann-Schwinger equation based approach is utilizedto obtain highly-accurate energies and eigenfunctions of two-componentFermi gases with interspecies zero-range interactions consisting of up to four particles underone-dimensional harmonic confinement.The resulting energy spectra agree quite well with the experimentally measured ones.For infinitely-strong repulsive interaction, theeigenfunctions of the system, which are populated by adiabaticallyincreasing the interaction strength from $0$ to $\infty$, differ from the eigenfunctions obtained through ageneralized Fermi-Fermi mapping, indicating shortcomings of the generalized Fermi-Fermi mapping.The correlations of the “upper branch" reveal, in resemblance with Stoner ferromagnetism,a competition between the repulsive interspecies interaction and the effective repulsion due to the Pauli exclusion principle.Full three-dimensional calculations are performed to assess the applicability regime of strictly one-dimensional models. Moreover, the full three-dimensional energy spectra are utilized to determine the third-order virial coefficient, which plays an important role in determining the equation of state in the high-temperature regime as functions of the interaction strength and confinement geometry.Motivated by recent experiments, the tunneling dynamics of two interacting one-dimensional $^6$Li atoms is simulated within a full time-dependent framework.It is shown that a WKB based trap calibration is, in general, inaccurateand an alternative trap parametrization is proposed. Simulation results in agreement with the experimentally measured two-particle tunneling rates are obtained only if the effective one-dimensional coupling constant accounts for the dependence of the transverse confinement on the position along the weak trap.