UC Merced

Due to phenomenal progress in trapping and cooling of cold atoms, ultracold atoms has been a successful platform for studying fundamental physics and simulating quantum many-body systems with the advantage of tuning the parameters in real space. In this dissertation, we theoretically investigated inhomogeneous structures of different ultracold atomic mixtures in quasi-one-dimensional box potentials to explore the rich phases of atomic mixtures. The realization of uniform box potentials in experiments allows us to study inhomogeneous structures, phase diagrams and interface structures in various atomic mixtures which arise from the competition between interaction energy and kinetic energy. The presence of real space constraints like box potentials or quenching of interactions permits the extraction of characteristic length scale of the systems. We examined the characteristic lengths of spatial change such as, the healing lengths in the case of boson-fermion mixtures and correlation lengths in the case of superfluid-normal phase transition. The analyses of the healing lengths at the boson-fermion interface confirms the energy competition mechanism behind the phase-separation structures. We modelled spatially tunable inhomogeneous interactions for attractive Fermi gases to study analogs of the proximity effect and the spatial Kibble-Zurek mechanism (KZM) in a unified framework. The introduction of inhomogeneity lead to the distortion of the order parameter which is characterized by the correlation length. We extracted the correlation lengths from the pair wavefunction and correlation function to determine the penetration of the order parameter in the region where interaction vanishes. In the setup resembling the proximity effect, we found that the correlation lengths follow the BCS coherence length while only the exponent from the pair correlation function agrees to the Kibble-Zurek scaling in the case of spatial KZM setup. We also extract the critical exponent by adding a uniform bosonic background to the attractive Fermi gases and found that it does not alter the scaling behavior in the miscible phase. With recent experimental progress in the field of atomic mixtures and box potentials, our results will characterize the density profiles, correlation lengths and scaling behavior of those multi-component quantum systems.