Akatürk, Emre2019-08-092019-08-092019-072019-072019-07-25http://hdl.handle.net/11693/52330Cataloged from PDF version of article.Thesis (Ph.D.): Bilkent University, Department of Physics, İhsan Doğramacı Bilkent University, 2019.Includes bibliographical references (leaves 49-59).Here, we present our work and findings on ultracold atomic systems. We first present a semi-analytical work on density wave instability (DWI) and collective modes of a bilayer dipolar system of bosons and fermions. We then show our results for quantum Monte Carlo (QMC) simulations on a bosonic system with an impurity in two-dimensions (2D). We investigate DWI on two parallel layers with antiparallel dipoles that have little to no pairing between interlayer particles. We observe that for both fermionic and bosonic bilayers, below a threshold intralayer coupling strength, no density wave instability emerges. At higher couplings, DWI forms below a critical layer spacing. We also investigate collective modes in this system. For the second problem, we present our investigations of a 2D Bose polaron, which is a system with bosonic particles and a mobile impurity. We use diffusion Monte Carlo (DMC) simulations to calculate physical quantities such as polaron energy and effective mass of the polaron as well as quantities that give insight to structural properties of the system such as pair correlation function and density profile. We model the boson-boson and boson-impurity interaction with hard spheres.x, 59 leaves : charts ; 30 cm.Englishinfo:eu-repo/semantics/openAccessAntiparallel dipolar bilayersDensity-wave instabilityCollective modesBose polaronImpurity-boson interactionsTwo-dimensionsThesisB160104