Chaos, Correlations and Entanglement in Strongly-correlated 1D Mixtures of Ultra-cold Bosons

Abstract

Okinawa Institute of Science and Technology Graduate UniversityDoctor of PhilosophyIn this thesis I focus on strongly-correlated multi-species systems of interacting bosons harmonically trapped in one-dimensional space from first principles. More specifically, in the first project, I study the emergence of quantum chaos in a binary mixture of few ultracold bosons in terms of the intra- and inter-species interactions. In particular, I answer an elementary question that is ‘What is the minimum number of interacting particles required to create chaos in a quantum system in the continuum?’. In the second project, I propose a robust scheme for engineering of correlated quantum states as ground states of systems of two distinguishable impurities immersed in a few-boson host medium. Particularly, by scrutinizing the ground-state properties of such system, I demonstrate that the two impurities exhibits non-classical correlations and form Bell states. Importantly, the proposed scheme can be implemented with current ultra-cold atomic settings, where particle numbers and interaction strengths are fully experimentally controllable. In the third project, I employ an ab initio approach to unveil quantum correlations, coherence, and spatial localization in threespecies mixtures of a few repulsively interacting bosons confined harmonically. The goal is to comprehensively explore the ground-state properties and hence illustrate the complete ground-state phase diagram of the three-species correlated system in terms of the intra- and inter-species interactions.doctoral thesi