Topologically Bose-Einstein condensates quantum phase transition strong interactions

Abstract

This article examine a Bose-Einstein condensate functioning inside a double-well potential that is experiencing a dynamical shift from the Josephson oscillations regime to the self-trapping regime. Statistical features of the Hamiltonian's ground state (or maximum excited state) in these two regimes for attracted (repulsive) interaction is examined. Our focus is on atomic Bose-Einstein condensates contained in quasi-one-dimensional closed-loop waveguides and how ellipticity-induced curvature impacts them. Intriguing phenomena resulting from the combination of curvature and interactions are revealed by our theoretical analysis. In highly curved areas, density modulations are seen, but they are canceled eliminated through strong repulsive interactions. If the waveguide is superflowy and has a high eccentricity, we also see phase accumulation at the flattest parts of the waveguide. In addition, waveguides that include vortices show transitions between states with varying angular moments. With consequences for both quantum technology and basic physics, these results provide light on how atomic condensates behave in curved waveguides. Novel quantum phenomena with engineering of quantum states in constrained geometries may be explored via the interaction between curvature and interactions. We examine the one-dimensional miscible-immiscible quantum phase change in a binary Bose-Hubbard model that is linearly connected. This model is able to account for the low-energy characteristics of a two-component condensate of Bose-Einstein in optical lattices. The distinctive physical properties of the phase transition governed by the linear coupling among the two components are calculated using the quantum many-body ground state that is derived via the density matrices renormalization group technique. In addition, we build the phase diagram and find the critical point by calculating the Binder cumulant. The change cannot be described within the framework of mean-field theory, as we show. On the other hand, the transition happens in a delocalized state that is highly correlated, has big quantum fluctuations, and spontaneously breaks the symmetry.