The anisotropic Bose-Hubbard dimer in the mean field approximation (2025)
This project studies the system formed by two coupled Bose-Einstein condensates, also known as the bosonic Josephson junction. A double-well model is used to trap the ultracold atoms, and special attention is paid to the understudied case of asymmetric wells. A brief introduction to Bose- Einstein condensates and their relationship to optical lattices is provided. The Bose-Hubbard model restricted to two wells is also described, and a large number of particles is considered, allowing for the use of the semiclassical mean-field approximation. By introducing anisotropy into this system, a symmetry breaking in phase space is found, which can be interpreted as a dissipative process emerging in semiclassical dynamics, although the total particle flux is conserved. Additionally, this same system is studied using the spin formalism considering a large number of bosons. Under this approach, the anisotropy affects the system in the same way as a Zeeman effect, where the dimer behaves as an N/2 spin model in the presence of an external magnetic field proportional to ∆. The expectation values of the spin components and their variances are studied, especially for ˆSz , which by definition represents the difference of particles for both wells and depends strongly on the anisotropy. The quantum fluctuations for ˆSx, ˆSy, and ˆSz decrease with increasing particle number, particularly as ∝ 1/N , suggesting that ˆSx, ˆSy, and ˆSz becomes more quantum localized near the semiclassical limit.