Static and dynamics properties of a miscible two-component Bose-Einstein condensate

One of the main reasons which makes Bose-Einstein condensates a successful topic of research is their flexibility for creating systems whose Hamiltonian can be engineered almost at will. A particularly relevant research topic in the field of Bose–Einstein condensation concerns the realization of binary mixtures in the presence of coherent coupling Ω. These systems show properties having analogies with the formation of stripe phases, which are related to supersolidity, or with the formation of domain walls, which are related to quark confinement in quantum chromodynamics. Technically, the realization of coherently coupled binary mixtures requires a deep knowledge of the system properties, even in absence of coherent coupling between the two states, and a highly precise control of the magnetic field. Both these topics are treated in this research work, which aims to lay the foundation for experimental studies in resonantly-coupled spinor BECs. More in detail, the simplest collective oscillation, i.e., the spin-dipole (SD) oscillation and the static SD polarizability are studied to test the miscibility properties of the system and its response to external perturbation of the trapping potentials, both at zero and at finite temperature in order to characterize the behaviour of the system at Ω = 0. This work also reports the theoretical study done to design a magnetic shield able to guarantee a precise control of the environmental magnetic field and suitable to be used to study the binary mixture in the presence of coherent coupling.