We investigate the weak excitations of a system made up of two condensates trapped in a Bose-Hubbard ring and coupled by an interspecies repulsive interaction. Our approach, based on the Bogoliubov approximation scheme, shows that one can reduce the problem Hamiltonian to the sum of sub-Hamiltonians ˆ H k , each one associated to momentum modes ± k . Each ˆ H k is then recognized to be an element of a dynamical algebra. This uncommon and remarkable property allows us to present a straightforward diagonalization scheme, to find constants of motion, to highlight the significant microscopic processes, and to compute their time evolution. The proposed solution scheme is applied to a simple but nontrivial closed circuit, the trimer. The dynamics of low-energy excitations, corresponding to weakly populated vortices, is investigated considering different choices of the initial conditions and the angular-momentum transfer between the two condensates is evidenced. Finally, the condition for which the spectral collapse and dynamical instability are observed is derived analytically.
Two-species boson mixture on a ring: A group-theoretic approach to the quantum dynamics of low-energy excitations / Penna, V.; Richaud, A.. - In: PHYSICAL REVIEW A. - ISSN 2469-9926. - STAMPA. - 96(2017). [10.1103/PhysRevA.96.053631]
|Titolo:||Two-species boson mixture on a ring: A group-theoretic approach to the quantum dynamics of low-energy excitations|
|Data di pubblicazione:||2017|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1103/PhysRevA.96.053631|
|Appare nelle tipologie:||1.1 Articolo in rivista|