Two-species boson mixture on a ring: A group theoretic approach to the quantum dynamics of low-energy excitations

Abstract

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 ${\hat{H}}_k$, each one associated to momentum modes $\pm k$. Each ${\hat{H}}_k$ 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 still very interesting 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.

11 pages, 7 figures

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• Mixtures of strongly interacting bosons in optical lattices
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Cited by in corpus (3)

• The mixing-demixing phase diagram of ultracold heteronuclear mixtures in a ring trimer
• Residual entropy and critical behavior of two interacting boson species in a double well
• Spatial Phase Separation of a Binary Mixture in a Ring Trimer