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

TL;DR

This paper analyzes the quantum dynamics of low-energy excitations in a two-species boson mixture on a ring using a group theoretic approach, providing a new diagonalization method and insights into vortex dynamics and instabilities.

Contribution

It introduces a novel group theoretic diagonalization scheme for coupled Bose-Hubbard rings, enabling detailed analysis of excitations and instabilities in two-species condensates.

Findings

Identifies constants of motion for the system.

Analyzes vortex dynamics and angular momentum transfer.

Derives conditions for spectral collapse and dynamical instability.

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.