Fragmented condensation in Bose-Hubbard trimers with tunable tunnelling

TL;DR

This paper investigates how tunable tunnelling in a Bose-Hubbard trimer affects ground state properties, revealing fragmented condensates and semifluxon excitations, with implications for quantum state control.

Contribution

It introduces a detailed analysis of ground states in a tunable Bose-Hubbard trimer, highlighting fragmentation and semifluxon excitations in the $ ext{π}$-phase configuration.

Findings

Fragmented condensates occur in the $ ext{π}$-phase case.

Fragmentation is robust against small tunnelling variations.

Low-energy spectrum explained by semifluxon excitations.

Abstract

We consider a Bose-Hubbard trimer, i.e. an ultracold Bose gas populating three quantum states. The latter can be either different sites of a triple-well potential or three internal states of the atoms. The bosons can tunnel between different states with variable tunnelling strength between two of them. This will allow us to study; i) different geometrical configurations, i.e. from a closed triangle to three aligned wells and ii) a triangular configuration with a $\pi$-phase, i.e. by setting one of the tunnellings negative. By solving the corresponding three-site Bose-Hubbard Hamiltonian we obtain the ground state of the system as a function of the trap topology. We characterise the different ground states by means of the coherence and entanglement properties. For small repulsive interactions, fragmented condensates are found for the $\pi$-phase case. These are found to be robust against small variations of the tunnelling in the small interaction regime. A low-energy effective many-body Hamiltonian restricted to the degenerate manifold provides a compelling description of the $\pi$-phase degeneration and explains the low-energy spectrum as excitations of discrete semifluxon states.