Fragmented condensation in Bose–Hubbard trimers with tunable tunnelling

A Gallemí,A Polls,J Martorell,R Mayol,M Guilleumas,B Juliá-Díaz

doi:10.1088/1367-2630/17/7/073014

Abstract

We consider a Bose–Hubbard (BH) 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 π-phase, i.e. by setting one of the tunnellings negative. By solving the corresponding three-site BH Hamiltonian we obtain the ground state of the system as a function of the trap topology. We characterize the different ground states by means of the coherence and entanglement properties. For small repulsive interactions, fragmented condensates are found for the π-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 π-phase degeneration and explains the low-energy spectrum as excitations of discrete semifluxon states.

Highlights

It is well known that bosons at sufficiently low temperatures tend to form Bose–Einstein condensates (BECs), which essentially consist on the macroscopic population of a single-particle state [1]
The many-body ground state may get fragmented [2], as naively the atoms have no reason to condense in only one of the degenerate single-particle states. This implies that a finite number of eigenvalues of the single-particle density matrix are of order of the total number of atoms
In the first two cases, the many-body ground state for small interactions NU J ∼ 1 is highly condensed, with one of the three eigenvalues of the one-body density matrix clearly scaling with the total number of particles

Summary

14 July 2015

A Gallemí, M Guilleumas, J Martorell, R Mayol, A Polls and B Juliá-Díaz. Author(s) and the title of the work, journal citation The latter can be either different sites of a triple-well potential or three internal states of the atoms. 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 π-phase, i.e. by setting one of the tunnellings negative. For small repulsive interactions, fragmented condensates are found for the π-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 π-phase degeneration and explains the low-energy spectrum as excitations of discrete semifluxon states

Introduction

Three-mode BH Hamiltonian

Quantum many-body properties of the system

Summary and conclusions