Eur. Phys. J. D (2022) 76: 16
https://doi.org/10.1140/epjd/s10053-022-00350-5

Regular Article – Cold Matter and Quantum Gases

The quantum vortex states in extended Bose–Hubbard model: effects of lattice geometries, inter-particle interactions and spatial inhomogeneity

Department of Physics, SP Pune University, 411007, Pune, India

^b bdey@physics.unipune.ac.in

Received: 2 August 2021
Accepted: 9 January 2022
Published online: 2 February 2022

Abstract

We study the effects of lattice geometries, inter-particle interactions and spatial inhomogeneity due to harmonic trap potential on the quantum vortex states of strongly interacting bosons in rotating two-dimensional optical lattice. The system is modelled by an extended Bose–Hubbard Hamiltonian. Using the numerical exact diagonalization method, we show how the rotation introduces vortex states of different ground-state symmetries and the transition between these states at discrete rotation frequencies. We consider optical lattices of different lattice geometries and show how the lattice geometry plays crucial roles in determining the maximum number of vortex states as well as the general characteristics of these quantum vortex states, such as the average angular momentum, the current at the perimeter of the lattice, phase winding, the maximum lattice current and also the saturation of the current between the two neighbouring lattice sites. We show the dependence of the lattice current flow on the inter-particle interactions which also depend on the geometry of the lattice. We also consider the effects of the spatial inhomogeneity introduced by the presence of an additional confining harmonic trap potential. It is shown that the curvature of the trap potential and the position of the minimum of the trap potential with respect to the axis of rotation or the centre of the lattice has significant effects on the general characteristics of these vortex states.