The aim of this work is to probe observable effects of vortex driven Superfluid-Mott insulator transition using the rotational Bose-Hubbard mode kept inhomogeneous by a Berry curvature, considering neutral bosons confined in a 1D confinement about the x-direction. The 1D model includes two-or-three-body onsite interaction in order to probe further into the interactions. Our theoretical results show notable effects. These effects include vortex escape, ground state degeneracy showing some symmetry breaking due to vortex nucleation, higher degenerate excited states and preferential accommodation of vortex energy. To validate our results, the critical values for the Superfluid to Mott-insulator transition for the 2 bosons , in agreement with Manuela et. al.(2004) where the critical value is in 1D Mott-insulator transition and also as calculated in Batrouni et al (1990), while in the 3 bosons interaction case the transition point is closely equal to obtained by Jaksch et al. (1998), Kunher and Moniem (1998), Pai and Pandit (2005). We have discussed these notable effects extensively and conclude from our results that the vortex has no significant effect on the on the 1D Superfluid to Mott insulation transition points, but has much significant effect on the energy spectra excitation and degeneracy . We hope to employ our result as feasible candidate for implementation of the Dirac’s principle of superposition of evolution of time proposed by Ibeh and Akpojortor (2020) in probing the problem of “negative time” in quantum mechanics.
