Vortical configuration of synthetically charged condensate boson atoms trapped in two dimensional deep optical lattice

In the present paper, we calculate the superfluid fraction and the critical synthetic magnetic field for vortices nucleation of synthetically charged condensate boson gases trapped in 2D deep optical lattice. The superfluid fraction is parametrized in terms of the moment of inertia, while the critical synthetic field is defined as the ratio between the magnetic free energy and the thermal average of the angular momentum. These calculations are realized in the semiclassical approximation. The effects of finite size effect, the interatomic interaction and the synthetic magnetic field strength are investigated. The extracted results show crucial dependence of the vortical configuration on the above mentioned parameters. •Superfluidity fraction and the critical synthetic field for vortices nucleation of synthetically charged boson atoms in deep optical lattice under a realistic experimental condition are investigated.•The moment of inertia and the thermal angular momentum average as well the in situ size are calculated in terms of the thermodynamic potential for the system under consideration.•The impact of finite size, and interatomic interaction and the synthetic magnetic field strength are investigated.