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We discuss a system of dilute Bose gas confined in a layered structure ofstacked square lattices (slab geometry). A derived phase diagram reveals anon-monotonic dependence of the ratio of tunneling to on-site repulsion on theartificial magnetic field applied to the system. The effect is reduced whenmore layers are added, which mimics a two- to quasi-three-dimensional geometrycrossover. Furthermore, we establish a correspondence between anisotropicinfinite (quasi three-dimensional) and isotropic finite (slab geometry) systemsthat share exactly the same critical values, which can be an important clue forchoosing experimental setups that are less demanding, but still leading to theidentical results. Finally, we show that the properties of the ideal Bose gasin a three-dimensional optical lattice can be closely mimicked by finite (slab)systems, when the number of two-dimensional layers is larger than ten forisotropic interactions or even less, when the layers are weakly coupled.

Synthetic magnetic field effects on neutral bosonic condensates in quasi three-dimensional anisotropic layered structures