Here we have shown it is possible to imprint a solenoidal vector field to a system of ultracold atomic gases confined to two dimensions in the xy plane using a laser beam propagating in the z-direction. First we have shown a system of ultracold atomic gases, whose state depends on external parameters λ and whose evolution is adiabatic, acquires a geometric phase ∮ A · dλ, where A is the synthetic vector potential of the same form as the solenoidal vector field A ~ ^φ/r. We have also shown A is a result of the light-matter interaction. Optical vortex laser beam, i.e. a laser beam with a phase eimφ, is needed forAto take the form that of a solenoidal vector field. Then we have introduced a composite particle in two-dimensional space consisting of a flux tube (a solenoid) and a charged particle. These composite particles are called anyons and have non-integer statistics. Non-integer statistics here (and elsewhere as per the author’s knowledge) meaning they acquire a phase that is neither 0 (like bosons) or π (like fermions) when one anyon comes a full circle around another identical one. We have put 2 such laser flux tubes imprinted in a Bose-Einstein condensate in an external scalar potential that of a harmonic oscillator and spun them around. Turns out, the phase we get actually is non-integer, but it shows dependence on the distance between the flux tubes and is, therefore, not topological.