Vortex splitting in the interference effect for a quantized vortex released from an optical lattice

For a quantized vortex in a harmonic trap and an optical lattice, we study the interference effect after the combined potentials are switched off. Both numerical and analytical calculations show that there is a vortex splitting in the interference effect of this freely expanding quantum gas, i.e. every interference peak is also a quantized vortex. The experimental scheme to verify this interference effect is discussed.