We explore the topological properties of double-Weyl semimetals with coldatoms in optical lattices. We first propose to realize a tight-binding model ofsimulating the double-Weyl semimetal with a pair of double-Weyl points byengineering the atomic hopping in a three-dimensional optical lattice. We showthat the double-Weyl points with topological charges of \$pm2$ behave as sinkand source of Berry flux in momentum space connecting by two Fermi arcs andthey are stabilized by the \$C_{4h}$ point-group symmetry. By applying arealizable \$C_4$ breaking term, we find that each double-Weyl point splitsinto two single-Weyl points and obtain rich phase diagrams in the parameterspace spanned by the strengths of an effective Zeeman term and the \$C_4$breaking term, which contains a topological and a normal insulating phases andtwo topological Weyl semimetal phases with eight and four single-Weyl points,apart from the double-Weyl semimetal phase. Furthermore, we demonstrate withnumerical simulations that (i) the mimicked double- and single-Weyl points canbe detected by measuring the atomic transfer fractions after a Blochoscillation; (ii) the Chern number of different quantum phases in the phasediagram can be extracted from the center shift of the hybrid Wannier functions,which can be directly measured with the time-of-flight imaging; (iii) the bandtopology of the \$C_4$ symmetric Bloch Hamiltonian can be detected simply frommeasuring the spin polarization at the high symmetry momentum points with acondensate in the optical lattice. The proposed system would provide apromising platform for elaborating the intrinsic exotic physics of double-Weylsemimetals and the related topological phase transitions.
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