“…To begin, we seek to identify pairs of nuclear spin states with identical magnetic moments that connect to a common excited rotational state, by calculating the rotational and hyperfine structure of the RbCs molecule in externally applied magnetic and optical fields [1,2,6,31]. We construct the Hamiltonian (see Methods) in a fully uncoupled basis set |N, M N |i Rb , m Rb |i Cs , m Cs , where N represents the angular momentum of the molecule with its projection along the quantisation axis M N , and i Rb = 3/2, i Cs = 7/2 denote the nuclear spins of Rb and Cs respectively, with their projections m Rb , m Cs .…”