Hyperfine structure in the microwave spectra of ultracold polar molecules.

We investigate the microwave spectra of ultracold alkali metal dimers in magnetic, electric and combined fields taking into account the hyperfine structure due to nuclear spins. We consider the molecules 41K87Rb and 7Li133Cs, which are the targets of current experiments, and demonstrate two extremes of large and small nuclear quadrupole couplings. We calculate the frequencies and intensities of transitions that may be used to transfer ultracold molecules between hyperfine states in a magnetic field, employing different polarizations of microwave radiation. In an electric field, the hyperfine levels display narrow avoided crossings at specific fields that we explain in terms of molecular alignment. The hyperfine splittings that arise in electric fields may hinder individual addressing in schemes that use ultracold molecules in quantum computation, but the structure of the spectra is suppressed in combined fields