Quantum logic for trapped atoms via molecular hyperfine interactions

We study the deterministic entanglement of a pair of neutral atoms trapped in an optical lattice by coupling to excited-state molecular hyperfine potentials. Information can be encoded in the ground-state hyperfine levels and processed by bringing atoms together pairwise to perform quantum logical operations through induced electric dipole-dipole interactions. The possibility of executing both diagonal- and exchange-type entangling gates is demonstrated for two three three-level atoms and a figure of merit is derived for the fidelity of entanglement. The fidelity for executing a CPHASE gate is calculated for two Rb-87 atoms, including hyperfine structure and finite atomic localization. The main source of decoherence is spontaneous emission, which can be minimized for interaction times fast compared to the scattering rate and for sufficiently separated atomic wave packets. Additionally, coherent couplings to states outside the logical basis can be constrained by the state-dependent trapping potential.