Creation of resilient entangled states and a resource for measurement-based quantum computation with optical superlattices

We investigate how to create entangled states with ultracold bosonic atoms trapped in optical lattices by dynamical manipulation of the shape of the lattice potential. We consider a period-two superlattice that allows both the splitting of each site into a double-well potential and also the variation of the height of the potential barrier between the sites. We show how to use this array of double-well potentials to entangle neighboring qubits encoded on the Zeeman levels of the atoms, without using the different vibrational states of the atoms. Finally, we present a method of realizing a Bell-pair encoded cluster state, a resource for measurement-based quantum computing which remains resilient to collective dephasing noise throughout the computation [NJP 10, 023005 (2008)].