We investigate how to create entangled states of ultracold atoms trapped in
optical lattices by dynamically manipulating the shape of the lattice
potential. We consider an additional potential (the superlattice) that allows
both the splitting of each site into a double well potential, and the control
of the height of potential barrier between sites. We use superlattice
manipulations to perform entangling operations between neighbouring qubits
encoded on the Zeeman levels of the atoms without having to perform transfers
between the different vibrational states of the atoms. We show how to use
superlattices to engineer many-body entangled states resilient to collective
dephasing noise. Also, we present a method to realize a 2D resource for
measurement-based quantum computing via Bell-pair measurements. We analyze
measurement networks that allow the execution of quantum algorithms while
maintaining the resilience properties of the system throughout the computation.Comment: 23 pages, 6 figures, IOP style, published in New Journal of Physics.
Minor corrections/few typos remove