Engineering entanglement: The fast-approach phase gate

Optimal-control techniques and a fast-approach scheme are used to implement a collisional controlled-phase gate in a model of cold atoms in an optical lattice, significantly reducing the gate time as compared to adiabatic evolution while maintaining high fidelity. Objective functionals are given for which optimal paths are obtained for evolution that yields a controlled-phase gate up to single-atom Rabi shifts. Furthermore, the fast-approach procedure is used to design a path to significantly increase the fidelity of nonadiabatic transport in a recent experiment. In addition, the entanglement power of phase gates is quantified.