Condensate in an optical lattice : from solid simulation to quantum information (II)

The sixth lesson continued the description of condensates in optical lattices by discussing their application to quantum information. We began by describing the realization of phase gates and the preparation of a collective entanglement of atoms in the lattice. These gates are based on bringing atoms from neighboring sites into contact. We exploit the possibility of selectively shifting the different spin states of the atoms, following the method described in the previous lesson. In this way, atomic wave functions are separated, pairs of atoms collide depending on their spin state, and the wave functions are recombined. The conditional phase shift induced by the collisions can be precisely controlled. We began by considering the case of two or three wells. Bell and GHZ states are then realized using double or triple traps. The degree of entanglement between the atoms oscillates as a function of the phase shift produced by the collisions. The method was then generalized to the case of N wells, in one-, two- or three-dimensional arrays. In this way, cluster states with remarkable connectivity properties are created. The second part of the lesson focused on the quantum simulation of spins on networks and the principle of the cluster state quantum computer. We showed that it is possible to realize lattices of cold atoms with Hamiltonians analogous to those governing the evolution of spins on lattices. In particular, the Ising model and the Heisenberg Hamiltonian can be realized. More generally, we can simulate a spin Hamiltonian with adjustable parameters. In this way, optical boson networks can be used to simulate quantum situations in Quantum Condensed Matter Physics that are incalculable with conventional computers. We concluded the lecture by briefly explaining the principle of the one-way quantum computer, which works by performing sequential measurements on a pre-prepared cluster state.