TY - JOUR T1 - Experimental Performance of a Quantum Simulator: Optimizing Adiabatic Evolution and Identifying Many-Body Ground States JF - Physical Review A Y1 - 2013 A1 - Philip Richerme A1 - Crystal Senko A1 - Jacob Smith A1 - Aaron Lee A1 - Simcha Korenblit A1 - Christopher Monroe AB - We use local adiabatic evolution to experimentally create and determine the ground state spin ordering of a fully-connected Ising model with up to 14 spins. Local adiabatic evolution -- in which the system evolution rate is a function of the instantaneous energy gap -- is found to maximize the ground state probability compared with other adiabatic methods while only requiring knowledge of the lowest $\sim N$ of the $2^N$ Hamiltonian eigenvalues. We also demonstrate that the ground state ordering can be experimentally identified as the most probable of all possible spin configurations, even when the evolution is highly non-adiabatic. VL - 88 UR - http://arxiv.org/abs/1305.2253v1 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.88.012334 ER - TY - JOUR T1 - Quantum Catalysis of Magnetic Phase Transitions in a Quantum Simulator JF - Physical Review Letters Y1 - 2013 A1 - Philip Richerme A1 - Crystal Senko A1 - Simcha Korenblit A1 - Jacob Smith A1 - Aaron Lee A1 - Rajibul Islam A1 - Wesley C. Campbell A1 - Christopher Monroe AB - We control quantum fluctuations to create the ground state magnetic phases of a classical Ising model with a tunable longitudinal magnetic field using a system of 6 to 10 atomic ion spins. Due to the long-range Ising interactions, the various ground state spin configurations are separated by multiple first-order phase transitions, which in our zero temperature system cannot be driven by thermal fluctuations. We instead use a transverse magnetic field as a quantum catalyst to observe the first steps of the complete fractal devil's staircase, which emerges in the thermodynamic limit and can be mapped to a large number of many-body and energy-optimization problems. VL - 111 UR - http://arxiv.org/abs/1303.6983v2 CP - 10 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.111.100506 ER - TY - JOUR T1 - Quantum Simulation of Spin Models on an Arbitrary Lattice with Trapped Ions JF - New Journal of Physics Y1 - 2012 A1 - Simcha Korenblit A1 - Dvir Kafri A1 - Wess C. Campbell A1 - Rajibul Islam A1 - Emily E. Edwards A1 - Zhe-Xuan Gong A1 - Guin-Dar Lin A1 - Luming Duan A1 - Jungsang Kim A1 - Kihwan Kim A1 - Christopher Monroe AB - A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range effective spin-spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. Here we show how appropriate design of laser fields can provide for arbitrary multidimensional spin-spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently existing trap technology and is scalable to levels where classical methods of simulation are intractable. VL - 14 U4 - 095024 UR - http://arxiv.org/abs/1201.0776v1 CP - 9 J1 - New J. Phys. U5 - 10.1088/1367-2630/14/9/095024 ER -