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      Effect of defects on the phonons and the effective spin-spin interactions of an ultracold Penning trap quantum simulator

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          Abstract

          We generalize the analysis of the normal modes for a rotating ionic Coulomb crystal in a Penning trap to allow for inhomogeneities in the system. Our formal developments are completely general, but we choose to examine a crystal of Be+ ions with BeH+ defects to compare with current experimental efforts. We examine the classical phonon modes (both transverse and planar) and we determine the effective spin-spin interactions when the system is driven by an axial spin-dependent optical dipole force. We examine situations with up to approximately 15% defects. We find that most properties are not strongly influenced by the defects, indicating that the presence of a small number of defects will not significantly affect experiments.

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          Simulating a quantum magnet with trapped ions

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            Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins

            The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed matter systems, potentially including high-temperature superconductivity. However, many properties of exotic strongly correlated spin systems (e.g., spin liquids) have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N~30 particles. Feynman divined that a quantum simulator - a special-purpose "analog" processor built using quantum particles (qubits) - would be inherently adept at such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach. However, simulations of quantum magnetism allowing controlled, tunable interactions between spins localized on 2D and 3D lattices of more than a few 10's of qubits have yet to be demonstrated, owing in part to the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction J_ij on a naturally occurring 2D triangular crystal lattice of hundreds of spin-1/2 particles (9Be+ ions stored in a Penning trap), a computationally relevant scale more than an order of magnitude larger than existing experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J_ij ~ 1/d_ij^a, where a is tunable over 0
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              Effective quantum spin systems with ion traps

              , (2004)
              We show that the physical system consisting of trapped ions interacting with lasers may undergo a rich variety of quantum phase transitions. By changing the laser intensities and polarizations the dynamics of the internal states of the ions can be controlled, in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analogue quantum simulator of spin systems with trapped ions, and observe and analyze quantum phase transitions with unprecedent opportunities for the measurement and manipulation of spins.
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                Author and article information

                Journal
                1309.2358

                Quantum physics & Field theory,Quantum gases & Cold atoms
                Quantum physics & Field theory, Quantum gases & Cold atoms

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