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      Control of the conformations of ion Coulomb crystals in a Penning trap

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          Abstract

          Laser-cooled atomic ions form ordered structures in radiofrequency ion traps and in Penning traps. Here we demonstrate in a Penning trap the creation and manipulation of a wide variety of ion Coulomb crystals formed from small numbers of ions. The configuration can be changed from a linear string, through intermediate geometries, to a planar structure. The transition from a linear string to a zigzag geometry is observed for the first time in a Penning trap. The conformations of the crystals are set by the applied trap potential and the laser parameters, and agree with simulations. These simulations indicate that the rotation frequency of a small crystal is mainly determined by the laser parameters, independent of the number of ions and the axial confinement strength. This system has potential applications for quantum simulation, quantum information processing and tests of fundamental physics models from quantum field theory to cosmology.

          Abstract

          Ion traps form the core of many studies of fundamental physics and are a possible route to quantum computation. Using a Penning trap, Mavadia et al. demonstrate the formation and control of different configurations of ion Coulomb crystals, which may be useful for future ion-based applications.

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          Most cited references 23

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          Quantum simulation of frustrated Ising spins with trapped ions.

          A network is frustrated when competing interactions between nodes prevent each bond from being satisfied. This compromise is central to the behaviour of many complex systems, from social and neural networks to protein folding and magnetism. Frustrated networks have highly degenerate ground states, with excess entropy and disorder even at zero temperature. In the case of quantum networks, frustration can lead to massively entangled ground states, underpinning exotic materials such as quantum spin liquids and spin glasses. Here we realize a quantum simulation of frustrated Ising spins in a system of three trapped atomic ions, whose interactions are precisely controlled using optical forces. We study the ground state of this system as it adiabatically evolves from a transverse polarized state, and observe that frustration induces extra degeneracy. We also measure the entanglement in the system, finding a link between frustration and ground-state entanglement. This experimental system can be scaled to simulate larger numbers of spins, the ground states of which (for frustrated interactions) cannot be simulated on a classical computer.
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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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              Engineered two-dimensional Ising interactions in 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, such as 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 predicted that a quantum simulator--a special-purpose 'analogue' processor built using quantum bits (qubits)--would be inherently suited to solving such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach, but simulations allowing controlled, tunable interactions between spins localized on two- or three-dimensional lattices of more than a few tens of qubits have yet to be demonstrated, in part because of the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction, J(i,j), on a naturally occurring, two-dimensional triangular crystal lattice of hundreds of spin-half particles (beryllium ions stored in a Penning trap). This is a computationally relevant scale more than an order of magnitude larger than previous experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J(i,j) proportional variant d(-a)(i,j), where 0 ≤ a ≤ 3 and d(i,j) is the distance between spin pairs. These power laws correspond physically to infinite-range (a = 0), Coulomb-like (a = 1), monopole-dipole (a = 2) and dipole-dipole (a = 3) couplings. Experimentally, we demonstrate excellent agreement with a theory for 0.05 ≲ a ≲ 1.4. This demonstration, coupled with the high spin count, excellent quantum control and low technical complexity of the Penning trap, brings within reach the simulation of otherwise computationally intractable problems in quantum magnetism.
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                Author and article information

                Journal
                Nat Commun
                Nat Commun
                Nature Communications
                Nature Pub. Group
                2041-1723
                07 October 2013
                : 4
                Affiliations
                [1 ]QOLS Group, Department of Physics, Imperial College London , South Kensington Campus, London SW7 2AZ, UK
                Author notes
                Article
                ncomms3571
                10.1038/ncomms3571
                3806409
                24096901
                Copyright © 2013, Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.

                This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. To view a copy of this licence visit http://creativecommons.org/licenses/by/3.0/.

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