Engineered twodimensional Ising interactions in a trappedion quantum simulator with hundreds of spins
Abstract
The presence of longrange quantum spin correlations underlies a variety of physical phenomena in condensedmatter systems, potentially including hightemperature superconductivity. However, many properties of exotic, strongly correlated spin systems, such as spin liquids, have proved difficult to study, in part because calculations involving Nbody entanglement become intractable for as few as N ~ 30 particles. Feynman predicted that a quantum simulatora specialpurpose `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 threedimensional lattices of more than a few tens of qubits have yet to be demonstrated, in part because of the technical challenge of realizing largescale qubit arrays. Here we demonstrate a variablerange Isingtype spinspin interaction, J_{i,j}, on a naturally occurring, twodimensional triangular crystal lattice of hundreds of spinhalf 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 spindependent optical dipole force can produce an antiferromagnetic interaction , where 0 <= a <= 3 and d_{i,j} is the distance between spin pairs. These power laws correspond physically to infiniterange (a = 0), Coulomblike (a = 1), monopoledipole (a = 2) and dipoledipole (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.
 Publication:

Nature
 Pub Date:
 April 2012
 DOI:
 10.1038/nature10981
 arXiv:
 arXiv:1204.5789
 Bibcode:
 2012Natur.484..489B
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Physics  Computational Physics
 EPrint:
 10 pages, 10 figures