Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins

Abstract

The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed matter systems, potentially including high-temperature superconductivity [1,2]. 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 [3]. Feynman divined that a quantum simulator -a special-purpose "analog" processor built using quantum particles (qubits) -would be inherently adept at such problems [4,5]. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach [6][7][8][9][10][11][12][13][14]. 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 i, j on a naturally occurring 2D triangular crystal lattice of hundreds of spin-1/2 particles ( 9 Be + ions stored in a Penning trap), a computationally relevant scale more than an order of magnitude larger than existing experiments. We show that a spindependent optical dipole force can produce an antiferromagnetic interaction J i, j ∝ d −a i, j , where a is tunable over 0 < a < 3; 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 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 simulation of interesting and otherwise computationally intractable problems in quantum magnetism.A challenge in condensed matter physics is the fact that many quantum-magnetic interactions cannot currently be modeled in a meaningful way. A canonical example is the spin-liquid postulated by Anderson [1]. He suggested this exotic state would arise in a collection of spin-1/2 particles residing on a triangular lattice and coupled by a nearest-neighbor antiferromagnetic Heisenberg interaction. The spin-liquid's Figure 1. The Penning trap confines hundreds of spin-1/2 particles (qubits) on a two-dimensional (2D) triangular lattice. Each qubit is the valence electron spin of a 9 Be + ion. (lower) A Penning trap confines ions by use of a combination of static electric and magnetic fields. The trap parameters are configured so that laser-cooled ions form a triangular 2D crystal. A general spin-spin interactionĤ I is generated by a spin-dependent excitation of the transverse (alongẑ) motional modes of the ion crystal. This coupling is implemented with an optical dipole force (ODF) due to a pair of off-resonance laser beams (left side) with angular separation θ R and dif...

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