Abstract. We discuss the experimental feasibility of quantum simulation with trapped ion crystals, using magnetic field gradients. We describe a micro structured planar ion trap, which contains a central wire loop generating a strong magnetic gradient of about 20 T/m in an ion crystal held about 160 µm above the surface. On the theoretical side, we extend a proposal about spin-spin interactions via magnetic gradient induced coupling (MAGIC) [Johanning, et al, J. Phys. B: At. Mol. Opt. Phys. 42, (2009) 154009]. We describe aspects where planar ion traps promise novel physics: Spin-spin coupling strengths of transversal eigenmodes exhibit significant advantages over the coupling schemes in longitudinal direction that have been previously investigated. With a chip device and a magnetic field coil with small inductance, a resonant enhancement of magnetic spin forces through the application of alternating magnetic field gradients is proposed. Such resonantly enhanced spin-spin coupling may be used, for instance, to create Schrödinger cat states. Finally we investigate magnetic gradient interactions in twodimensional ion crystals, and discuss frustration effects in such twodimensional arrangements.

We investigate the dynamics of ion crystals in zigzag configuration in transverse magnetic field gradients. A surface-electrode Paul trap is employed to trap 40 Ca + ions and features submerged wires to generate magnetic field gradients of up to 16.3(9) T/m at the ions position. With the gradient aligned in the direction perpendicular to the axis of weakest confinement, along which linear ion crystals are formed, we demonstrate magnetic field gradient induced coupling between the spin and ion motion. For crystals of three ions on their linear-to-zigzag structural transition we perform sideband spectroscopy upon directly driving the spins with a radiofrequency field. Furthermore, we observe the rich excitation spectrum of vibrational modes in a planar crystal comprised of four ions.

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It is expected that ion trap quantum computing can be made scalable through protocols that make use of transport of ion qubits between sub-regions within the ion trap. In this scenario, any magnetic field inhomogeneity the ion experiences during the transport, may lead to dephasing and loss of fidelity. Here we demonstrate how to measure, and compensate for, magnetic field gradients inside a segmented ion trap, by transporting a single ion over variable distances. We attain a relative magnetic field sensitivity of ∆B/B0 ∼ 5 · 10 −7 over a test distance of 140 µm, which can be extended to the mm range, still with sub µm resolution. A fast experimental sequence is presented, facilitating its use as a magnetic field gradient calibration routine, and it is demonstrated that the main limitation is the quantum shot noise.