Microwave trapped-ion quantum logic gates avoid spontaneous emission as a fundamental source of decoherence. However, microwave two-qubit gates are still slower than laser-induced gates and hence more sensitive to fluctuations and noise of the motional mode frequency. We propose and implement amplitude-shaped gate drives to obtain resilience to such frequency changes without increasing the pulse energy per gate operation. We demonstrate the resilience by noise injection during a two-qubit entangling gate with 9 Be + ion qubits. In absence of injected noise, amplitude modulation gives an operation infidelity in the 10 −3 range.Trapped ions are a leading platform for scalable quantum logic [1, 2] and quantum simulations [3]. Major challenges towards larger-scale devices include the integration of tasks and components that have been so far only demonstrated individually, as well as single and multiqubit gates with the highest possible fidelity to reduce the overhead in quantum error correction. Microwave control of trapped-ion qubits has the potential to address both challenges [4,5] as it allows the gate mechanism, potentially including control electronics, to be integrated into scalable trap arrays. Because spontaneous emission as a fundamental source of decoherence is absent and microwave fields are potentially easier to control than the laser beams that are usually employed, microwaves are a promising approach for high fidelity quantum operations. In fact, microwave two-qubit gate fidelities seem to improve more rapidly than laser-based gates. However, observed two-qubit gate speeds of laser-based gates [6,7] are still about an order of magnitude faster than for microwave gates [8][9][10]. This makes gates more susceptible to uncontrolled motional mode frequency changes, as transient entanglement with the motional degrees of freedom is the key ingredient in multi-qubit gates for trapped ions. As other error sources have been addressed recently, this is of growing importance. Merely increasing Rabi frequencies may not be the most resource-efficient approach, as it will increase energy dissipation in the device. A more efficient use of available resources could be obtained using pulse shaping or modulation techniques. In fact, a number of recent advances in achieving highfidelity operations or long qubit memory times have been proposed or obtained by tailored control fields. Examples include pulsed dynamic decoupling [11], Walsh modulation [12], additional dressing fields to increase coherence times [13], phase [14], amplitude [15][16][17][18][19][20] and fre-quency modulation [21] as well multi-tone fields [22][23][24]. In many cases, these techniques lead to significant advantages. For multi-qubit gates, one mechanism is to optimize the trajectory of the motional mode in phase space for minimal residual spin-motional entanglement in case of experimental imperfections. This effectively reduces the distance between the origin and the point in phase space at which the gate terminates in case of errors.Here we propo...

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.

A cryogenic radio-frequency ion trap system designed for quantum logic spectroscopy of highly charged ions is presented. It includes a segmented linear Paul trap, an in-vacuum imaging lens and a helical resonator. We demonstrate ground state cooling of all three modes of motion of a single 9 Be + ion and determine their heating rates as well as excess axial micromotion. The trap shows one of the lowest levels of electric field noise published to date. We investigate the magnetic-field noise suppression in cryogenic shields made from segmented copper, the resulting magnetic field stability at the ion position and the resulting coherence time. Using this trap in conjunction with an electron beam ion trap and a deceleration beamline, we have been able to trap single highly charged Ar 13+ (Ar XIV) ions concurrently with single Be + ions, a key prerequisite for the first quantum logic spectroscopy of a highly charged ion.

We develop an intuitive model of 2D microwave near-fields in the unusual regime of centimeter waves localized to tens of microns. Close to an intensity minimum, a simple effective description emerges with five parameters which characterize the strength and spatial orientation of the zero and first order terms of the near-field, as well as the field polarization. Such a field configuration is realized in a microfabricated planar structure with an integrated microwave conductor operating near 1 GHz. We use a single 9 Be + ion as a high-resolution quantum sensor to measure the field distribution through energy shifts in its hyperfine structure. We find agreement with simulations at the sub-micron and few-degree level. Our findings give a clear and general picture of the basic properties of oscillatory 2D near-fields with applications in quantum information processing, neutral atom trapping and manipulation, chip-scale atomic clocks, and integrated microwave circuits.PACS numbers: 03.67. Bg, 03.67.Lx, 37.10.Rs, 37.10.Ty, 37.90.+j Static or oscillatory electromagnetic fields have important applications in atomic and molecular physics for atom trapping and manipulation. Neutral atoms can be trapped in static magnetic fields in different types of magnetic traps [1]. Atomic ions can be trapped either in superpositions of static and oscillatory electric fields (Paul trap) or in superimposed static electromagnetic fields (Penning trap) [2]. Atom and molecule decelerators rely on the distortion of atomic energy levels by spatially inhomogeneous fields [3]. Common to all of these field configurations is that their basic properties can be well described in terms of static solutions to the field equations and that the behavior of the field near its intensity minimum is often critical to the application. Prominent examples include Majorana losses in neutral atom magnetic traps [1] and micromotion in Paul traps [4].Recently, motivated by advances in microfabricated atom traps, interest has grown in microwave near-fields which originate from microfabricated structures. Dimensions are typically small compared to the wavelength, but for the relatively high frequencies involved, eddy currents and phase effects become important, and the resulting field patterns are much richer than in the quasistatic case. Examples include rf potentials for neutral atoms [5] with applications in atom interferometry, quantum gates [6,7] and chip-scale atomic clocks [8] as well as microwave near-fields for trapped-ion quantum logic [9][10][11]. Also, neutral atomic clouds [12] and single ions [13] have been used to characterise near-fields at sub-mm length scales or measure magnetic field gradients [14]. The behavior of these high-frequency oscillatory fields may also become relevant for coupling atomic and molecular quantum systems to microwave circuits in the quantum regime [15,16]. Of particular importance in this context are 2D field configurations which can be realized e. g. in integrated waveguides. Notwithstanding the strong experimental int...