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arXiv:1102.3645 · The European Physical Journal D

Designing spin-spin interactions with one and two dimensional ion crystals in planar micro traps

J. Welzel, A. Bautista-Salvador, C. Abarbanel, V. Wineman-Fisher, C. Wunderlich, R. Folman, F. Schmidt-Kaler

Published Jul 27, 2011• 45 citations
arXivHTMLPDF

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) [J. Phys. B At. Mol. Opt. Phys. 42, 154009 (2009)]. 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 two-dimensional ion crystals, and discuss frustration effects in such two-dimensional arrangements.

DOI
10.1140/epjd/e2011-20098-y

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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) [J. Phys. B At. Mol. Opt. Phys. 42, 154009 (2009)]. 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 two-dimensional ion crystals, and discuss frustration effects in such two-dimensional arrangements.
Abstract 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 current wires to generate magnetic field gradients of up to 16.3(9) T m −1 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. We perform sideband spectroscopy upon directly driving the spins with a radiofrequency field for crystals of three ions on their linear-to-zigzag structural transition. Furthermore, we observe the rich excitation spectrum of vibrational modes in a planar crystal comprised of four ions.
In modern ion quantum technology the fields of quantum information and microfabrication are being merged to build devices in which ions are confined near trap electrodes at the micrometer scale -with novel functionality where ion qubits enabling quantum devices. A long term goal in this field is to build a trapped-ion based quantum computer. Today’s quest, however, requires a progressive ion trap development in which materials selection, trap’s design and fabrication methods play a fundamental role. Here, we report on two fabrication methods for planar traps. We present the characterization of a planar trap with integrated electromagnets which is designed to coherently manipulate 40Ca+ ions’ internal states via magnetic field gradients and long-wavelength radiation. By implementing radiofrequency spectroscopy, in the presence of static magnetic fields, and by moving a single 40Ca+ ion about 600 µm along the trap axis we measured the total static magnetic field which yields a gradient of 1.11 +/- 0.18 T/m*A in this direction. We anticipate in this trap magnetic gradients of 10 T/m*A perpendicular to the trap axis. A second generation of this trap, a novel hybrid planar trap, is built by combining the capabilities of thick film technology and laser-induced glass micromachining to structure independent current-carrying wires beneath an ion trap. Into the vacuum chamber, we also incorporate surface cleaning tools such as ion-beam bombardment to diminish possible adsorbed contaminants which may reflect in excessive ion heating rates. Based on numerical simulations, we predict that the wires underneath the ion trap, although far from trap center, will be capable of producing high magnetic field gradients of about 3 T/m*A. Already such robust fields will allow to investigate strong v_ss=30 kHz spin-spin interactions in 40Ca+ ion crystals in planar traps.
Two-dimensional crystals of trapped ions are a promising system with which to implement quantum simulations of challenging problems such as spin frustration. Here, we present a design for a surface-electrode elliptical ion trap which produces a 2-D ion crystal and is amenable to microfabrication, which would enable higher simulated coupling rates, as well as interactions based on magnetic forces generated by currents which may be incorporated into the trap structure. Working in an 11 K cryogenic environment, we experimentally verify to within 10% a numerical model of the structure of ion crystals in the trap, given the measured trap anisotropy. We also explore the possibility of implementing quantum simulation using magnetic forces, and calculate J-coupling rates on the order of 103 s-1 for a trap scale of 10 μm, using a current of 1 A.
Quantum simulation of interacting many-body spin systems is routinely performed with cold trapped ions, and systems with hundreds of spins have been studied in one and two dimensions. In the most common realizations of these platforms, spin degrees of freedom are encoded in low-lying electronic levels, and interactions among the spins are mediated through crystal vibrations. Here we propose a new approach which enables the quantum simulation of two-dimensional spin systems with interaction strengths that are increased by orders of magnitude. This, together with the unprecedented longevity of trapped ions, opens an avenue for the exploration of phenomena that take place on long timescales, e.g., slow and collective relaxation in frustrated and kinetically constrained systems. Our platform makes use of the strong dipolar interactions among electronic Rydberg states and planar confinement provided by a Penning trap. We investigate how the strong electric and magnetic fields that form this trap affect the properties of the Rydberg states and show that spin-spin interaction strengths on the order of MHz are achievable under experimentally realistic conditions. As a brief illustration of the capabilities of this quantum simulator, we study the entanglement in a frustrated spin system realized by three ions.
Two-dimensional (2D) quantum magnetism is a paradigm in strongly correlated many-body physics. The understanding of 2D quantum magnetism can be expedited by employing a controllable quantum simulator that faithfully maps 2D-spin Hamiltonians. The 2D quantum simulators can exhibit exotic phenomena such as frustrated quantum magnetism and topological order and can be used to show quantum computational advantages. Many experimental platforms are being developed, including Rydberg atoms and superconducting annealers. However, with trapped-ion systems, which showed the most advanced controllability and quantum coherence, quantum magnetism was explored in one-dimensional chains. Here, we report simulations of frustrated quantum magnetism with 2D ion crystals. We create a variety of spin-spin interactions for quantum magnets, including those that exhibit frustration by driving different vibrational modes and adiabatically prepare the corresponding ground states. The experimentally measured ground states are consistent with the theoretical predictions and are highly degenerate for geometrically frustrated spin models in two dimensions. Quantum coherence of the ground states is probed by reversing the time evolution of the B-field to the initial value and then measuring the extent to which the remaining state coincides with the initial state. Our results open the door for quantum simulations with 2D ion crystals.
We propose a potential scheme to generate entangled photons by manipulating trapped ions embedded in two-mode microcavities assisted by a magnetic field gradient. By means of the spin-spin coupling due to the magnetic field gradient and the Coulomb repulsion between the ions, we show how to efficiently generate entangled photons by detecting the internal states of the trapped ions. We emphasize that our scheme is advantageous to create complete sets of entangled multiphoton states. The requirements and the experimental feasibility of our proposal are discussed in detail.