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arXiv:1009.0036 · Journal of Applied Physics

A cryogenic surface-electrode elliptical ion trap for quantum simulation

Robert Clark, Ziliang Carter Lin, Kenan S. Diab, Isaac L. Chuang

Published Apr 1, 2011• 8 citations
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Abstract

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.

DOI
10.1063/1.3565053

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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 simulations of spin systems could enable the solution of problems that otherwise require infeasible classical resources. Such a simulation may be implemented using a well-controlled system of effective spins, such as a two-dimensional lattice of locally interacting ions. We propose here a layered planar rf trap design that can be used to create arbitrary two-dimensional lattices of ions. The design also leads naturally to ease of microfabrication. As a first experimental demonstration, we confine S88r+ ions in a millimeter-scale lattice trap and verify numerical models of the trap by measuring the motional frequencies. We also confine 440 nm diameter charged microspheres and observe ion-ion repulsion between ions in neighboring lattice sites. Our design, when scaled to smaller ion-ion distances, is appropriate for quantum simulation schemes, e.g., that of Porras and Cirac [Phys. Rev. Lett. 92, 207901 (2004)]. We note, however, that in practical realizations of the trap, an increase in the secular frequency with decreasing ion spacing may make a coupling rate that is large relative to the decoherence rate in such a trap difficult to achieve.
Current classical computing methods are unable to simulate quantum many-body interactions efficiently.Analog quantum simulators with even small numbers of quantum degrees of freedom are expected to enable the investigation of systems not fully accessible in traditional computing such as condensed-matter systems, quantum chemistry, and material science.Two-dimensional lattices of trapped ions are a good candidate to realize an analog quantum simulator for their addressability, individual control and individual detection.Here, we report on multiple unique lattice surface ion trap designs, microfabricated at Sandia National Laboratories, capable of trapping and interacting up to 4 ions.Ions are held in close proximity in individual all radio-frequency potential minima and interact via their Coulomb repulsion.The Coulomb coupling between ions allows for simulation of spin-spin interactions 1-6 .Control electrodes of the trap can be used to adjust principal axes of the ion's motion and thus enable individual control over the interaction between ions.The lattice trap array architecture tested in this work can be scaled to larger two-dimensional lattices of trapped ions.
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.
We present a detailed study of quantum simulations of coupled spin systems in surface-electrode (SE) ion-trap arrays, and illustrate our findings with a proposed implementation of the hexagonal Kitaev model (Kitaev A 2006 Ann. Phys. 321 2). The effective (pseudo)spin interactions making up such quantum simulators are found to be proportional to the dipole–dipole interaction between the trapped ions, and are mediated by motion that can be driven by state-dependent forces. The precise forms of the trapping potentials and the interactions are derived in the presence of an SE and a cover electrode. These results are the starting point to derive an optimized SE geometry for trapping ions in the desired honeycomb lattice of Kitaev's model, where we design the dipole–dipole interactions in a way that allows for coupling all three bond types of the model simultaneously, without the need for time discretization. Finally, we propose a simple wire structure that can be incorporated into a microfabricated chip to generate localized state-dependent forces which drive the couplings prescribed by this particular model; such a wire structure should be adaptable to many other situations.
The major challenges in trapped-ion quantum computation are to scale up few-ion experiments to many qubits and to improve control techniques so that quantum logic gates can be carried out with higher fidelities. This thesis reports experimental progress in both of these areas. In the early part of the thesis we describe the fabrication of a surface-electrode ion trap, the development of the apparatus and techniques required to operate it and the successful trapping of 40Ca+ ions. Notably we developed methods to control the orientation of the principal axes and to minimise ion micromotion. We propose a repumping scheme that simplifies heating rate measurements for ions with low-lying D levels, and use it to characterise the electric field noise in the trap. Surface-electrode traps are important because they offer a route to dense integration of electronic and optical control elements using existing microfabrication technology. We explore this scaling route by testing a series of three traps that were microfabricated at Sandia National Laboratories. Investigations of micromotion and charging of the surface by laser beams were carried out and improvements to future traps are suggested. Using one of these traps we also investigated anomalous electrical noise from the electrode surfaces and discovered that it can be reduced by cleaning with a pulsed laser. A factor of two decrease was observed; this represents the first in situ removal of this noise source, an important step towards higher gate fidelities. In the second half of the thesis we describe the design and construction of an experiment for the purpose of replacing laser-driven multi-qubit quantum logic gates with microwave-driven ones. We investigate magnetic-field-independent hyperfine qubits in 40Ca+ as suitable qubits for this scheme. We make a design study of how best to integrate an ion trap with the microwave conductors required to implement the gate and propose a novel integrated resonant structure. The trap was fabricated and ions were successfully loaded. Single-qubit experiments show that the microwave fields above the trap are in excellent agreement with software simulations. There are good prospects for demonstrating a multi-qubit gate in the near future. We conclude by discussing the possibilities for larger-scale quantum computation by combining microfabricated traps and microwave control.
Trapped ions in Paul traps (radio frequency ion traps) are a promising candidate for the realization of a quantum computer. To date, experimental demonstrations of quantum computing and information processing with trapped ions have been limited to small numbers of quantum bits (qubits). The most prominent challenge to realise ion-trap quantum computation is to scale the system and control a large number of trapped ions coherently. Surface-electrode ion trap designs which are amenable to various microfabrication techniques offer a path to achieve this. In this work, design, fabrication and key operations of two types of surface-electrode ion traps, i.e. a Y-junction trap and a two-dimensional (2D) hexagonal lattice trap developed towards scaling ion-trap architectures, are presented. The steps involved in the fabrication of the ion-trap devices included photolithography, wet etch (hydrofluoric acid etch) and dry etch (deep reactive ion and inductively coupled plasma etching), and metal evaporation. The devices were fabricated on SOI substrates with different buried oxide thicknesses (i.e. 5 µm and 10 µm) and different metals for the trap electrodes (i.e. gold and aluminium). An extremely high-breakdown voltage up to 1 kV was measured in vacuum for the SOI-built test devices with a 10 µm-thick buried oxide formed by oxide film-to-oxide film bonding process. This is attributed to the deep V-shaped undercut profile of the buried oxide layer which resulted in a large breakdown path length, and so mitigating surface breakdown effects. Owing to the V-shaped undercut profile, the surface breakdown voltage was improved by 15% for the devices fabricated on SOI substrates with a 10 µm-thick buried oxide. In the first experiment, the demonstration of ytterbium (174Yb+) ion trapping in the 2D hexagonal lattice trap is achieved with a relatively long lifetime of a laser-cooled ion up to 90 minutes and ≤ 5 minutes without cooling in ultra-high vacuum system. The 2D lattice trap design allows for reliable trapping of 2D ion lattices, rudimentary shuttling between lattice sites and deterministic introducing of defects into the ion lattice. Based on all these abilities, such a 2D lattice trap with the predicted reduction of lattice spacing down to 32 µm can be configured as a versatile architecture for 2D quantum simulations with trapped ions. In the second experiment, microparticle trapping in the 2D lattice trap, performed in air, is achieved with the longest trapping lifetime of 60 minutes. Both gold and aluminium-coated electrodes also lead to comparable trapping performances. Furthermore, the in situ levitation of microparticles is successfully demonstrated at the maximum levitation height of 30 µm. This ability provides additional control on the trapping height which increases the overall functionality of the 2D lattice trap.