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arXiv:0802.3162 · Physical Review A

Ideal intersections for radio-frequency trap networks

Janus H. Wesenberg

Published Jan 16, 2009• 17 citations
arXivHTMLPDF

Abstract

We investigate the possible form of ideal intersections for two-dimensional rf trap networks suitable for quantum information processing with trapped ions. We show that the lowest order multipole component of the rf field that can contribute to an ideal intersection is a hexapole term uniquely determined by the tangents of the intersecting paths. The corresponding ponderomotive potential does not provide any confinement perpendicular to the paths if these intersect at right angles, indicating that ideal right-angle $\mathsf{X}$ intersections are impossible to achieve with hexapole fields. Based on this result, we propose an implementation of an ideal oblique-$\mathsf{X}$ intersection using a three-dimensional electrode structure.

DOI
10.1103/physreva.79.013416

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We investigate the possible form of ideal intersections for two-dimensional rf trap networks suitable for quantum information processing with trapped ions. We show that the lowest order multipole component of the rf field that can contribute to an ideal intersection is a hexapole term uniquely determined by the tangents of the intersecting paths. The corresponding ponderomotive potential does not provide any confinement perpendicular to the paths if these intersect at right angles, indicating that ideal right-angle X\mathsf{X}X intersections are impossible to achieve with hexapole fields. Based on this result, we propose an implementation of an ideal oblique-X\mathsf{X}X intersection using a three-dimensional electrode structure.
Abstract Junctions are fundamental elements that support qubit locomotion in two-dimensional ion trap arrays and enhance connectivity in emerging trapped-ion quantum computers. In surface ion traps they have typically been implemented by shaping radio frequency (RF) electrodes in a single plane to minimize the disturbance to the pseudopotential. However, this method introduces issues related to RF lead routing that can increase power dissipation and the likelihood of voltage breakdown. Here, we propose and simulate a novel two-layer junction design incorporating two perpendicularly rotoreflected (rotated, then reflected) linear ion traps. The traps are vertically separated, and create a trapping potential between their respective planes. The orthogonal orientation of the RF electrodes of each trap relative to the other provides perpendicular axes of confinement that can be used to realize transport in two dimensions. While this design introduces manufacturing and operating challenges, as now two separate structures have to be precisely positioned relative to each other in the vertical direction and optical access from the top is obscured, it obviates the need to route RF leads below the top surface of the trap and eliminates the pseudopotential bumps that occur in typical junctions. In this paper the stability of idealized ion transfer in the new configuration is demonstrated, both by solving the Mathieu equation analytically to identify the stable regions and by numerically modeling ion dynamics. Our novel junction layout has the potential to enhance the flexibility of microfabricated ion trap control to enable large-scale trapped-ion quantum computing.
We develop a constructive framework for designing radio-frequency (RF) trap networks from planar data and show that non-smooth field-free guide lines are possible in such networks. Given analytic Cauchy data on a symmetry plane, namely the potential and its normal derivative, Laplace's equation determines a local three-dimensional continuation. The odd subclass of this harmonic extension maps an arbitrary analytic generating function P(x,y)P(x,y)P(x,y) to a harmonic potential whose in-plane radio-frequency null set is exactly P(x,y)=0P(x,y)=0P(x,y)=0. This yields explicit field-free guide networks beyond smooth straight-line intersections, including cusp guides, cotangential contacts, and periodic lattices. We further derive Fourier-space formulas for periodic extensions and present square-lattice network families with tunable local crossing angle and rounded connectivity. These results provide a compact parametrization for the design space for quantum charge-coupled device (QCCD) architectures.
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We have analyzed a linear radio-frequency ion trap of finite length employing a four-sectored hollow cylinder enclosed between two end caps. Solutions to Laplace’s equation determine the effective potential inside the trap due to the rf trapping field, the static confining potential from dc-biased end caps, and the potential arising when a dc bias is present on the cylinder sectors. The finite length of a linear trap results in field distortion at the trap ends due to fringing effects. We have demonstrated that near the ends, the effective potential arising from the rf fields acts to propel ions out of the trap. We have further shown that the addition of a dc bias on two neighboring cylinder sectors generates an inhomogeneous field in the trap which produces a force on the ions along the trap’s long axis in a direction dependent on the sign of the bias. An exact analytic determination of the potential can be used to determine the profile of the trapped ion cloud.
Multipole radio-frequency (RF) traps are central to collisional experiments in cryogenic environments. They also offer possibilities to generate new type of ion crystals topologies and in particular the potential to create infinite 1D/2D structures: ion rings and ion tubes. However, multipole traps have also been shown to be very sensitive to geometrical misalignment of the trap rods, leading to additional local trapping minima. The present work proposes a method to correct non-ideal potentials, by modifying the applied RF amplitudes for each trap rod. This approach is discussed for the octupole trap, leading to the restitution of the ideal Mexican-Hat-like pseudo-potential, expected in multipole traps. The goodness of the compensation method is quantified in terms of the choice of the diagnosis area, the residual trapping potential variations, the required adaptation of the applied RF voltage amplitudes, and the impact on the trapped ion structures. Experimental implementation for macroscopic multipole traps is also discussed, in order to propose a diagnostic method with respect to the resolution and stability of the trap drive. Using the proposed compensation technique, we discuss the feasibility of generating a homogeneous ion ring crystal, which is a measure of quality for the obtained potential well.
We present a three-dimensional scalable linear ion trap scheme for ion trapping and discuss its applications for the optical frequency standard and scalable quantum information processing with its parallel strings of trapped Ca-40(+) ions. The geometry here contains nine equal-distance parallel rods driven by rf, which form trapping potentials for radial confinement and two end ring electrodes biased at a few volts for axial confinement. Its feasibility is calculated by using the finite element analysis method.