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arXiv:0902.1686 · Physical Review Letters

Optimal Surface-Electrode Trap Lattices for Quantum Simulation with Trapped Ions

Roman Schmied, Janus H. Wesenberg, Dietrich G. Leibfried

Published Jun 9, 2009• 102 citations
arXivHTMLPDF

Abstract

Trapped ions offer long internal state (spin) coherence times and strong interparticle interactions mediated by the Coulomb force. This makes them interesting candidates for quantum simulation of coupled lattices. To this end, it is desirable to be able to trap ions in arbitrary conformations with precisely controlled local potentials. We provide a general method for optimizing periodic planar radio-frequency electrodes for generating ion trapping potentials with specified trap locations and curvatures above the electrode plane. A linear-programming algorithm guarantees globally optimal electrode shapes that require only a single radio-frequency voltage source for operation. The optimization method produces final electrode shapes that are smooth and exhibit low fragmentation. Such characteristics are desirable for practical fabrication of surface-electrode trap lattices.

DOI
10.1103/physrevlett.102.233002

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Trapped ions offer long internal state (spin) coherence times and strong interparticle interactions mediated by the Coulomb force. This makes them interesting candidates for quantum simulation of coupled lattices. To this end, it is desirable to be able to trap ions in arbitrary conformations with precisely controlled local potentials. We provide a general method for optimizing periodic planar radio-frequency electrodes for generating ion trapping potentials with specified trap locations and curvatures above the electrode plane. A linear-programming algorithm guarantees globally optimal electrode shapes that require only a single radio-frequency voltage source for operation. The optimization method produces final electrode shapes that are smooth and exhibit low fragmentation. Such characteristics are desirable for practical fabrication of surface-electrode trap lattices.
We report a linear surface-electrode trap that can be used to form parallel ion strings. By adjusting the balance of the radio-frequency (RF) voltages applied to central and RF electrodes, the RF pseudopotential can be varied from single-well to double-well in the radial direction. Ions located on two parallel lines of the RF potential null are in principle free from excess micromotion if appropriate static voltages are applied. Calcium ions were trapped for the evaluation of the designed electrode. An ion string in the single-well potential and two ion strings in the double-well potential were observed by changing the RF voltages. Such traps could be used for quantum simulation of coupled spin systems.
We investigate electrode geometries required to produce periodic 2-dimensional ion-trap arrays with the ions placed between two planes of electrodes. We present a generalization of previous methods for traps containing a single electrode plane to this new geometry, and show that for a given ion-electrode distance and applied voltages, the inter-ion distance can be reduced by a factor of up to 3 relative to single-plane traps. This represents an increase by a factor of 9 in the trap density and a factor of 27 in the exchange coupling between the oscillatory motion of neighboring ions. The resulting traps are also considerably deeper for bi-layer structures than for single-plane traps. These results could offer a useful path towards 2-dimensional ion arrays for quantum simulation. We also discuss issues with the fabrication of such traps.
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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.
Ion traps can provide both physical implementation of quantum information processing and direct observation of quantum systems. Recently, surface ion traps have been developed using microfabrication technologies and are considered to be a promising platform for scalable quantum devices. This paper presents detailed guidelines for designing the electrodes of surface ion traps. First, we define and explain the key specifications including trap depth, q-parameter, secular frequency, and ion height. Then, we present a numerical-simulation-based design procedure, which involves determining the basic assumptions, determining the shape and size of the chip, designing the dimensions of the radio frequency (RF) electrode, and analyzing the direct current (DC) control voltages. As an example of this design procedure, we present a case study with tutorial-like explanations. The proposed design procedure can provide a practical guideline for designing the electrodes of surface ion traps.