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arXiv:quant-ph/9812033 · Physical Review A

Individual addressing and state readout of trapped ions utilizing rf micromotion

Dietrich G. Leibfried

Published Nov 1, 1999• 36 citations
arXivHTMLPDF

Abstract

A scheme for the individual addressing of ions in a trap is described that does not rely on light beams tightly focused onto only one ion. The scheme utilizes ion micromotion that may be induced in a linear trap by dc offset potentials. Thus coupling an individual ion to the globally applied light fields corresponds to a mere switching of voltages on a suitable set of compensation electrodes. The proposed scheme is especially suitable for miniaturized rf (Paul) traps with typical dimensions of about $20\ensuremath{-}40 \ensuremath{\mu}\mathrm{m}.$

DOI
10.1103/physreva.60.r3335

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A scheme for the individual addressing of ions in a trap is described that does not rely on light beams tightly focused onto only one ion. The scheme utilizes ion micromotion that may be induced in a linear trap by dc offset potentials. Thus coupling an individual ion to the globally applied light fields corresponds to a mere switching of voltages on a suitable set of compensation electrodes. The proposed scheme is especially suitable for miniaturized rf (Paul) traps with typical dimensions of about 20\ensuremath−40\ensuremathμm.20\ensuremath{-}40 \ensuremath{\mu}\mathrm{m}.20\ensuremath−40\ensuremathμm.
Excess "micromotion" of trapped ions due to the residual radio-frequency (rf) trapping field at their location is often undesirable and is usually carefully minimized. Here, we induce precise amounts of excess micromotion on individual ions by adjusting the local static electric field they experience. Micromotion modulates the coupling of an ion to laser fields, ideally tuning it from its maximum value to zero as the ion is moved away from the trap's rf null. We use tunable micromotion to vary the Rabi frequency of stimulated Raman transitions over two orders of magnitude, and to individually control the rates of resonant fluorescence from three ions under global laser illumination without any changes to the driving light fields. The technique is amenable to situations where addressing individual ions with focused laser beams is challenging, such as tightly packed linear ion strings or two-dimensional ion arrays illuminated from the side.
For experiments with ions confined in a Paul trap, minimization of micromotion is often essential. In order to diagnose and compensate micromotion we have implemented a method that allows for finding the position of the radio-frequency (rf) null reliably and efficiently, in principle, without any variation of direct current (dc) voltages. We apply a trap modulation technique and focus-scanning imaging to extract three-dimensional ion positions for various rf drive powers and analyze the power dependence of the equilibrium position of the trapped ion. In contrast to commonly used methods, the search algorithm directly makes use of a physical effect as opposed to efficient numerical minimization in a high-dimensional parameter space. Using this method we achieve a compensation of the residual electric field that causes excess micromotion in the radial plane of a linear Paul trap down to $0.09\phantom{\rule{4pt}{0ex}}\text{V}\phantom{\rule{0.16em}{0ex}}{\text{m}}^{\ensuremath{-}1}$. Additionally, the precise position determination of a single harmonically trapped ion employed here can also be utilized for the detection of small forces. This is demonstrated by determining light pressure forces with a precision of 135 yN. As the method is based on imaging only, it can be applied to several ions simultaneously and is independent of laser direction and thus well suited to be used with, for example, surface-electrode traps.
We propose and demonstrate four procedures for three-dimensional micromotion compensation by combining two methods: the RF-photon correlation method and the displacement method based on trap RF amplitude modulation. In ion traps, the structure of the electrodes or the vacuum chamber may restrict the laser beam incidence direction, causing a limitation in the compensation scheme. We present four protocols, ensuring that at least one of them can be applied to experimental systems with various individual constraints. We also discuss the compensation accuracy and practical applicability of each of these four approaches. This work provides a practical guideline for performing full three-axis micromotion compensation and contributes to the advancement of endcap traps, which are highly suitable for single-ion trapping.
We demonstrate a method of micromotion minimization of a trapped ion in a linear Paul trap based on the precision measurement of the ion trapping position displacement due to a stray electric field in the radial plane by ion fluorescence imaging. The amount of displacement in the radial plane is proportional to the strength of a stray electric field. Therefore, we evaluated the micromotion compensation condition by measuring the ion displacements from the ion equilibrium position using two different radial trap frequencies with various combinations of the compensation voltage. The residual electric field uncertainty of this technique reached a few volts per meter. This compensation technique does not depend on the orientation of the incident cooling laser or the detuning and imaging direction. Therefore, this method is suitable for a planar ion trap, a stylus ion trap, which limits the propagation angle of lasers, or miniaturized ion trap systems for sensing and metrological applications.
Micromotion is the driven motion of trapped ions in rf traps. In practical traps, the micromotion is often greatly enhanced due to “dirty effects” such as stray dc fields from surface patch effects and/or rf phase differences between the endcaps of a quadrupole trap. Large micromotions can have adverse effects on precision measurements and quantum experiments that the trapped ions are best suited for. We present here a new approach to reduce and eliminate the enhanced micromotion. The approach uses a novel Paul-Straubel-Kingdon trap in which ions are loaded indirectly to avoid contamination of the trap surfaces.