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arXiv:2102.00788 · Journal of Applied Physics

Measurement of ion displacement via RF power variation for excess micromotion compensation

Ryoichi Saito, Kota Saito, Takashi Mukaiyama

Published Mar 25, 2021• 10 citations
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Abstract

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.

DOI
10.1063/5.0046121

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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.
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.
Stray electric fields induce excess micromotion in ion traps, limiting experimental performance. We present a new micromotion-compensation technique that utilizes a dark ion in a multi-species bright-dark-bright linear ion crystal. Stray electric fields in the radial plane of the trap deform the crystal axially due to the different masses of dark and bright ions. We exploit the mode softening near the transition to the zig-zag configuration to enhance the crystal deformation and, as a result, increase the method’s sensitivity dramatically. We corroborate our results with a modified ion-displacement compensation method using a single bright ion. Our modification allows us to compensate stray fields on the 2D radial plane from a 1D measurement of the ion position on the camera by controlling the asymmetry of the two radial modes of the trap. Both methods require only a fixed imaging camera and continuous ion-fluorescence detection. As such, they can be readily implemented in most ion-trapping experiments without additional hardware modifications.
Precise control of charged particles in radio-frequency (Paul) traps requires minimising excess micromotion induced by stray electric fields. We present a method to detect and compensate such fields through amplitude modulation of the radio-frequency trapping field. Modulation at frequencies close to the motional modes of the trapped particle excites coherent motion whose amplitude linearly depends on the stray field. In trapped-ion experiments, this motion can be detected by recording the arrival times of photons scattered during laser cooling. Only a single laser beam is required to resolve fields in multiple directions. In a demonstration using a 88Sr+^{88}\mathrm{Sr}^{+}88Sr+ ion in a surface electrode trap, we achieve a sensitivity of 0.1 V m−1 / Hz0.1\, \mathrm{V}\, \mathrm{m}^{-1}\, /\, \sqrt{\mathrm{Hz}}0.1Vm−1/Hz​ and a minimal uncertainty of 0.015 V m−10.015\, \mathrm{V}\, \mathrm{m}^{-1}0.015Vm−1.
Excess micromotion induced by stray DC electric fields limits the control fidelity of trapped-ion experiments. Various techniques have been developed to detect and compensate ion displacements from the RF null by monitoring modulated fluorescence, ion positions, or micromotion sidebands. Although these approaches are effective, they do not probe the displacement through a ground-state-cooled motional mode and therefore offer limited compatibility with quantum-enhanced sensing protocols. Here, we demonstrate a micromotion compensation method based on the driven coherent amplitude of a ground-state-cooled motional mode. In this approach, the ion displacement is converted into a coherent motional excitation by an auxiliary RF drive and detected through the qubit. We determine the optimal compensation field with a 1σ1σ1σ statistical uncertainty of 8 mV/m. The method is naturally compatible with quantum-enhanced sensing protocols employing nonclassical motional states, including Fock, squeezed, and Schrödinger-cat states, providing a pathway toward quantum-enhanced micromotion compensation.
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.
When a charged particle in a Paul trap is displaced from the node of the AC trapping field, excess micromotion arises as an undesired effect. Excess micromotion heats the particle, limits the precision with which the particle can be localised, and acts as a decoherence channel in quantum mechanical experiments. However, thus far there is no standard procedure for micromotion compensation with mesoscopic particles. Here, we experimentally demonstrate three different methods for minimizing the micromotion of a nanoparticle in a linear Paul trap along three axes. The most precise method allows us to nullify the stray field to within 2.9 V/m, which is comparable to reported values in trapped-ion experiments.