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Bulletin of the Russian Academy of Sciences Physics

Detecting and Compensating for Excess Ion Micromotion in the Single Ion Optical Frequency Standard

N. A. Pavlov, S. V. Chepurov

Published Jun 1, 2022• 1 citation
Publisher

Abstract

Abstract A cross-correlation method for detecting and compensating for excess ion micromotion is compared to conventional direct monitoring of the position of an ion with high-sensitivity ultraviolet cameras. The sensitivity of determining the position of an ion in the proposed approach is no worse than 20 nm, ensuring the Lamb‒Dicke regime for trapped ions.

DOI
10.3103/s106287382206020x

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Measurement Science and Technology•Jun 12, 2015•1 citation
Abstract A cross-correlation method for detecting and compensating for excess ion micromotion is compared to conventional direct monitoring of the position of an ion with high-sensitivity ultraviolet cameras. The sensitivity of determining the position of an ion in the proposed approach is no worse than 20 nm, ensuring the Lamb‒Dicke regime for trapped ions.
As relative systematic frequency uncertainties in trapped-ion spectroscopy are approaching the low 10−18 range, motional frequency shifts account for a considerable fraction of the uncertainty budget. Micromotion, a driven motion fundamentally connected to the principle of the Paul trap, is a particular concern in these systems. In this article, we experimentally investigate at this level three common methods for minimizing and determining the micromotion amplitude. We develop a generalized model for a quantitative application of the photon-correlation technique, which is applicable in the commonly encountered regime where the transition linewidth is comparable to the rf drive frequency. We show that a fractional frequency uncertainty due to the 2nd-order Doppler shift below |Δν/ν|=1×10−20 can be achieved. The quantitative evaluation is verified in an interleaved measurement with the conceptually simpler resolved sideband method. If not performed deep within the Lamb-Dicke regime, a temperature-dependent offset at the level of 10−19 is observed in resolved sideband measurements due to sampling of intrinsic micromotion. By direct comparison with photon-correlation measurements, we show that the simple to implement parametric heating method is sensitive to micromotion at the level of |Δν/ν|=1×10−20 as well.
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.
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.
In this paper, direct observation of micromotion for multiple ions in a laser-cooled trapped ion crystal is discussed along with a measurement technique for micromotion amplitude. Micromotion is directly observed using a time-resolving, single-photon-sensitive camera that provides both fluorescence and position data for each ion on the nanosecond time scale. Micromotion amplitude and phase for each ion in the crystal are measured, allowing this method to be sensitive to tilts and shifts of the ion chain from the null of the radio-frequency quadrupole potential in the linear trap. Spatial resolution makes this micromotion detection technique suitable for complex ion configurations, including two-dimensional geometries. It does not require any additional equipment or laser beams, and the modulation of the cooling lasers or trap voltages is not necessary for detection as it is in other methods.
We investigate sideband spectroscopy of a trapped ion using a probe laser phase modulated at the trap drive frequency. The enhanced sensitivity of our technique provides us 1000-fold improvement in our control of excess micromotion. It allows us to monitor the evolution of stray fields on a timescale of a few minutes and detect differential phases of $5\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{rad}$ between applied ac potentials. We also demonstrate the ability to suppress Doppler shifts from excess motion to well below the limit imposed by the intrinsic motion of the ion in its motional ground state. The technique we introduce can be readily implemented in any ion-trap system that utilizes sideband spectroscopy for micromotion compensation and can be seamlessly integrated into experiments in a fully automated way.
Abstract Optical clocks based on narrow linewidth transitions in single cold ions confined in RF traps are being developed at a number of laboratories worldwide. For these ion clock systems, excess micromotion can cause both Stark and Doppler frequency shifts and also a degradation of frequency stability as a result of a reduced excitation rate to the clock transition. At NPL, we detect micromotion in our 88 Sr + optical clocks by observing the correlation between photon arrival times and the zero crossing of the RF trap drive signal. Recently, two nominally identical 88 Sr + optical clocks have been operated over several days and their frequencies compared against one another. During this time the dc voltages on the endcap and compensation voltage electrodes required to minimise the micromotion can change significantly, particularly following the loading of an ion. This paper describes an automatic method to monitor and minimise micromotion applicable to single ion clocks and which we demonstrate using our two NPL 88 Sr + ion clocks.