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Measurement Science and Technology

Automatic minimisation of micromotion in a 88 Sr + optical clock

G. P. Barwood, Guozheng Huang, Hugh A. Klein, Patrick Robert Gill

Published Jun 12, 2015• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0957-0233/26/7/075203

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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.
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.
Abstract Ensuring robust operation of optical clock systems requires increasingly complex automation of experimental protocols. This includes real-time monitoring of system output for data validation and for high accuracy assessment of systematic frequency shifts. We report here on recent advances in the control system of the 171 Yb+ ion optical clock at NPL (National Physical Laboratory, UK) and describe how this has led to improvements in systematic shift metrology and reduced the overall uncertainty budget for the optical clock. Additionally we present an assessment of the rf trap drive-induced ac Zeeman effect for our experimental system. These system advances enable us to provide improved contributions to the international efforts in the redefinition of the SI second and other applications such as tests of fundamental physics.
The present decade has seen great advances in optical frequency standards following the development of femtosecond laser frequency combs. With this technology, combined with a stable and narrow probe laser source (50-100 Hz linewidth), we made a systematic study of the 5s 2S1/2-4d 2D5/2 (S-D) transition frequency of the 88Sr+ ion as a function of the quantization axis in the trap. This study revealed the presence of systematic shifts caused by residual micromotion in our rf Paul trap and led to an evaluation of those shifts. Also, a method was developed based on the measurement of the Zeeman spectrum of the clock transition to cancel the electric quadrupole shift caused by patch potentials on the trap electrodes. From these results, we also determined the absolute frequency of the S-D clock transition frequency at 674 nm with a fractional frequency uncertainty of 3.4 × 10-14. We have since made improvements to our probe laser system and have observed 5 Hz Fourier transform limited linewidths on a Zeeman component of the S-D transition of the 88Sr+ ion. To observe such a narrow transition it is essential to have a known and well behaved drift of the laser frequency during the few minutes it takes to measure the ion resonance using the quantum jump signal. Our approach to minimize the drift rate and its sensitivity to temperature fluctuations has been to stabilize the cavity at the temperature where its coefficient of thermal expansion is zero. We will present an overview of our recent progress made on the frequency standard based on the laser-cooled and trapped single ion of 88Sr+.
Micromotion of ions in Paul traps has several adverse effects, including alterations of atomic transition line shapes, significant second-order Doppler shifts in high-accuracy studies, and limited confinement time in the absence of cooling. The ac electric field that causes the micromotion may also induce significant Stark shifts in atomic transitions. We describe three methods of detecting micromotion. The first relies on the change of the average ion position as the trap potentials are changed. The second monitors the amplitude of the sidebands of a narrow atomic transition, caused by the first-order Doppler shift due to the micromotion. The last technique detects the Doppler shift induced modulation of the fluorescence rate of a broad atomic transition. We discuss the detection sensitivity of each method to Doppler and Stark shifts, and show experimental results using the last technique.
We report our recent progress made with the NRC88Sr+single-ion optical frequency standard. The long-term operation of the standard was improved by actively stabilizing the cooling, repump and clearout laser sources, and by using a femtosecond fiber laser frequency comb to link the probe laser frequency to the microwave time standards. With the femtosecond fiber comb, we have demonstrated continuous operation for a period of eight days and continuous measurement of the probe laser source for three days. Micromotion shifts have been the dominant source of uncertainty in our rf Paul trap because laser beam access is only possible along one axis in the current design. With the aim of reducing to a minimum these shifts, we have constructed an endcap trap designed for minimization of micromotion along three orthogonal axes. We report on the successful trapping of single ions with this endcap trap. Since electrode contamination during trap loading can also induce micromotion shifts as a result of evolving patch potentials, we have increased the trap loading efficiency with photo-ionization.
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.