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Physical Review Letters

Electric Quadrupole Shift Cancellation in Single-Ion Optical Frequency Standards

P. Dubé, Alan A. Madej, J. E. Bernard, L. Marmet, J.-S. Boulanger, S. Cundy

Published Jul 12, 2005• 153 citations
Publisher

Abstract

The electric quadrupole shift is presently the most significant source of uncertainty on the systematic shifts for several single-ion optical frequency standards. We present a simple method for cancelling this shift based on measurements of the Zeeman spectrum of the clock transition. This method is easy to implement and yields very high cancellation levels. A fractional uncertainty of 5 x 10(-18) for the canceled quadrupole shift is estimated for a measurement of the absolute frequency of the 5s (2)S(1/2)-4d (2)D(5/2) clock transition of 88Sr+.

DOI
10.1103/physrevlett.95.033001

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The electric quadrupole shift is an important source of systematic uncertainty in several single-ion optical frequency standards. In this paper, we review the electric quadrupole shift cancellation method based on the Zeeman spectrum of the clock transition. The method is demonstrated with an actual frequency measurement of the 5s2S1/2-4d2D5/2transition of88Sr+. This cancellation method also removes shifts from the tensor part of the Stark effect. Further analysis of the data provides an evaluation of the micromotion shifts which are then applied to correct the observed ion clock frequency. Recent improvements to our probe laser system and the observation of Fourier-transform limited linewidths of 5 Hz at 445 THz are also reported

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The electric quadrupole shift is presently the most significant source of uncertainty on the systematic shifts for several single-ion optical frequency standards. We present a simple method for cancelling this shift based on measurements of the Zeeman spectrum of the clock transition. This method is easy to implement and yields very high cancellation levels. A fractional uncertainty of 5 x 10(-18) for the canceled quadrupole shift is estimated for a measurement of the absolute frequency of the 5s (2)S(1/2)-4d (2)D(5/2) clock transition of 88Sr+.
The electric quadrupole shift is an important source of systematic uncertainty in several single-ion optical frequency standards. In this paper, we review the electric quadrupole shift cancellation method based on the Zeeman spectrum of the clock transition. The method is demonstrated with an actual frequency measurement of the 5s2S1/2-4d2D5/2transition of88Sr+. This cancellation method also removes shifts from the tensor part of the Stark effect. Further analysis of the data provides an evaluation of the micromotion shifts which are then applied to correct the observed ion clock frequency. Recent improvements to our probe laser system and the observation of Fourier-transform limited linewidths of 5 Hz at 445 THz are also reported
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+.
The frequency of the 5s 2S(1/2)-4d 2D(5/2) electric quadrupole clock transition in a single, trapped, laser-cooled 88Sr+ ion has been measured by using an optical frequency comb referenced to a cesium fountain primary frequency standard. The frequency of the transition is measured as 444,779,044,095,484.6 (1.5) hertz, with a fractional uncertainty within a factor of 3 of that of the cesium standard. Improvements required to obtain a cesium-limited frequency measurement are described and are expected to lead to a 88Sr+ optical clock with stability and reproducibility exceeding that of the primary cesium standard.
We explore the potential of the electric quadrupole transitions 7s2S1/27s {}^{2}{S}_{1/2}7s2S1/2​-6d2D3/26d {}^{2}{D}_{3/2}6d2D3/2​, 6d2D5/26d {}^{2}{D}_{5/2}6d2D5/2​ in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive A{}^{A}ARa+{}^{+}+ candidates, with A=A=A= 223--229, are identified. In particular, we show that the transition 7s2S1/2(F=2,mF=0)7s {}^{2}{S}_{1/2} (F=2,{m}_{F}=0)7s2S1/2​(F=2,mF​=0)-6d2D3/2(F=0,mF=0)6d {}^{2}{D}_{3/2} (F=0,{m}_{F}=0)6d2D3/2​(F=0,mF​=0) at 828 nm in 223Ra^{223}\mathrm{Ra}223Ra+{}^{+}+, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of ${10}^{\ensuremath{-}17}$. With more experimental effort, the 223,225,226Ra^{223,225,226}\mathrm{Ra}223,225,226Ra+{}^{+}+ clocks could be pushed to a projected performance reaching the ${10}^{\ensuremath{-}18}$ level.
Abstract Optical clocks with ultralow uncertainty are strong candidates for the next redefinition of the SI second. The 171 Yb + single-ion clock is particularly attractive owing to its two clock transitions (E2 and E3) and its potential for low uncertainty. A major contribution to the uncertainty budget arises from the electric-quadrupole shift, caused by the interaction between the atomic quadrupole moment and the electric-field gradient at the trap center and strongly dependent on the orientation of the quantization axis. To evaluate this shift, a simplified orthogonal magnetic-field method was employed: three mutually orthogonal magnetic-field directions are generated together with an auxiliary non-orthogonal field. With a dual-condition locking scheme, we measure the E2 transition frequency differences between magnetic-field configurations, infer the electric-field gradient, and apply corrections for the associated quadratic Zeeman shifts. The uncertainty due to magnetic-field misalignment is quantified using a calibrated current-to-field model. The resulting electric-quadrupole shift correction for the 2 S 1/2 → 2 F 7/2 (E3) transition is 3.24 mHz, corresponding to a fractional uncertainty of 1.1×10 −18 in the absolute frequency measurement.
We present a method that uses radio-frequency pulses to cancel the quadrupole shift in optical clock transitions. Quadrupole shifts are an inherent inhomogeneous broadening mechanism in trapped ion crystals and impose one of the limitations forcing current optical ion clocks to work with a single probe ion. Canceling this shift, at each interrogation cycle of the ion frequency, reduces the complexity in using N>1 ions in clocks, thus allowing for a reduction of the instability in the clock frequency by sqrt[N] according to the standard quantum limit. Our sequence relies on the tensorial nature of the quadrupole shift, and thus also cancels other tensorial shifts, such as the tensor ac stark shift. We experimentally demonstrate our sequence on three and seven ^{88}Sr^{+} ions trapped in a linear Paul trap, using correlation spectroscopy. We show a reduction of the quadrupole shift difference between ions to the ≈10 mHz level where other shifts, such as the relativistic second-order Doppler shift, are expected to limit our spectral resolution. In addition, we show that using radio-frequency dynamic decoupling we can also cancel the effect of first-order Zeeman shifts.