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arXiv:1811.10177 · Physical Review A

Oscillating quadrupole effects in high-precision metrology

K. J. Arnold, R. Kaewuan, Ting Rei Tan, M. D. Barrett

Published Feb 25, 2019• 6 citations
arXivHTMLPDF

Abstract

The influence of oscillating quadrupole fields on atomic energy levels is examined theoretically, and general expressions for the quadrupole matrix elements are given. The results are relevant to any ion-based clock in which one of the clock states supports a quadrupole moment. Clock shifts are estimated for $^{176}\mathrm{Lu}^{+}$ and indicate that coupling to the quadrupole field would not be a limitation to clock accuracy at the $\ensuremath{\lesssim}{10}^{\ensuremath{-}19}$ level. Nevertheless, a method is suggested that would allow this shift to be calibrated. This method utilizes a resonant quadrupole coupling that enables the quadrupole moment of the atom to be measured. A proof-of-principle demonstration is given using $^{138}\mathrm{Ba}^{+}$, in which the quadrupole moment of the ${D}_{5/2}$ state is estimated to be $\mathrm{\ensuremath{\Theta}}=3.229(89)e{a}_{0}^{2}$.

DOI
10.1103/physreva.99.022515

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The influence of oscillating quadrupole fields on atomic energy levels is examined theoretically, and general expressions for the quadrupole matrix elements are given. The results are relevant to any ion-based clock in which one of the clock states supports a quadrupole moment. Clock shifts are estimated for 176Lu+^{176}\mathrm{Lu}^{+}176Lu+ and indicate that coupling to the quadrupole field would not be a limitation to clock accuracy at the \ensuremath≲10\ensuremath−19\ensuremath{\lesssim}{10}^{\ensuremath{-}19}\ensuremath≲10\ensuremath−19 level. Nevertheless, a method is suggested that would allow this shift to be calibrated. This method utilizes a resonant quadrupole coupling that enables the quadrupole moment of the atom to be measured. A proof-of-principle demonstration is given using 138Ba+^{138}\mathrm{Ba}^{+}138Ba+, in which the quadrupole moment of the D5/2{D}_{5/2}D5/2​ state is estimated to be \ensuremathΘ=3.229(89)ea02\mathrm{\ensuremath{\Theta}}=3.229(89)e{a}_{0}^{2}\ensuremathΘ=3.229(89)ea02​.
An optical clock based upon a single mercury ion in a radio-frequency trap has the potential for both high stability and high accuracy. The systematic uncertainty of this frequency standard is limited by contributions due to two types of external fields. The clock has previously been operated with a magnetic bias field that destabilizes dark states that limit the rates of laser cooling and state detection. This bias field has previously resulted in a substantial second-order Zeeman shift. We now destabilize the dark states with a polarization-scrambling technique that allows us to operate with only a minimal magnetic field. The second uncertainty that we address here is the magnitude of the quadrupole shift due to the interaction of stray electric-field gradients with the quadrupole moment of the ion. We describe the steps that we are taking to evaluate this shift in the near future. 1
We investigate the feasibility of precision frequency metrology with large ion crystals. For clock candidates with a negative differential static polarizability, we show that micromotion effects should not impede the performance of the clock. Using Lu+{\mathrm{Lu}}^{+}Lu+ as a specific example, we show that quadrupole shifts due to the electric fields from neighboring ions do not significantly affect clock performance. We also show that effects from the tensor polarizability can be effectively managed with a compensation laser at least for a small number of ions ($\ensuremath{\lesssim}{10}^{3}$). These results provide new possibilities for ion-based atomic clocks, allowing them to achieve stability levels comparable to neutral atoms in optical lattices and a viable path to greater levels of accuracy.
We propose a new ion-trap geometry to carry out accurate measurements of the quadrupole shifts in the 171 Yb ion. This trap will minimize the quadrupole shift due to the harmonic component of the confining potential by an order of magnitude. This will be useful to reduce the uncertainties in the clock frequency measurements of the 6s 2 S 1/2 → 4f 13 6s 2 2 F 7/2 and 6s 2 S 1/2 → 5d 2 D 3/2 transitions, from which we can deduce the precise values of the quadrupole moments ( Θ s) of the 4f 13 6s 2 2 F 7/2 and 5d 2 D 3/2 states. Moreover, it may be able to affirm the validity of the measured Θ value of the 4f 13 6s 2 2 F 7/2 state, for which three independent theoretical studies defer almost by one order of magnitude from the measurement. We also calculate Θ s using the relativistic coupled-cluster (RCC) method. We use these Θ values to estimate the quadrupole shift that can be measured in our proposed ion trap experiment.
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 dynamic decoupling of a multilevel quantum probe to distinguish small frequency shifts that depend on m_{j}^{2}, where m_{j}^{2} is the angular momentum of level |j⟩ along the quantization axis, from large noisy shifts that are linear in m_{j}, such as those due to magnetic field noise. Using this method we measured the electric-quadrupole moment of the 4D_{5/2} level in ^{88}Sr^{+} to be 2.973_{-0.033}^{+0.026}ea_{0}^{2}. Our measurement improves the uncertainty of this value by an order of magnitude and thus helps mitigate an important systematic uncertainty in ^{88}Sr^{+} based optical atomic clocks and verifies complicated many-body quantum calculations.
We explore the potential of the electric quadrupole transitions 7s 2S1/27s\,^2S_{1/2}7s2S1/2​ - 6d 2D3/26d\,^2D_{3/2}6d2D3/2​, 6d 2D5/26d\,^2D_{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^AARa+^++ candidates with A=A=A= 223 - 229 are identified. In particular, we show that the transition 7s 2S1/2 (F=2,mF=0)7s\,^2S_{1/2}\,(F=2,m_F=0)7s2S1/2​(F=2,mF​=0) - 6d 2D3/2 (F=0,mF=0)6d\,^2D_{3/2}\,(F=0,m_F=0)6d2D3/2​(F=0,mF​=0) at 828 nm in 223^{223}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 10−1710^{-17}10−17. With more experimental effort, the 223,225,226^{223,225,226}223,225,226Ra+^++ clocks could be pushed to a projected performance reaching the 10−1810^{-18}10−18 level.