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arXiv:1905.03486 · Physical Review Letters

Suppressing Inhomogeneous Broadening in a Lutetium Multi-ion Optical Clock

Ting Rei Tan, R. Kaewuam, K. J. Arnold, Sapam Ranjita Chanu, Zhiqiang Zhang, Marianna S. Safronova, M. D. Barrett

Published Aug 7, 2019• 34 citations
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Abstract

We demonstrate precision measurement and control of inhomogeneous broadening in a multi-ion clock consisting of three $^{176}{\mathrm{Lu}}^{+}$ ions. Microwave spectroscopy between hyperfine states in the $^{3}{D}_{1}$ level is used to characterize differential systematic shifts between ions, most notably those associated with the electric quadrupole moment. By appropriate alignment of the magnetic field, we demonstrate suppression of these effects to the $\ensuremath{\sim}{10}^{\ensuremath{-}17}$ level relative to the ${^{1}S}_{0}\ensuremath{\leftrightarrow}{^{3}D}_{1}$ optical transition frequency. Correlation spectroscopy on the optical transition demonstrates the feasibility of a 10-s Ramsey interrogation in the three ion configuration with a corresponding projection noise limited stability of $\ensuremath{\sigma}(\ensuremath{\tau})=8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}/\sqrt{\ensuremath{\tau}}$.

DOI
10.1103/physrevlett.123.063201

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We propose and experimentally demonstrate a scheme that realizes hyperfine averaging during a Ramsey interrogation of a clock transition. The method eliminates the need to average over multiple optical transitions, reduces the sensitivity of the clock to its environment, and reduces inhomogeneous broadening in a multi-ion clock. The method is compatible with autobalanced Ramsey spectroscopy, which facilitates the elimination of residual shifts due to imperfect implementation and ac stark shifts from the optical probe. We demonstrate the scheme using correlation spectroscopy of the ^{1}S_{0}↔^{3}D_{1} clock transition in a three-ion Lu^{+} clock. From the demonstration we are able to provide a measurement of the ^{3}D_{1} quadrupole moment, Θ(^{3}D_{1})=0.634(9)ea_{0}^{2}.
We study and characterize a quasicontinuous dynamical decoupling scheme that effectively suppresses dominant frequency shifts in a multi-ion optical clock. Addressing the challenge of inhomogeneous frequency shifts in such systems, our scheme mitigates primary contributors, namely, the electric quadrupole and the linear Zeeman shifts. Based on ^{88}Sr^{+} ions, we implement the scheme in linear chains of up to 7 ions and demonstrate a significant suppression of the shift by more than 3 orders of magnitude, leading to relative frequency inhomogeneity below 7×10^{-17}. Additionally, we evaluate the associated systematic shift arising from the radio-frequency drive used in the QCDD scheme, showing that, in the presented realization, its contribution to the systematic relative frequency uncertainty is below 10^{-17}, with the potential for further improvement. These results provide a promising avenue toward implementing multi-ion clocks exhibiting an order of magnitude or more improvement in stability while maintaining a similar high degree of accuracy to that of single-ion clocks.
Trapped-ion optical clocks are capable of achieving systematic fractional frequency uncertainties of 10−1810^{-18}10−18 and possibly below. However, the stability of current ion clocks is fundamentally limited by the weak signal of single-ion interrogation. We present an operational, versatile platform for extending clock spectroscopy to arrays of Coulomb crystals consisting of several tens of ions, while allowing systematic shifts as low as 10−1910^{-19}10−19. The concept is applicable to all clock transitions with low differential electric quadrupole moments. We observe 3D excess micromotion amplitudes of all individual ions inside a Coulomb crystal with nm resolution and prove that the related frequency shifts can be controlled simultaneously at the 10−1910^{-19}10−19 level. Using this method, we demonstrate regions of 400400400 μ\muμm and 222 mm length in our trap array with time dilation shifts due to micromotion close to 1×10−191\times10^{-19}1×10−19 and below 10−1810^{-18}10−18, respectively. Further measurements of the trapping environment and cooling dynamics calculations for mixed In+{}^++ / Yb+{}^++ crystals show that achievable clock uncertainties due to multi-ion operation in our setup are below 1×10−191\times10^{-19}1×10−19. This work will enable clock operation with multiple ions and open up the possibility of new interrogation schemes which allow optical clock stabilities beyond classical limits.
Scaling trapped-ion optical clocks to hundreds of ions remains a major challenge due to inhomogeneous frequency shifts in large ion crystals. Here, we propose a circular surface-trap architecture for a multi-ion optical clock with hundreds of ions. The rotational symmetry of the ion crystal suppresses the main sources of inhomogeneity, quadrupole shift.We investigate the feasibility of a clock based on a ring crystal of 400 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ions and propose a suitable experimental setup configuration. We have shown that circular configuration of ions leads to suppression by two orders of magnitude of the quadrupole shift comparing to the linear trap. Combined with stray-field compensation and dynamical decoupling techniques, this architecture provides a pathway toward multi-ion optical clocks with fractional frequency uncertainty at the 10−1810^{-18}10−18 level and an expected 20-fold improvement in frequency stability compared to single ion clocks.
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.
We present the experimental realization of a continuous dynamical decoupling scheme which suppresses leading frequency shifts in a multi-ion frequency reference based on 40Ca+^{40}\mathrm{Ca}^+40Ca+. By near-resonant magnetic coupling of the 2S1/2^2\mathrm{S}_{1/2}2S1/2​ and 2D5/2^2\mathrm{D}_{5/2}2D5/2​ Zeeman sub-levels using radio-frequency dressing fields, engineered transitions with reduced sensitivity to magnetic-field fluctuations are obtained. A second stage detuned dressing field reduces the influence of amplitude noise in the first stage driving fields and decreases 2\textsuperscript{nd}-rank tensor shifts, such as the electric quadrupole shift. Suppression of the quadratic dependence of the quadrupole shift to 3(2) mHz/μm23(2)\,\text{mHz}/μm^23(2)mHz/μm2 and coherence times of 290(20) ms290(20)\,\text{ms}290(20)ms on the optical transition are demonstrated even within a laboratory environment with significant magnetic field noise. Besides removing inhomogeneous line shifts in multi-ion clocks, the demonstrated dynamical decoupling technique may find applications in quantum computing and simulation with trapped ions by a tailored design of decoherence-free subspaces.