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arXiv:1507.02028 · Physical Review A

Prospects for atomic clocks based on large ion crystals

K. J. Arnold, Elnur Hajiyev, Eduardo Javier Paez, Chern Hui Lee, M. D. Barrett, J. J. Bollinger

Published Sep 8, 2015• 62 citations
arXivHTMLPDF

Abstract

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 ${\mathrm{Lu}}^{+}$ 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.

DOI
10.1103/physreva.92.032108

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Extension of the Ion Optical Clock to Multi-Ion Systems

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The optical clock is a fundamental applications of the coherence of ultracold atoms. Most of the implementations with trapped ions are based on the single-ion optical clock by Dehmelt [1], and some of them have successfully achieved inaccuracies in the 10-18level [2]. The idea has been extended to systems consisting of many neutral atoms by Katori with proper engineering on light shift associated with the optical lattice [3]. The enhanced stability is the great advantage obtained by multiple atoms. Extension of the single-ion system to multi-ion systems requires considerations on the inhomogeneous electric quadrupole shift originating from non-uniform electric field gradient at the location of each ion. A straightforward approach is to use ion species with null quadrupole moment such as In+, Al+[4]. We present another approach using ions with non-zero quadrupole moment. In the approach we use a planar surface trap to arrange the ions in an equally-spaced manner to vanish the inhomogeneous shift. We show that a clock with multiple Ca+ions can be operated even without a reference cavity for the clock laser, and that superradiant clock is expected when the ions are coupled to a cavity.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2019•0 citations
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≲103\ensuremath{\lesssim}{10}^{3}\ensuremath≲103). 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.
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.
Abstract Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn2+ ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn2+ has a unique combination of features that is not available in previously considered ions: a 1S0 ↔ 3P0 clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn2+ Coulomb-crystal clocks.
We propose to build a bad-cavity laser using forbidden transitions in large ensembles of cold ions that form a Coulomb crystal in a linear Paul trap. This laser might realize an active optical frequency standard able to serve as a local oscillator in next-generation optical clock schemes. In passive optical clocks, large ensembles of ions appear less promising, as they suffer from inhomogeneous broadening due to quadrupole interactions and micromotion-related shifts. In bad-cavity lasers, however, the radiating dipoles can synchronize and generate stable and narrow-linewidth radiation. Furthermore, for specific ions, micromotion-induced shifts can be largely suppressed by operating the ion trap at a magic frequency. We discuss the output radiation properties and perform quantitative estimations for lasing on the ${}^{3}{D}_{2}\ensuremath{\rightarrow}{}^{1}{S}_{0}$ transition in 176Lu+^{176}\mathrm{Lu}{}^{+}176Lu+ ions in a spherically symmetric trap.
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.
The optical clock is a fundamental applications of the coherence of ultracold atoms. Most of the implementations with trapped ions are based on the single-ion optical clock by Dehmelt [1], and some of them have successfully achieved inaccuracies in the 10-18level [2]. The idea has been extended to systems consisting of many neutral atoms by Katori with proper engineering on light shift associated with the optical lattice [3]. The enhanced stability is the great advantage obtained by multiple atoms. Extension of the single-ion system to multi-ion systems requires considerations on the inhomogeneous electric quadrupole shift originating from non-uniform electric field gradient at the location of each ion. A straightforward approach is to use ion species with null quadrupole moment such as In+, Al+[4]. We present another approach using ions with non-zero quadrupole moment. In the approach we use a planar surface trap to arrange the ions in an equally-spaced manner to vanish the inhomogeneous shift. We show that a clock with multiple Ca+ions can be operated even without a reference cavity for the clock laser, and that superradiant clock is expected when the ions are coupled to a cavity.