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We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10 −18 , we propose 115 In + ions sympathetically cooled by 172 Yb + . We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of the ions at a level at which the corresponding secondorder Doppler shift contributes less than 10 −18 to the relative uncertainty of the frequency standard.

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 |∆ν/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 photoncorrelation measurements, we show that the simple to implement parametric heating method is sensitive to micromotion at the level of |∆ν/ν| = 1 × 10 −20 as well.

We present an experiment to characterize our new linear ion trap designed for the operation of a many-ion optical clock using 115 In + as clock ions. For the characterization of the trap as well as the sympathetic cooling of the clock ions we use 172 Yb + . The trap design has been derived from finite element method (FEM) calculations and a first prototype based on glass-reinforced thermoset laminates was built. This paper details on the trap manufacturing process and micromotion measurement. Excess micromotion is measured using photon-correlation spectroscopy with a resolution of 1.1 nm in motional amplitude, and residual axial rf fields in this trap are compared to FEM calculations. With this method, we demonstrate a sensitivity to systematic clock shifts due to excess micromotion of |(∆ν/ν) mm | = 8.5 × 10 −20 . Based on the measurement of axial rf fields of our trap, we estimate a number of twelve ions that can be stored per trapping segment and used as an optical frequency standard with a fractional inaccuracy of ≤ 1 × 10 −18 due to micromotion.Submitted to: New J. Phys.

The use of special quantum states to achieve sensitivities below the limits established by classically behaving states has enjoyed immense success since its inception. 1,2 In bosonic interferometers, squeezed states, 3, 4 number states 4-6 and cat states 6 have been implemented on various platforms and have demonstrated improved measurement precision over interferometers based on coherent states. 7, 8 Another metrologically useful state is an equal superposition of two eigenstates with maximally different energies; this state ideally reaches the full interferometric sensitivity allowed by quantum mechanics. 9-11 By leveraging improvements to our apparatus made primarily to reach higher operation fidelities in quantum information processing, we extend a technique 12 to create number states up to n = 100 and to generate superpositions of a harmonic oscillator ground state and a number state of the form 1 √ 2 (|0 + |n ) with n up to 18 in the motion of a single trapped ion. While experimental imperfections prevent us from reaching the ideal Heisenberg limit, we observe enhanced sensitivity to changes in the oscillator frequency that initially increases linearly with n, with maximal value at n = 12 where we observe 3.2(2) dB higher sensitivity compared to an ideal measurement on a coherent state with the same average occupation number. The quantum advantage from using number-state superpositions can be leveraged towards precision measurements on any harmonic oscillator system; here it enables us to track 1 arXiv:1807.11934v3 [physics.atom-ph]