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### Abstract:

The indium ion is one of the original candidates in the first proposal for single-ion clocks with systematic uncertainties at the 10-18 level [1]. In+ has an alkaline-earth-like electron configuration, with a 1S0 - 3P0 clock transition frequency that has a low sensitivity to magnetic fields. It has the highest clock frequency of all presently investigated optical clocks [2]. Such high transition energies give it a very small sensitivity to blackbody radiation (BBR), which causes problematic frequency shifts in most other clocks, including optical lattice clocks. Direct state detection and laser cooling on the 1S0 - 3P1 transition are a further advantage for an 115In+ clock. The electric quadrupole moments of the two clock states are orders of magnitude smaller than those for the 2S1/2 - 2D5/2 quadrupole transitions of alkaline-like ions (Ca+, Sr+, Yb+). This makes the transition frequency insensitive to the electric field gradients imposed by adjacent ions. With direct readout available, In+ is thus ideal for a multi-ion clock, which can overcome the inherent stability limitations of a single-ion system. Despite the appeal of the 115In+ ion for a high-performance optical clock, its adoption has been hampered by concerns about technical reliability. Only two groups previously measured the clock transition frequency with fractional uncertainties approaching 1e-14, reported 2000[3] and 2007[4]. In 2017, we measured the clock frequency with an uncertainty of 5e-15 [5], which prompted an update of the frequency value recommended by the International Committee for Weights and Measures (CIPM). This initial frequency determination was performed by averaging 36 measurements of the magnetically unresolved spectrum, and was limited by the systematic uncertainty of the first order Zeeman shift as well as the statistical uncertainty. We recently improved our In+ clock by direct laser stabilization to the clock transition and controlled magnetic field application to resolve Zeeman sublevels [6]. In this presentation, we report on the first frequency ratio measurement of an 115In+ single ion clock and a 87Sr optical lattice clock. The measurement employs two independent Er-doped fiber frequency combs which reference a common hydrogen maser that serves as a flywheel oscillator. From 89 000 s of measurement time, the frequency ratio is determined to be 2.952 748 749 874 863 3(23) with 7.7e-16 relative uncertainty. If we adopt the CIPM recommended value for the 87Sr clock frequency, we find 1 267 402 452 901 040.0(1.1) Hz for the absolute In+ clock frequency [7]. [1] H. G. Dehmelt, “Monoion oscillator as potential ultimate laser frequency standard,” IEEE Transactions on Instrumentation Meas. pp. 83–87 (1982). [2] F. Riehle, P. Gill, F. Arias, and L. Robertsson, “The CIPM list of recommended frequency standard values: guidelines and procedures,” Metrologia. 55, 188–200 (2018). [3] J. von Zanthier, T. Becker, M. Eichenseer, A. Y. Nevsky, C. Schwedes, E. Peik, H. Walther, R. Holzwarth, J. Reichert, T. Udem, T. W. Hänsch, P. V. Pokasov, M. N. Skvortsov, and S. N. Bagayev, Opt. Lett. 25, 1729 (2000). [4] Y. Wang, R. Dumke, T. Liu, A. Stejskal, Y. Zhao, J. Zhang, Z. Lu, L. Wang, T. Becker, and H. Walther, Opt. Commun. 273, 526 (2007). [5] N. Ohtsubo, Y. Li, K. Matsubara, T. Ido, and K. Hayasaka, Opt. Express 25, 11725 (2017). [6] N. Ohtsubo, Y. Li, N. Nemitz, H. Hachisu, K. Matsubara, T. Ido, and K. Hayasaka, Hyperfine Interact. 240, 39 (2019). [7] N. Ohtsubo, Y. Li, N. Nemitz, H. Hachisu, K. Matsubara, T. Ido, and K. Hayasaka, Optics Letters, accepted