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values. Aer evaluating various factors — systematic shi in In+ due to residual magnetic elds and other physical conditions, systematic shi due to frequency link from the frequency standard, and others — the clock frequency was nally determined to be 1 267 402 452 901 049.9 (6.9) Hz. e frequency values obtained in this study and those re-ported in the past research are compared in Fig.11 (“Garching, 2000” indicates the values from reference [12], and “Erlangen, 2007” from reference [13]). As described above, the measurements reported here successfully deter-mined In+ clock transition frequency with the least uncer-tainty ever (5.4 ×10-15) [14]. Zeeman shi due to residual magnetic elds is the most dominant factor aecting the magnitude of uncertainty. erefore, further improvements in terms of polarization in magnetic sublevels and imple-mentation of an eective magnetic shield are expected to reduce uncertainty, leading to realize more reliable optical frequency standards.5SummaryIn this report, we described research and development of state-of-the-art control and measurement methods tar-geted at ionic quantum systems. is work was conducted as a part of our eorts to explore quantum node applica-tions. As a step to achieve our goal, we constructed a coher-ent optical source system that enables manipulating and observing an ionic quantum system, and established a technique to sympathetically cool In+ using Ca+. e sympathetically-cooled In+ ion was applied to clock transi-tion frequency measurements leading to the rst successful measurements on the 10-15 level. Additional application of sideband cooling, with some improvement in the current method, places expectations on reducing frequency shi due to time dilation down to the level of 10-17. Realization of quantum state measurement of In+ by means of vacuum ultraviolet light promises another expectation: substantial upgrade of the stability of optical frequency standards under operating conditions.e optical frequency standards based on ions are cur-rently operated solely in single-ion mode. However, a combination of a type of ion trap technique — suited for sympathetic cooling and multi-ion operation — and a quantum state measurement method such as presented in this report is expected to lead the way to a new scheme called “multi-ion optical frequency standard [15]” that will provide signicant progress in stability. In addition, trans-fer of the quantum state associated with the clock transition of sideband-cooled In+ to Ca+ through the action of linear ion trapped phonons enables the creation of the state of quantum entanglement with the In+ ticking standard time-base within a separate ion trap. Actualization of such quantum state operations promises the future implementa-tion of ultimate quantum networks among atomic clocks [16].Acknowledgmentse authors express deep gratitude and appreciation to Dr. Hidekazu HACHISU who operated the Sr optical lattice clock and granted us to use its data, and those who helped us in many ways through the course of this study including Mr. Hiroshi ISHIJIMA, Mr. Michiaki MIZUNO, Dr. Yuko HANADO, Dr. Masahiro TAKEOKA, and Dr. Masahide SASAKI.ReferenceR1D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Review of Modern Physics, 75, 281 (2003). 2M. Keller, B. Lange, K. Hayasaka, W. Lange, and H. Walther, “Continuous generation of single photons with controlled waveform in an ion-trap cavity system,” Nature 431, 1075(2004). 3R. Blatt and C. F. Roos, “Quantum simulations with trapped ions,” Nature Physics 8, 277–284 (2012).4A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Review of Modern Physics 87, 637 (2015).5J. Labaziewicz, P. Richerme, K. Brown, I. L. Chuang, and K. Hayasaka, “Compact, filtered diode laser system for precision spectroscopy,” Optics Letters 32, 572 (2007).6Kazuhiro Hayasaka, “Modulation-free optical locking of an external-cavity di-ode laser to a filter cavity,” Optics Letters 36, 2188 (2011).7Y. Kawai, U. Tanaka, K. Hayasaka, and S. Urabe, “Mode-hop-free operation of a distributed Bragg reflector diode laser in an external fiber-cavity configura-tion,” Applied Physics B 121, 213 (2015).8K. Wakui, K. Hayasaka, and T. Ido, “Generation of vacuum ultraviolet radiation FiF11Comparison of In+ clock transition frequency: past and current experimentsGarching, 20001 267 402 452 899 920 (230)Erlangen 20071 267 402 452 901 265 (256)Tokyo, 20171 267 402 452 901 049.9 (6.9)899600900000900400900800901200901600Absolute frequency ‒1 267 402 452 000 000 [Hz]774-4 Quantum State Engineering of Trapped Ions