H. N. Hausser, Jonas Keller, T. Nordmann, Nishant Bhatt, J. Kiethe, H. Liu, Ingrid Maria Richter, Moritz von Boehn, Johannes Rahm, S. Weyers, Erik Benkler, B. Lipphardt, Sören Dörscher, Kilian Stahl, J. Klose
We present a scalable mixed-species Coulomb crystal clock based on the S01↔P30 transition in In+115. Yb+172 ions are cotrapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In+-3Yb+ crystal, achieving a relative systematic uncertainty of 2.5×10-18 and a relative frequency instability of 1.6×10-15/τ/1 s. We report on absolute frequency measurements with an uncertainty of 1.3×10-16 and optical frequency comparisons with clocks based on Yb+171 (E3) and Sr87. With a fractional uncertainty of 4.4×10-18, the former is - to our knowledge - the most accurate frequency ratio value reported to date. For the In+115/Sr87 ratio, we improve upon the best previous measurement by more than an order of magnitude. We also demonstrate operation with four In+115 clock ions, which reduces the instability to 9.2×10-16/τ/1 s.
We present a scalable mixed-species Coulomb crystal clock based on the S01↔P30 transition in In+115. Yb+172 ions are cotrapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In+-3Yb+ crystal, achieving a relative systematic uncertainty of 2.5×10-18 and a relative frequency instability of 1.6×10-15/τ/1 s. We report on absolute frequency measurements with an uncertainty of 1.3×10-16 and optical frequency comparisons with clocks based on Yb+171 (E3) and Sr87. With a fractional uncertainty of 4.4×10-18, the former is - to our knowledge - the most accurate frequency ratio value reported to date. For the In+115/Sr87 ratio, we improve upon the best previous measurement by more than an order of magnitude. We also demonstrate operation with four In+115 clock ions, which reduces the instability to 9.2×10-16/τ/1 s.
We present a scalable mixed-species Coulomb crystal clock based on the ^{1}S_{0}↔^{3}P_{0} transition in ^{115}In^{+}. ^{172}Yb^{+} ions are cotrapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In^{+}-3Yb^{+} crystal, achieving a relative systematic uncertainty of 2.5×10^{-18} and a relative frequency instability of 1.6×10^{-15}/sqrt[τ/1 s]. We report on absolute frequency measurements with an uncertainty of 1.3×10^{-16} and optical frequency comparisons with clocks based on ^{171}Yb^{+} (E3) and ^{87}Sr. With a fractional uncertainty of 4.4×10^{-18}, the former is-to our knowledge-the most accurate frequency ratio value reported to date. For the ^{115}In^{+}/^{87}Sr ratio, we improve upon the best previous measurement by more than an order of magnitude. We also demonstrate operation with four ^{115}In^{+} clock ions, which reduces the instability to 9.2×10^{-16}/sqrt[τ/1 s].
Clocks have been among the most accurate man-made devices for centuries. Atomic clocks, which have been defining time by means of a microwave transition in the 133Cs atom since 1967, represent a major step in this development. A redefinition of the SI unit of time based on optical atomic clocks is currently under discussion. This forthcoming redefinition requires, among other criteria, the repeated demonstration of the consistency of different optical frequency standards in the low 10−18 range. In this work, the first evaluation of the systematic shifts and their uncertainties in a 115In+–172Yb+ Coulomb crystal clock is presented. This clock utilizes the 1S0 ↔ 3P0 transition in 115In+. 172Yb+ ions are co-trapped with the 115In+ ions in a segmented Paul trap and used for sympathetic cooling. With a systematic uncertainty of 2.5×10−18 when operating with a 1In+–3Yb+ crystal and 2.6×10−18 when operating with a 2In+–4Yb+ crystal, this clock is one of the most accurate clocks in the world. In addition, the operation of the clock with multiple clock ions is the first of its kind at this level of uncertainty. Measurements with up to four clock ions show a reduction in instability from 1.6×10−15/√ τ for a single indium ion to 9.2(4)×10−16/√τ when operating with four indium ions. By using an additional quench laser, the instability in another series of measurements was reduced from a single-ion instability of 1.5×10−15/√ τ to a four-ion instability of 7.1(15)×10−16/√τ , which is consistent with the expected scaling of 1/√N with the number of clock ions N. In this work, the hyperfine structure of the 3P0 ↔ 1P1 transition used for quenching was also resolved for the first time and the hyperfine constants were determined to be AHFS = 265.42(75)MHz and BHFS = 291.4(135) MHz. In frequency comparisons with other clocks, the optical frequency ratios 115In+/171Yb+(E3) and 115In+/87Sr were determined. With a relative total uncertainty of 4.2 × 10−18, the former ratio is the most accurate frequency ratio of different species published to date. It is also the first to meet one of the requirements defined on the roadmap for redefining the SI unit of the second: Measurements of frequency ratios with relative total measurement uncertainties below 5 × 10−18. The determination of the absolute frequency results in an uncertainty of 1.3 × 10−16 for the 1S0 ↔ 3P0 transition in 115In+, which is limited by that of the cesium fountains. The results obtained summarized: ν115In+ ν171Yb+(E3) =1.973 773 591 557 215 788(8) ν115In+ ν87Sr =2.952 748 749 874 860 781(27) ν115In+ =1 267 402 452 901 038.87(16) Hz
Abstract Multi-ion optical clocks offer the possibility of overcoming the low signal-to-noise ratio of single-ion clocks, while still providing low systematic uncertainties. We present simultaneous spectroscopy of up to four 115 In + clock ions in a linear Coulomb crystal, sympathetically cooled with 172 Yb + ions. In first clock comparisons, we see agreement below 1 × 10 −17 with results obtained using a single In + ion, for which we have evaluated the systematic uncertainty to be 2.5 × 10 −18 . Operation with four clock ions reduces the instability from 1.6 × 10 − 15 / t / ( 1 s ) to 9.2 × 10 − 16 / t / ( 1 s ) . We derive a model for decay-related dead time during state preparation, which matches the observed scaling of instability with clock ion number N , and indicates that 1 / N scaling can be achieved with the addition of a repump laser.
Trapped-ion optical clocks are capable of achieving systematic fractional frequency uncertainties of 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 10−19. 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 10−19 level. Using this method, we demonstrate regions of 400μm and 2 mm length in our trap array with time dilation shifts due to micromotion close to 1×10−19 and below 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 1×10−19. 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.
We report a single-ion optical atomic clock with a fractional frequency uncertainty of 5.5×10^{-19} and fractional frequency stability of 3.5×10^{-16}/sqrt[τ/s], based on quantum logic spectroscopy of a single ^{27}Al^{+} ion. A cotrapped ^{25}Mg^{+} ion provides sympathetic cooling and quantum logic readout of the ^{27}Al^{+}^{1}S_{0}↔^{3}P_{0} clock transition. A Rabi probe duration of 1 s, enabled by laser stability transfer from a remote cryogenic silicon cavity across a 3.6 km fiber link, results in a threefold reduction in instability compared to previous ^{27}Al^{+} clocks. Systematic uncertainties are lower due to an improved ion trap electrical design, which reduces excess micromotion, and a new vacuum system, which reduces collisional shifts. We also perform a direction-sensitive measurement of the ac magnetic field due to the rf ion trap, eliminating systematic uncertainty due to field orientation.
174Yb+-113Cd+ sympathetic-cooling bi-species Coulomb crystal applied to microwave frequency standard
We reported the realization of a 174Yb+-113Cd+ bi-species Coulomb crystal comprising 174Yb+ ions as coolant and verified its potential for application as a 113Cd+ microwave frequency standard employing sympathetic cooling.The two species of massive ions stably trapped in a Paul trap make up this large two-component crystal. The 113Cd+ ions are trapped in the center, which reduces considerably RF heating and excess micromotion to which the 113Cd+ ions are subjected. Under this scheme, the uncertainty due to the second-order Doppler effect is reduced to 5×10−16, which represents an order of magnitude improvement over sympathetic cooled 40Ca+-113Cd+ crystal. The uncertainty from the second-order Zeeman effect, which contributes the largest uncertainty to the microwave-ion frequency standard, is reduced to 4×10−16. The relevant AC Stark shift uncertainty is estimated to be 4×10−19. These results indicate using 174Yb+ as coolant ions for 113Cd+ is far superior and confirm the feasibility of a sympathetic-cooled cadmium-ion microwave clock system employing a 174Yb+-113Cd+ two-component crystal.