A definition of a frequency standard that utilizes multiple clock transitions within a single atom is considered. Under experimentally achievable conditions, it is shown that the operating conditions of the system can be constrained by the definition of all available clock frequencies. Systems calibrated to the standard would then provide identical levels of performance, with the exclusion of relativistic effects as these do not influence frequency ratios. This would provide a globally certifiable optical frequency reference. An implementation using three clock transitions in176Lu+is considered.
A definition of a frequency standard that utilizes multiple clock transitions within a single atom is considered. Under experimentally achievable conditions, it is shown that the operating conditions of the system can be constrained by the definition of all available clock frequencies. Systems calibrated to the standard would then provide identical levels of performance, with the exclusion of relativistic effects as these do not influence frequency ratios. This would provide a globally certifiable optical frequency reference. An implementation using three clock transitions in176Lu+is considered.
Optical atomic frequency references1 have far surpassed their microwave frequency predecessors, leading to an anticipated redefinition of the SI (International System of Units) second2. However, as the scientific community seeks consensus on a new standard, and several state-of-the-art optical standards now report evaluated fractional uncertainties below 10−18, verification by same-species comparisons to comparable levels remains an outstanding challenge. Here we report two 176Lu+ single-ion optical frequency references, each with evaluated fractional frequency uncertainty near 1 × 10−19, which are directly compared by correlation spectroscopy and demonstrate agreement, with a measured relative frequency difference of [−0.1 ± (5.7)stat ± (1.0)sys] × 10−19, where ‘stat’ and ‘sys’ indicate the statistical and systematic uncertainty, respectively. Our optical references have been comprehensively assessed with evaluated uncertainties below 10−18, supported by a same-species comparison of independent systems to the 5.7 × 10−19 level. This accuracy, achieved in practical room-temperature systems, will contribute to improving international timekeeping and towards chronometric levelling3,4 at the millimetre scale, as well as tests of fundamental physics5 such as Lorentz invariance6, general relativity7, searches for dark matter8,9 and variation of fundamental constants10,11. Two independent 176Lu+ single-ion optical clocks achieve fractional frequency uncertainties near 10−19 and agree at 5.7 × 10−19, advancing precision timekeeping.
Transitions between discrete energy levels in well-isolated atomic systems are highly reproducible and therefore make ideal references for highly accurate frequency standards or clocks. In particular, a single laser-cooled ion confined in a radiofrequency ion trap closely approximates the spectroscopic ideal of a particle at rest in a perturbation-free environment. Narrow optical transitions in such systems are therefore very promising for the realization of optical clocks with accuracy around 2 orders of magnitude higher than current microwave primary standards. In this paper the fundamental aspects, current performance and applications of trapped ion optical clocks are reviewed and the potential for future improvements is considered.
We have developed a high performance atomic frequency standard based on Doppler-free direct frequency comb excitation of a two-photon transition in 87 Rb. We demonstrate equivalent performance compared to an identical system based on cw laser excitation of the clock transition. This approach greatly simplifies optical clock architecture and eliminates the need for cw lasers in many two-photon frequency standards. The clock transition linewidth and ac-Stark shift measured directly with the frequency comb are shown to be nearly identical to those obtained using a cw laser of equal average power. We directly count this reference via the frequency comb repetition rate, achieving instabilities of 1.9 × 10 −13 at 1 s averaging down to 7.8(38) × 10 −15 at 2600 s, currently limited by temperature dependent shifts.
Optical atomic clocks have been rapidly developing in recent decades, resulting in major improvements in both precision and accuracy. As a result, they have become instrumental in multiple areas of applied and fundamental research. Despite all atomic frequency references having more than two energy-levels, the commonly used model for evaluating their ultimate limits assumes a two-level atom. This leads to frequency interrogation protocols and theoretical stability bounds that are suboptimal for a true multi-level atom. The most fundamental stability bound assumes two noise sources - quantum projection noise and spontaneous decay from the excited state. In this work, we analyze a model that includes these noise types and is generalized beyond the two-level assumption, where spontaneous decay can branch to more than a single ground state. This model allows for detection and exclusion of atomic frequency interrogations in which the atom decayed, leading to a frequency stability improvement of up to ≈4.5 dB compared with the two-level model. Furthermore, we identify an even greater stability enhancement of ≈5.4 dB for frequency comparisons between atoms in an odd parity Bell state. These enhancements are particularly relevant for the numerous trapped-ion optical clock species that operate close to lifetime-limited stability. We calculate new stability limits for those cases and provide a detailed experimental protocol for frequency interrogation with an 27Al+ optical ion clock.
We report high-precision frequency ratio measurements between optical atomic clocks based on ^{27}Al^{+}, ^{171}Yb, and ^{87}Sr. With total fractional uncertainties at or below 3.2×10^{-18}, these measurements meet an important milestone criterion for redefinition of the second in the International System of Units. Discrepancies in ^{87}Sr ratios at approximately 1×10^{-16} and the Al^{+}/Yb ratio at 1.6×10^{-17} in fractional units compared to our previous measurements underscore the importance of repeated, high-precision comparisons by different laboratories. A key upgrade from our previous work is the use of a common ultrastable reference delivered to all clocks via a 3.6-km phase-stabilized fiber link between two institutions, enabling better accuracy and stability in frequency transfer. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2-3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of 1.3×10^{-16} at 1 s. Identifying individual clock stabilities with a three-corner-hat measurement, we demonstrate the most stable optical lattice and trapped-ion clocks used in a multispecies comparison. By enabling faster comparisons, this stability will improve sensitivity to nonwhite noise processes and other underlying limits of state-of-the-art optical frequency standards.
A multi-ion optical clock with 5×10−19 uncertainty
Today's most accurate clocks are based on laser spectroscopy of electronic transitions in single trapped ions and feature fractional frequency uncertainties below 1×10−18. Scaling these systems to multiple, simultaneously interrogated ions reduces measurement times, driving recent advances in multi-ion clocks. However, maintaining state-of-the-art systematic uncertainties while increasing the number of ions remains a central challenge. Here, we report on a multi-ion optical atomic clock with a fractional frequency uncertainty of 5.3×10−19 and up to 10 \Sr ions. Ion-resolved state detection enables minimization of position-dependent shifts, with residual effects suppressed below the 10−20-level. Clock operation with eight to ten ions reduces the measurement time by a factor of 4.8 compared to single-ion operation. A comparison with an established \Yb single-ion clock yields an unperturbed frequency ratio of 0.6926711632159660405(20), with a statistical uncertainty of 0.9×10−18 and a combined uncertainty of 2.9×10−18. These results demonstrate robust multi-ion clock operation with reduced averaging time and state-of-the-art accuracy.