Andrew D. Ludlow

An Atomic Clock with 10–18 Instability

Tick, Tick, Tick… Many aspects of everyday life from communication to navigation rely on the precise ticking of the microwave transitions of the atoms in atomic clocks. Optical transitions occur at much higher frequency and so offer the opportunity to reduce the scale of the ticks even more. Hinkley et al. (p. 1215, published online 22 August; see the Perspective by Margolis) compare the ticking of two optical clocks and report an instability near the 10−18 level. Such performance will improve tests of general relativity and pave the way for a redefinition of the second. An ytterbium-based optical clock exhibits a precision of nearly one part per quintillion. [Also see Perspective by Margolis] Atomic clocks have been instrumental in science and technology, leading to innovations such as global positioning, advanced communications, and tests of fundamental constant variation. Timekeeping precision at 1 part in 1018 enables new timing applications in relativistic geodesy, enhanced Earth- and space-based navigation and telescopy, and new tests of physics beyond the standard model. Here, we describe the development and operation of two optical lattice clocks, both using spin-polarized, ultracold atomic ytterbium. A measurement comparing these systems demonstrates an unprecedented atomic clock instability of 1.6 × 10–18 after only 7 hours of averaging.

Probing Interactions Between Ultracold Fermions

At ultracold temperatures, the Pauli exclusion principle suppresses collisions between identical fermions. This has motivated the development of atomic clocks with fermionic isotopes. However, by probing an optical clock transition with thousands of lattice-confined, ultracold fermionic strontium atoms, we observed density-dependent collisional frequency shifts. These collision effects were measured systematically and are supported by a theoretical description attributing them to inhomogeneities in the probe excitation process that render the atoms distinguishable. This work also yields insights for zeroing the clock density shift.

Nuclear spin effects in optical lattice clocks

We present a detailed experimental and theoretical study of the effect of nuclear spin on the performance of optical lattice clocks. With a state-mixing theory including spin-orbit and hyperfine interactions, we describe the origin of the {sup 1}S{sub 0}-{sup 3}P{sub 0} clock transition and the differential g factor between the two clock states for alkaline-earth-metal(-like) atoms, using {sup 87}Sr as an example. Clock frequency shifts due to magnetic and optical fields are discussed with an emphasis on those relating to nuclear structure. An experimental determination of the differential g factor in {sup 87}Sr is performed and is in good agreement with theory. The magnitude of the tensor light shift on the clock states is also explored experimentally. State specific measurements with controlled nuclear spin polarization are discussed as a method to reduce the nuclear spin-related systematic effects to below 10{sup -17} in lattice clocks.

Ultrastable optical clock with two cold-atom ensembles

Optical clocks with a record low zero-dead-time instability of 6 × 10–17 at 1 second are demonstrated in two cold-ytterbium systems. The two systems are interrogated by a shared optical local oscillator to nearly eliminate the Dick effect. Atomic clocks based on optical transitions are the most stable, and therefore precise, timekeepers available. These clocks operate by alternating intervals of atomic interrogation with the ‘dead’ time required for quantum state preparation and readout. This non-continuous interrogation of the atom system results in the Dick effect, an aliasing of frequency noise from the laser interrogating the atomic transition1,2. Despite recent advances in optical clock stability that have been achieved by improving laser coherence, the Dick effect has continually limited the performance of optical clocks. Here we implement a robust solution to overcome this limitation: a zero-dead-time optical clock that is based on the interleaved interrogation of two cold-atom ensembles3. This clock exhibits vanishingly small Dick noise, thereby achieving an unprecedented fractional frequency instability assessed to be for an averaging time τ in seconds. We also consider alternate dual-atom-ensemble schemes to extend laser coherence and reduce the standard quantum limit of clock stability, achieving a spectroscopy line quality factor of Q > 4 × 1015.

Generation of ultrastable microwaves via optical frequency division

Researchers demonstrate a microwave generator based on a high-Q optical resonator and a frequency comb functioning as an optical-to-microwave divider. They generate 10 GHz electrical signals with a fractional frequency instability of ≤8 × 10−16 at 1 s.

Sr Lattice Clock at 1 x 10-16 Fractional Uncertainty by Remote Optical Evaluation with a Ca Clock

Optical atomic clocks promise timekeeping at the highest precision and accuracy, owing to their high operating frequencies. Rigorous evaluations of these clocks require direct comparisons between them. We have realized a high-performance remote comparison of optical clocks over kilometer-scale urban distances, a key step for development, dissemination, and application of these optical standards. Through this remote comparison and a proper design of lattice-confined neutral atoms for clock operation, we evaluate the uncertainty of a strontium (Sr) optical lattice clock at the 1 × 10–16 fractional level, surpassing the current best evaluations of cesium (Cs) primary standards. We also report on the observation of density-dependent effects in the spin-polarized fermionic sample and discuss the current limiting effect of blackbody radiation–induced frequency shifts.

Making optical atomic clocks more stable with 10 −16 -level laser stabilization

Scientists demonstrate a cavity-stabilized laser system with a reduced thermal noise floor, exhibiting a fractional frequency instability of 2 × 10−16. They use this system as a stable optical source in an ytterbium optical lattice clock to resolve an ultranarrow 1 Hz linewidth for the 518 THz clock transition. Consistent measurements with a clock instability of 5 × 10−16/√τ are reported.

New limits on coupling of fundamental constants to gravity using 87Sr optical lattice clocks.

The 1S0-3P0 clock transition frequency nuSr in neutral 87Sr has been measured relative to the Cs standard by three independent laboratories in Boulder, Paris, and Tokyo over the last three years. The agreement on the 1 x 10(-15) level makes nuSr the best agreed-upon optical atomic frequency. We combine periodic variations in the 87Sr clock frequency with 199Hg+ and H-maser data to test local position invariance by obtaining the strongest limits to date on gravitational-coupling coefficients for the fine-structure constant alpha, electron-proton mass ratio mu, and light quark mass. Furthermore, after 199Hg+, 171Yb+, and H, we add 87Sr as the fourth optical atomic clock species to enhance constraints on yearly drifts of alpha and mu.

Coherent Optical Phase Transfer over a 32-km Fiber with 1 s Instability at 10 − 17

The phase coherence of an ultrastable optical frequency reference is fully maintained over actively stabilized fiber networks of lengths exceeding 30 km. For a 7-km link installed in an urban environment, the transfer instability is 6 x 10{-18} at 1 s. The excess phase noise of 0.15 rad, integrated from 8 mHz to 25 MHz, yields a total timing jitter of 0.085 fs. A 32-km link achieves similar performance. Using frequency combs at each end of the coherent-transfer fiber link, a heterodyne beat between two independent ultrastable lasers, separated by 3.5 km and 163 THz, achieves a 1-Hz linewidth.

The absolute frequency of the 87 Sr optical clock transition

The absolute frequency of the 1 S0– 3 P0 clock transition of 87 Sr has been measured to be 429 228 004 229 873.65 (37) Hz using lattice-confined atoms, where the fractional uncertainty of 8.6 × 10 −16 represents one of the most accurate measurements of an atomic transition frequency to date. After a detailed study of systematic effects, which reduced the total systematic uncertainty of the Sr lattice clock to 1.5 × 10 −16 , the clock frequency is measured against a hydrogen maser which is simultaneously calibrated to the US primary frequency standard, the NIST Cs fountain clock, NIST-F1. The comparison is made possible using a femtosecond laser based optical frequency comb to phase coherently connect the optical and microwave spectral regions and by a 3.5 km fibre transfer scheme to compare the remotely located clock signals. (Some figures in this article are in colour only in the electronic version)