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An Atomic Clock with 10–18 Instability

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Science  13 Sep 2013:
Vol. 341, Issue 6151, pp. 1215-1218
DOI: 10.1126/science.1240420

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.

Abstract

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.

Quantum mechanical absorbers such as atoms serve as the best available time and frequency references: They are isolatable, possess well-defined transition frequencies, and exist in abundant identical copies. With more than 50 years of development, clocks based on microwave oscillators referenced to atomic transitions now define the Système International (SI) second and play central roles in network synchronization, global positioning systems, and tests of fundamental physics (1, 2). Under development worldwide, optical clocks oscillate 105 times faster than their microwave predecessors, dividing time into finer intervals (3). Although microwave clocks such as the Cs fountain have demonstrated time and frequency measurements of a few parts in 1016 (4, 5), optical clocks now measure with a precision of 1 part in 1017 (69).

A clock’s instability specifies how its ticking fluctuates over time, a characteristic generally quantified by the Allan deviation (10). No time or frequency standard can make measurements better than the statistical precision set by its instability. Further, a clock’s systematic uncertainty is often constrained by its long-term instability. For these reasons, and because many timing applications require only exquisite instability, the instability represents perhaps the most important property of an atomic standard.

In pursuit of lower instability, an optical lattice clock uses a stabilized laser referenced to many (103 to 106) alkaline earth (or similar) atoms confined in an optical standing wave. Alignment of the clock interrogation laser along the direction of tight lattice confinement eliminates most Doppler and motional effects while probing the ultranarrow-band electronic clock transition. These atoms are interrogated simultaneously, improving the atomic detection signal-to-noise ratio and, thus, instability, which is limited fundamentally by quantum projection noise (QPN) (11). Like other cycled atomic clocks, the lattice clock suffers from a technical noise source known as the Dick effect, arising when an oscillator’s noise is periodically sampled (12, 13). Cavity-stabilized lasers with low thermal noise have reduced the Dick effect, enabling clock instability below 10–15 at short times (14). Recently, an uncorrelated comparison of two strontium lattice clocks revealed clock instability of 3 × 10–16 at short times, averaging to 1 × 10–17 in 1000 s (8) or, in another case, reaching the 10–17 level in 20,000 s (9). Here, by comparing two independent optical lattice clocks using ultracold 171Yb, we demonstrate a clock instability of 1.6 × 10–18 in 25,000 s.

Both clock systems, referred to here as Yb-1 and Yb-2, independently cool and collect 171Yb atoms from thermal beams into magneto-optical traps [see Fig. 1 and (15)]. Two stages of laser cooling, first on the strong 1S0-1P1 cycling transition at 399 nm, followed by the weaker 1S0-3P1 intercombination transition at 556 nm, reduce the atomic temperature from 800 K to 10 μK. Each cold atom sample is then loaded into an optical lattice with ~300Er trap depth (Er/kB = 100 nK; Er, recoil energy; kB, Boltzmann’s constant) formed by retroreflecting ~600 mW of laser power, fixed at the “magic” wavelength λm ≈ 759 nm (16) by a reference cavity. At λm, both electronic states of the clock transition are Stark-shifted equally (17, 18). For the measurements described here, ~5000 atoms captured by each lattice are then optically pumped to one of the two ground-state spin projections mF = ±1/2 using the 1S0-3P1 transition. After this state preparation, applying a 140-ms-long π pulse of 578-nm light resonant with the 1S0-3P0 clock transition yields the spectroscopic line shape shown in Fig. 1C, with a Fourier-limited linewidth of 6 Hz. Experimental clock cycles alternately interrogate both mF spin states canceling first-order Zeeman and vector Stark shifts. The optical local oscillator (LO) is an ultrastable laser servo-locked to a high-finesse optical cavity (14) and is shared by both Yb systems. Light is frequency-shifted into resonance with the clock transition of each atomic system by independent acousto-optic modulators (AOMs). Resonance is detected by monitoring the 1S0 ground-state population (Ng) and 3P0 excited-state population (Ne). A laser cycles ground-state atoms on the 1S0-1P1 transition while a photomultiplier tube (PMT) collects the fluorescence, giving a measure of Ng. After 5 to 10 ms of cycling, these atoms are laser-heated out of the lattice. At this point, Ne is optically pumped to the lowest-lying 3D1 state, which decays back to the ground state. The 1S0-1P1 transition is cycled again, now measuring Ne. Combining these measurements yields a normalized mean excitation Ne/(Ne + Ng). During spectroscopy, special attention was paid to eliminating residual Stark shifts stemming from amplified spontaneous emission of the lattice lasers, eliminating residual Doppler effects from mechanical vibrations of the apparatus correlated with the experimental cycle, and controlling the cold collision shift due to atomic interactions within the lattice (19).

Fig. 1 Experimental realization of the Yb optical lattice clocks.

(A) Laser light at 578 nm is prestabilized to an isolated, high-finesse optical cavity using Pound-Drever-Hall detection and electronic feedback to an AOM and laser piezoelectric transducer. Fibers deliver stabilized laser light to the Yb-1 and Yb-2 systems. Resonance with the atomic transition is detected by observing atomic fluorescence collected onto a PMT. The fluorescence signal is digitized and processed by a microcontroller unit (MCU), which computes a correction frequency, f1,2(t). This correction frequency is applied to the relevant AOM by way of a direct digital synthesizer (DDS) and locks the laser frequency onto resonance with the clock transition. (B) Relevant Yb atomic energy levels and transitions, including laser-cooling transitions (399 and 556 nm), the clock transition (578 nm), and the optical-pumping transition used for excited-state detection (1388 nm). (C) A single-scan, normalized excitation spectrum of the 1S0-3P0 clock transition in 171Yb with 140-ms Rabi spectroscopy time; the red line is a free-parameter sinc2 function fit.

By measuring the normalized excitation while modulating the clock laser frequency by ±3 Hz, an error signal is computed for each Yb system. Subsequently, independent microprocessors provide a digital frequency correction f1,2(t) at time t to their respective AOMs, thereby maintaining resonance on the line center. In this way, though derived from the same LO, the individual laser frequencies for Yb-1 and Yb-2 are decoupled and are instead determined by their respective atomic samples (for all but the shortest time scales). The frequency correction signals f1,2(t) are shown in Fig. 2A for a 5000-s interval. Because the experimental cycles for each clock system are unsynchronized and have different durations, f1,2(t) signals are interpolated to a common time base and subtracted to compute the frequency difference between Yb-1 and Yb-2, as shown in Fig. 2, B to D. Measurements such as these were repeated several times for intervals of ~15,000 s, demonstrating a clock instability reaching 4 × 10–18 at 7500 s. While collecting data over a 90,000-s interval, we observed the instability curve in Fig. 3, shown as the total Allan deviation for a single Yb clock. Before data analysis, ~25% of the attempted measurement time was excluded due to laser unlocks and auxiliary servo failures (15). Each clock servo had an attack time of a few seconds, evidenced by the instability bump near 3 s. At averaging times τ = 1 to 5 s, the instability is comparable to previous measurements (14) of the free-running laser system, and at long times, the instability averages down like white frequency noise as Embedded Image (for τ in seconds), reaching 1.6 × 10–18 at 25,000 s.

Fig. 2 Frequency comparison between the Yb optical lattice clocks.

(A) Correction frequencies, f1,2(t), are shown in red and black. Dominant LO fluctuations are due to the cavity and are, thus, common to the atomic systems. (B) Frequency difference, f2(t) – f1(t), between the two Yb clock systems for a 5000-s interval. (C) Data set f2(t) – f1(t) over a 90,000-s interval. Gaps represent data rejected before data analysis due to servo unlocks. (D) Histogram of all data and a Gaussian fit Embedded Image.

Fig. 3 Measured instability of a Yb optical lattice clock.

Total Allan deviation of a single Yb clock, Embedded Image (red circles), and its white-frequency-noise asymptote of Embedded Image (red solid line). The blue dashed line represents the estimated combined instability contributions from the Dick effect Embedded Image and QPN Embedded Image; the shaded region denotes uncertainty in these estimates. Error bars indicate 1σ confidence intervals.

Also shown in Fig. 3 is an estimate of the combined instability contribution (blue dashed line) from the Dick effect and QPN (shaded region denotes the uncertainty of the estimate). These contributions must be reduced if 10–18 instability is desired at time scales under 100 s. Substantial reductions of QPN are possible with the use of higher atom numbers and longer interrogation times. Further stabilization of the optical LO will continue to reduce the Dick effect, by both lowering the laser frequency noise down-converted in the Dick process and allowing increased spectroscopy times for higher duty cycles. Improved LOs will use optical cavities exhibiting reduced Brownian thermal-mechanical noise by exploiting cryogenic operation (20), crystalline optical coatings (21), longer cavities, or other techniques (14). Figure 4 demonstrates the advantage of improving the present LO, with four times less laser frequency noise and four times longer interrogation time (corresponding to a short-term laser instability of ~5 × 10–17). The red dotted line gives the Dick instability, whereas the black dashed line indicates the QPN limit, assuming a moderate 50,000 atom number.

Fig. 4 Calculated instability limits toward the goal of 1 × 10–18 in 100 s.

The Dick limit (red dotted line) is reduced by using a hypothetical LO four times as stable as the LO used in our experiment. The QPN limit is shown under the same conditions (black dashed line), assuming 50,000 atoms. The inset illustrates an interleaved interrogation of two atomic systems, allowing continuous monitoring of the LO for suppression of the Dick effect. Dead times from atomic preparation or readout in one system are synchronized with clock interrogation in the second system. The solid blue line indicates the suppressed Dick instability in the interleaved interrogation scheme using Ramsey spectroscopy with an unimproved LO.

Noting that the calculated Dick effect remains several times higher than the QPN limit, we consider an alternative idea first proposed for microwave ion clocks: interleaved interrogation of two atomic systems (13). By monitoring the LO laser frequency at all times with interleaved atomic systems, the aliasing problem at the heart of the Dick effect can be highly suppressed. The solid blue line in Fig. 4 illustrates the potential of a simple interleaved clock interrogation using Ramsey spectroscopy. Even with the present LO, the Dick effect is decreased well below the QPN limit afforded by a much-improved LO (black dashed line). In this case, spin squeezing of the atomic sample could reduce the final instability beyond the standard quantum limit set by QPN (22). The two-system, interleaved technique requires spectroscopy times that last one half or more of the total experimental cycle. By extending the Yb clock Ramsey spectroscopy time to >250 ms, we achieved a 50% duty cycle for each system, demonstrating the feasibility of this technique. Further suppression of the Dick effect can be achieved with the use of a more selective interleaving scheme. Duty cycles ≥50% can also be realized with the aid of nondestructive state detection (23).

Another important property of a clock is its accuracy, which results from uncertainty in systematic effects that alter a standard’s periodicity from its natural, unperturbed state. In 2009, we completed a systematic analysis of Yb-1 at the 3 × 10–16 uncertainty level (16). Since then, we reduced the dominant uncertainty due to the blackbody Stark effect by one order of magnitude (24). With its recent construction, Yb-2 has not yet been systematically evaluated. The fact that the instability reaches the 10–18 level indicates that key systematic effects (e.g., the blackbody Stark effect, atomic collisions, lattice light shifts) on each system are well controlled over the relevant time scales. The mean frequency difference in Fig. 2 was 〈f2(t) – f1(t)〉 = –30 mHz, which is within the Yb-1 uncertainty at 10–16. Systematic effects on each system can now be efficiently characterized beyond the 10–17 level. With continued progress, we envision 10–18 instability in only 100 s and long-term instability well below 10–18.

Clock measurement at the 10–18 level can be used to resolve spatial and temporal fluctuations equivalent to 1 cm of elevation in Earth’s gravitational field (2528), offering a new tool for geodesy, hydrology, geology, and climate change studies. Space-based implementations can probe alternative gravitational theories, e.g., by measuring red-shift deviations from general relativity with a precision that is three orders of magnitude higher than the present level (28). Though present-day temporal and spatial variation of fundamental constants is known to be small (6, 29, 30), 10–18-level clock measurements can offer tighter constraints. Finally, timekeeping improvements can benefit navigation systems, telescope array synchronization (e.g., very-long-baseline interferometry), secure communication, and interferometry and can possibly lead to a redefinition of the SI second (9).

Supplementary Materials

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: We thank the Defense Advanced Research Projects Agency Quantum Assisted Sensing and Readout program, NASA Fundamental Physics, and NIST for financial support; D. Hume for experimental assistance; and T. Fortier and S. Diddams for femtosecond optical frequency comb measurements.
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