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arXiv:1210.0064 · Physical Review Letters

Comparison of Two Independent Sr Optical Clocks with 1 × 10 − 17 Stability at 10 3 s

Travis Nicholson, Michael J. Martin, Jason Williams, Benjamin Bloom, Michael Bishof, Matthew D. Swallows, Sara Campbell, Jun Ye

Published Dec 5, 2012• 204 citations
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Abstract

Many-particle optical lattice clocks have the potential for unprecedented measurement precision and stability due to their low quantum projection noise. However, this potential has so far never been realized because clock stability has been limited by frequency noise of optical local oscillators. By synchronously probing two $^{87}\mathrm{Sr}$ lattice systems using a laser with a thermal noise floor of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, we remove classically correlated laser noise from the intercomparison, but this does not demonstrate independent clock performance. With an improved optical oscillator that has a $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ thermal noise floor, we demonstrate an order of magnitude improvement over the best reported stability of any independent clock, achieving a fractional instability of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ in 1000 s of averaging time for synchronous or asynchronous comparisons. This result is within a factor of 2 of the combined quantum projection noise limit for a 160 ms probe time with $\ensuremath{\sim}{10}^{3}$ atoms in each clock. We further demonstrate that even at this high precision, the overall systematic uncertainty of our clock is not limited by atomic interactions. For the second Sr clock, which has a cavity-enhanced lattice, the atomic-density-dependent frequency shift is evaluated to be $\ensuremath{-}3.11\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ with an uncertainty of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$.

DOI
10.1103/physrevlett.109.230801

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Many-particle optical lattice clocks have the potential for unprecedented measurement precision and stability due to their low quantum projection noise. However, this potential has so far never been realized because clock stability has been limited by frequency noise of optical local oscillators. By synchronously probing two 87Sr^{87}\mathrm{Sr}87Sr lattice systems using a laser with a thermal noise floor of 1\ifmmode×\else\texttimes\fi10\ensuremath−151\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}1\ifmmode×\else\texttimes\fi10\ensuremath−15, we remove classically correlated laser noise from the intercomparison, but this does not demonstrate independent clock performance. With an improved optical oscillator that has a 1\ifmmode×\else\texttimes\fi10\ensuremath−161\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}1\ifmmode×\else\texttimes\fi10\ensuremath−16 thermal noise floor, we demonstrate an order of magnitude improvement over the best reported stability of any independent clock, achieving a fractional instability of 1\ifmmode×\else\texttimes\fi10\ensuremath−171\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}1\ifmmode×\else\texttimes\fi10\ensuremath−17 in 1000 s of averaging time for synchronous or asynchronous comparisons. This result is within a factor of 2 of the combined quantum projection noise limit for a 160 ms probe time with \ensuremath∼103\ensuremath{\sim}{10}^{3}\ensuremath∼103 atoms in each clock. We further demonstrate that even at this high precision, the overall systematic uncertainty of our clock is not limited by atomic interactions. For the second Sr clock, which has a cavity-enhanced lattice, the atomic-density-dependent frequency shift is evaluated to be \ensuremath−3.11\ifmmode×\else\texttimes\fi10\ensuremath−17\ensuremath{-}3.11\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}\ensuremath−3.11\ifmmode×\else\texttimes\fi10\ensuremath−17 with an uncertainty of 8.2\ifmmode×\else\texttimes\fi10\ensuremath−198.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}8.2\ifmmode×\else\texttimes\fi10\ensuremath−19.
Abstract Optical clocks are the most precise measurement devices. Here we experimentally characterize one such clock based on the 1S0-3P0 transition of neutral 171Yb atoms confined in an optical lattice. Given that the systematic evaluation using an interleaved stabilization scheme is unable to avoid noise from the clock laser, synchronous comparisons against a second 171Yb lattice system were implemented to accelerate the evaluation. The fractional instability of one clock falls below 4 × 10−17 after an averaging over a time of 5,000 seconds. The systematic frequency shifts were corrected with a total uncertainty of 1.7 × 10−16. The lattice polarizability shift currently contributes the largest source. This work paves the way to measuring the absolute clock transition frequency relative to the primary Cs standard or against the International System of Units (SI) second.
Atomic clock frequency ratios with fractional uncertainty ≤3.2×10−18\leq 3.2 \times 10^{-18}≤3.2×10−18
We report high-precision frequency ratio measurements between optical atomic clocks based on 27^{27}27Al+^++, 171^{171}171Yb, and 87^{87}87Sr. With total fractional uncertainties at or below 3.2×10−183.2 \times 10^{-18}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^{87}87Sr ratios at approximately 1×10−161\times10^{-16}1×10−16 and the Al+^++/Yb ratio at 1.6×10−171.6\times10^{-17}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 innovation in this 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. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2 to 3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of 1.3×10−161.3 \times 10^{-16}1.3×10−16 at 1 second. By enabling faster comparisons, this stability will improve sensitivity to non-white noise processes and other underlying limits of state-of-the-art optical frequency standards.
Rapid progress in the precision and accuracy of optical atomic clocks over the last decade has advanced the frontiers of timekeeping, metrology, and quantum science. However, the stabilities of most optical clocks remain limited by the local oscillator rather than the atoms themselves, leaving room for further progress. Here we implement a "multiplexed" one-dimensional optical lattice clock, in which spatially-resolved, movable ensembles of ultra-cold strontium atoms are trapped in the same optical lattice, interrogated simultaneously by a shared clock laser, and read-out in parallel. By performing synchronized Ramsey interrogations of ensemble pairs we observe atom-atom coherence times up to 26 seconds, a 270-fold improvement over the atom-laser coherence time, demonstrate a relative stability of 9.7(4)×10−18/τ9.7(4)\times10^{-18}/\sqrtτ9.7(4)×10−18/τ​ (where τττ is the averaging time in seconds), and reach a fractional uncertainty of 8.9(3)×10−208.9(3)\times 10^{-20}8.9(3)×10−20 after 3.3 hours of averaging. These results demonstrate that applications requiring ultra-high-precision comparisons between optical atomic clocks need not be limited by the stability of the local oscillator. With multiple ensemble pairs, we realize a miniaturized clock network consisting of 6 atom ensembles, resulting in 15 unique pairwise clock comparisons with relative stabilities below 3×10−17/τ3\times10^{-17}/\sqrtτ3×10−17/τ​. Finally, we demonstrate the capability to simultaneously load spatially-resolved, heterogeneous ensemble pairs of all four stable isotopes of strontium in a lattice. The unique capabilities offered by this platform pave the way for future studies of precision isotope shift measurements, spatially resolved characterization of limiting clock systematics, development of clock-based gravitational wave and dark matter detectors, and novel tests of relativity including measurements of the gravitational redshift at sub-centimeter scales.
We demonstrate the frequency comparison of two optical lattice clocks at the relative stabilities close to the quantum projection noise (QPN) limit of optical lattice clocks. This stable frequency comparison is accomplished by synchronous interrogations of two clocks by a common probe laser, which allows us to cancel out the probe laser's frequency noise. We perform the frequency comparison of a one-dimensional (1D) optical lattice clock with spin-polarized fermions 87Sr and a three-dimensional (3D) optical lattice clock with unity-occupation bosons 88Sr and achieve the Allan standard deviation of σγ(τ)=4×10-16 τ-1/2, which corresponds to the QPN limited stability for N=1,000 atoms and the spectrum linewidth γ=8 Hz. The relative stability reaches 1×10-17 with an averaging time of 1,600 s. Finally, we discuss the prospects to realize 10-18 fractional inaccuracies and the possible application of frequency comparison with synchronous interrogations to remote clocks' comparison for relativistic geodesy.
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.
Neutral atom optical standards require the highest levels of laser precision to operate near the limit set by quantum fluctuations. We develop state-of-the-art ultra-stable laser systems to achieve a factor of 10 enhancement in clock measurement precision and additionally demonstrate optical linewidths below 50 mHz. The most stable of these lasers reaches its thermal noise floor of 1 × 10-16 fractional frequency instability, allowing the attainment of near quantum-noise-limited clock operation with single-clock instabilities of 3×10-16 at 1 s. We utilize this high level of spectral resolution to operate a 87Sr optical lattice clock in a regime in which quantum collisions play a dominant role in the dynamics, enabling the study of quantum many-body physics. With a fractional level of precision of near 1 × 10-16 at 1 s, we clearly resolve the signatures of many-body interactions. We find that the complicated interplay between the p wave-dominated elastic and inelastic interaction processes between lattice-trapped atoms leads to severe lineshape distortion, shifts, and loss of Ramsey fringe contrast. We additionally explore the theoretical prediction that these many-body interactions will modify the quantum fluctuations of the system and we find that in certain parameter regimes the quantum noise distribution exhibits a quadrature dependence. We further present technological advancements that will permit ultra-stable lasers to operate with reduced thermal noise, leading to a potential gain of an additional factor of 10 in stability. This indicates that laser fractional frequency instabilities of 1 × 10-17 are within experimental reach, as is a fully-quantum-limited regime of optical clock operation.