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Cited by 385Advanced Frequency and Time StandardsQuantum Information and CryptographyNetwork Time Synchronization Technologies

Ultrastable optical clock with two cold-atom ensembles

Open access
Schioppo, M., Brown, R. C., McGrew, W. F., Hinkley, N., Fasano, R. J., Beloy, K., Yoon, T. H., Milani, G. +5 more·2017·Nature Photonics
DOI 10.1038/nphoton.2016.231
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Abstract

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.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper demonstrates a zero-dead-time optical clock using interleaved interrogation of two ytterbium cold-atom ensembles sharing one optical local oscillator, suppressing Dick noise and achieving fractional frequency instability of 6×10⁻¹⁷/√τ. It also reports long-interrogation Ramsey spectroscopy with Q > 4×10¹⁵ and estimates reaching 1×10⁻¹⁸ instability in a few thousand seconds.

Key findings

  • The zero-dead-time (ZDT) clock is estimated to reach 6×10⁻¹⁷/√τ, while the synchronized measurement used to evaluate it averages down as 8×10⁻¹⁷/√τ and the anti-synchronized single-clock measurement gives 1.4×10⁻¹⁶/√τ. The computed Dick instability for ZDT is <3×10⁻¹⁸/√τ, below the quantum projection noise (QPN) limit.
  • Table 1 gives single-clock instability budgets in units of 10⁻¹⁷/√τ: anti-synchronized total 11, synchronized total 4, and ZDT total 3, with ZDT contributions of QPN 1/√2, technical 3/√2, phase 2, and Dick <0.3.
  • Long-interrogation Ramsey spectroscopy with the OLO pre-stabilized by one atomic system achieves free-evolution times of 2.4 s and 4 s on the second system, Fourier-limited linewidths of (210 ± 20) mHz and (120 ± 20) mHz, 40% contrast, and Q > 4×10¹⁵.
  • With Dick noise suppressed, the paper states it is possible to reach 1×10⁻¹⁸ instability in a few thousand seconds, an order of magnitude faster than previous clock stability demonstrations.

Methods

  • Two ytterbium optical lattice clocks are used: Yb-1 traps 5,000 atoms and Yb-2 traps 10,000 atoms, both interrogated by a shared OLO at 578 nm derived from a 1156 nm quantum dot laser stabilized to a 29 cm high-finesse Fabry-Perot cavity with finesse 877,000 and power storage time 270 µs.
  • Ramsey spectroscopy is performed in anti-synchronized, synchronized, and zero-dead-time interleaved configurations; the ZDT scheme combines atomic responses from the two ensembles into a shared error signal and frequency correction.
  • Analysis includes an instability budget for QPN, technical detection noise, residual phase noise, and Dick noise; Allan deviation of the frequency difference; sensitivity-function calculations; and long-interrogation Ramsey fringe measurements.

Limitations

  • Stated: a direct measurement of ZDT clock instability would require comparing two independent ZDT systems, i.e. four atomic ensembles; lacking these, the authors evaluate stability using synchronized interrogation and infer the ZDT result from a √2 improvement.
  • Stated: the long-interrogation scheme does not eliminate dead time, so its inherent Dick noise suppression is modest compared with the ZDT configuration; the supplementary three-system scheme cannot determine long-timescale atom frequency drifts because they are common-mode between the ZDT systems.
  • Evident: the ZDT instability is inferred rather than directly measured, and technical detection noise (δ_det ≈ 3%) contributes 3×10⁻¹⁷/√τ, larger than the QPN contribution; phase-noise compensation is measured to be effective at ≤2×10⁻¹⁷ in 1 s and is noted as improvable.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1038/nphoton.2016.231

Cites

41 of 41 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 24 cited sources checked · 0 supported · 0 flagged

  • Findingreasoning
    § Ultra-stable optical clock with two cold-atom ensembles

    The zero-dead-time optical clock based on interleaved interrogation of two cold-atom ensembles exhibits vanishingly small Dick noise.

    “This clock exhibits vanishingly small Dick noise”
    Quote in the paperSubstantial claim
  • Findingown data
    § Methods

    The frequency instability of the clock laser has been measured using the atomic transition as an independent frequency discriminator at the fractional level of 1.5 × 10^-16 in the averaging time interval 1 s to 1000 s.

    “The frequency instability of the clock laser has been measured using the atomic transition as an independent frequency discriminator at the fractional level of   1.5  10  16 in the averaging time interval 1 s to 1000 s.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Methods

    Using a Mach-Zehnder interferometer, the compensation was measured to be effective at 2 × 10−17 instability in 1 s.

    “Using a Mach-Zehnder interferometer, we have measured this compensation to be effective at   2  10  17 instability in 1 s”
    Quote in the paperSubstantial claim
  • Findingown data
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    The Allan deviation of the AOMs frequency difference f1(t)-f2(t) results in a measured single clock instability of 1.4 × 10^-16 / sqrt(tau).

    “The Allan deviation of the AOMs frequency difference f1(t)-f2(t) results in a measured single clock instability of  1.4  10  16 /  .”
    Quote in the paperSubstantial claim
  • Findingown data
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    Ramsey spectroscopy on the second system with a free evolution time of 4 s corresponds to a (Fourier-limited) fringe linewidth of (120 ± 20) mHz with 40% contrast.

    “b. Here the free evolution time for Ramsey spectroscopy on the second system is 4 s, corresponding to a (Fourier-limited) fringe linewidth of (120  20) mHz with 40% contrast.”
    Quote in the paperSubstantial claim
  • May combine two claims. 15
  • Classified as probably not a substantial claim. 7

  • May combine two claims.

    Findingown data
    § Methods

    During a one-year interval, a constant drift of -35 mHz/s has been observed and linearly compensated with residual non-linear deviations not exceeding 1 mHz/s in one day.

    “During this interval a constant drift of -35 mHz/s has been observed and linearly compensated with residual non-linear deviations not exceeding 1 mHz/s in one day.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    By using the atomic system rather than relying on OLO coherence, the authors observed unprecedented clock stability, enabling very high precision with averaging times much shorter than previously possible.

    “By so doing, we have observed unprecedented clock stability, enabling very high precision with averaging times much shorter than previously possible.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    Ramsey spectroscopy with the pre-stabilized OLO for a free-evolution-time on the second atomic system of 2.4 s leads to a (Fourier-limited) fringe linewidth of (210 ± 20) mHz with 40% contrast.

    “a, Ramsey spectroscopy with the pre-stabilized OLO for a free-evolution-time on the second atomic system of 2.4 s, leading to a (Fourier-limited) fringe linewidth of  (210  20) mHz with 40% contrast.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    The resulting synchronized measurement stability is 8 × 10^-17 / sqrt(tau).

    “The resulting synchronized measurement stability is  8  10  17 /  .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    Each fringe has a linewidth of 1.9 Hz, with the central component having a contrast greater than 90%.

    “Each fringe has a linewidth of 1.9 Hz, with the central component having a contrast &gt;90%.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingnone given
    § Supplementary information

    A duty cycle of 2/3 is achievable with the current OLO and atomic preparation sequence.

    “A duty cycle of 2/3 is achievable with our current OLO and atomic preparation sequence.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data
    § Supplementary information

    Figure 5 demonstrates an operational sequence in which two zero-dead-time clocks are stabilized to three atomic systems.

    “Figure 5 demonstrates an operational sequence in which two zero-dead-time clocks are stabilized to three atomic systems.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    An alternative approach reduces dead-time with multiple non-destructive measurements repeated after a single period of atomic preparation.

    “An alternative approach reduces dead-time with multiple non-destructive measurements repeated after a single period of atomic preparation 24 .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [24] Westergaard, P. G., Lodewyck, J. & Lemonde, P. Minimizing the Dick effect in an optical lattice clock. IEEE Trans. Ultra. Ferro. Freq. Cont. 57, 623–628 (2010). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    During quantum state preparation and readout, OLO frequency fluctuations are not observed by the atomic system.

    “During quantum state preparation and readout, OLO frequency fluctuations are not observed by the atomic system.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    With OLO-induced noise removed, optical lattice clocks can reach performance given by atomic detection noise and its fundamental QPN limit.

    “With OLO-induced noise removed, optical lattice clocks can reach performance given by atomic detection noise and its fundamental QPN limit.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    Either the ZDT configuration or the long interrogation scheme could be optimal, depending on the relative magnitude of Dick noise and QPN.

    “Therefore, either the ZDT configuration or the long interrogation scheme could be optimal, depending on the relative magnitude of Dick noise and QPN.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    In the ZDT scheme, the observed stability will be improved by sqrt(2) because the atomic measurements and OLO corrections accumulate twice as often, leading to an estimated ZDT clock instability of 6 × 10^-17 / sqrt(tau).

    “In the ZDT scheme, the observed stability will be improved by 2 because the atomic measurements and OLO corrections accumulate twice as often, leading to an estimated ZDT clock instability of 6  10  17 /  .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    The synchronized measurement and ZDT clock are sensitive to the same noise processes, so the synchronized measurement can be used to experimentally evaluate the ZDT clock.

    “As a result, the synchronized measurement and ZDT clock are sensitive to the same noise processes, as displayed in Table 1, and thus the synchronized measurement can be used to experimentally evaluate the ZDT clock.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    The improved stability and reduced measurement time demonstrated here greatly enhances atomic clock utility in tests of fundamental physics, opening the door to 10^-19-level timekeeping precision.

    “The improved stability and reduced measurement time demonstrated here greatly enhances atomic clock utility in tests of fundamental physics, opening the door to 10 -19 -level timekeeping precision.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    Because of the relaxed requirements on the OLO performance, this scheme can reduce the total complexity of the optical clock, extending its usability outside the laboratory.

    “Furthermore, because of the relaxed requirements on the OLO performance, this scheme can reduce the total complexity of the optical clock, extending its usability outside the laboratory.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    A distinct optical clock architecture combining two atomic ensembles has the potential to nearly eliminate aliased OLO noise.

    “A distinct optical clock architecture combining two atomic ensembles has the potential to nearly eliminate aliased OLO noise 3,25 .”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [3] Dick, G. J., Prestage, J. D., Greenhall, C. A. & Maleki, L. Local oscillator induced degradation of medium-term stability in passive atomic frequency standards. In Proc. 22nd Precise Time and Time Interval Meeting (ed. Sydnor, R. L.) 487–508 (NASA, 1990).

      Not checked in the free run.

    • cites [25] Biedermann, G. W. et al. Zero-dead-time operation of interleaved atomic clocks. Phys. Rev. Lett. 111, 170802 (2013). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    The authors have demonstrated a robust, universal scheme for eliminating Dick noise in an optical clock.

    “We have demonstrated a robust, universal scheme for eliminating Dick noise in an optical clock.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Interpretationnone given
    § Methods

    The Fourier-limited linewidth for Ramsey spectroscopy is about 1.6 times narrower than that for Rabi spectroscopy.

    “Indeed the Fourier-limited linewidth for Ramsey spectroscopy is about 1.6 times narrower than that for Rabi spectroscopy.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § the standard quantum limit of clock stability, achieving a spectroscopy line quality factor Q  4  10 15 .

    The combined atomic system provides quasi-continuous monitoring of the OLO frequency, significantly reducing the aliasing effect.

    “The combined atomic system provides quasi-continuous monitoring of the OLO frequency, which significantly reduces the aliasing effect.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Study design and conductreasoning
    § Methods

    This light is far-detuned from the atomic transition to prevent excitation, and enables the active phase stabilizer to maintain phase continuity between Ramsey pulses.

    “This light is far-detuned from the atomic transition to prevent excitation, and enables the active phase stabilizer to maintain phase continuity between Ramsey pulses.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given
    § Supplementary information

    It is possible to make m zero-dead-time clocks out of n atomic systems, given a duty cycle n/m.

    “it is also possible to make m zero-dead-time error signals'clocks'-out of n atomic systems, given a duty cycle n m / .”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Interpretationreasoning
    § Methods

    Differential magnetic field fluctuations between the two atomic systems must be maintained below the mG level.

    “differential magnetic field fluctuations between the two atomic systems must be maintained below the mG level.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Each atomic interrogation remains sensitive to a relatively large first-order Zeeman shift.
22 of 22

  • The authors state this as an assumption.

    Each atomic ensemble exhibits unit sensitivity during its Ramsey free-evolution-time and zero sensitivity during its dead-time.

    “Each atomic ensemble exhibits unit sensitivity during its Ramsey free-evolution-time and zero sensitivity during its dead-time.”

  • The authors state this as an assumption.

    The OLO frequency noise is a white frequency noise process.

    “For a white frequency noise process, the ZDT clock is 2 more stable than the synchronized measurement”

  • The paper relies on this without support.

    Dick noise is a significant limitation in optical clocks.

    “eliminating Dick noise in an optical clock”

  • The paper relies on this without support.

    Each half of the interleaved, zero-dead-time clock remains sensitive to the Dick effect.

    “each half of the interleaved, zerodead-time clock remains sensitive to the Dick effect.”

  • The paper relies on this without support.

    There is a 2π ambiguity in the round-trip phase detection process.

    “due to the  2  ambiguity of the round-trip phase detection process”

  • The paper relies on this without support.

    Each atomic interrogation remains sensitive to a relatively large first-order Zeeman shift.

    “because each atomic interrogation remains sensitive to a relatively large first-order Zeeman shift”
6 of 6

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Secondary frequency standards can have a relative accuracy down to the range 10^-17 to 10^-18.

    “SFS can have a relative accuracy down to the range 10 -17 - 10 -18 [75, 76, 77].”

    From Chronometric Geodesy: Methods and Applications (2019) · cites this paper as [76]

    The optical-clock discussion (page unavailable) reports stability at 6 × 10^-17 with averaging and an instability level of 1 × 10^-18 after a few thousand seconds. These figures support the stated numerical range for stability, but the paper does not establish relative accuracy in that range or identify the clocks as secondary frequency standards. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • Considering a systematic variation in the sea level of order 2 mm/yr, different definitions of a reference surface for the gravity potential could yield differences in the redshift correction of the AFS of order 2 × 10^-18 in a decade, which is of the same order than the best current SFS accuracies.

    “Nevertheless, to state an order of magnitude, considering a systematic variation in the sea level of order 2 mm/yr, different definitions of a reference surface for the gravity potential could yield differences in the redshift correction of the AFS of order 2 × 10 -18 in a decade, which is of the same order than the best current SFS accuracies [77, 76].”

    From Chronometric Geodesy: Methods and Applications (2019) · cites this paper as [76]

    Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

    Experimental — accuracy not yet measured

  • Current generation optical atomic clocks report fractional performance below the 10^-17 level.

    “with the current generation of optical atomic clocks reporting fractional performance below the 10 -17 level 1-5 .”

    From Atomic clock performance enabling geodesy below the centimetre level (2018) · cites this paper as [4]

  • The clock laser is stabilized to a 29-cm cavity made of ultra-low expansion glass with an instability assessed as ≤1.5 × 10^-16 by using the atoms as a frequency discriminator.

    “The clock laser is stabilized to a 29-cm cavity made of ultra-low expansion glass with an instability assessed as ≤1.5 × 10 -16 by using the atoms as a frequency discriminator 4 .”

    From Atomic clock performance enabling geodesy below the centimetre level (2018) · cites this paper as [4]

Cites

Flagged first, then by citations

Research works printed but not linked: 2

  1. Poli, N., Oates, C. W., Gill, P. & Tino, G. M. Optical atomic clocks. Riv. Nuovo Cimento 36, 555–624 (2013).
  2. Kohlhaas, R. et al. Phase locking a clock oscillator to a coherent atomic ensemble. Phys. Rev. X 5, 021011 (2015).

Cited by

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Related

Authors
Schioppo, M., Brown, R. C., McGrew, W. F., Hinkley, N., Fasano, R. J., Beloy, K., Yoon, T. H., Milani, G., Nicolodi, D., Sherman, J. A., Phillips, N. B., Oates, C. W., & Ludlow, A. D.
Affiliations
National Institute of Standards and Technology (US)
Corresponding author
Ludlow, A. D.
ORCID
Venue
Nature Photonics
Publisher
Springer Science and Business Media LLC
Published
2016-11-28
Volume
11
Issue
1
Pages
48-52
ISSN
  • 1749-4885 (ISSN-L)
  • 1749-4893
DOI
10.1038/nphoton.2016.231
OpenAlex
W2513789975
Semantic Scholar
3fcc7c90ae3331780567c3e8a16495a5c5df8f0f
Cited by
385
References
41
Citations by year
2026: 19 · 2025: 36 · 2024: 40 · 2023: 41 · 2022: 38 · 2021: 42 · 2020: 38 · 2019: 47 · 2018: 56 · 2017: 28
FWCI
20.65
Type
journal article
Language
en
Open access
Licence
www.springer.com/tdm (tdm)
Locations
  • Nature Photonics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • PORTO@Iris (submittedVersion)
  • PORTO Publications Open Repository TOrino (Politecnico di Torino) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Aeronautics and Space Administration
  • National Institute of Standards and Technology
  • Defense Advanced Research Projects Agency
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Frequency and Time Standards
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Computer Networks and Communications › Network Time Synchronization Technologies
Keywords
optical atomic clocks, ytterbium, cold atom ensembles, Dick effect, fractional frequency instability, standard quantum limit, laser coherence, optical local oscillator

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