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Systematic evaluation of an atomic clock at 2e-18 total uncertainty
T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, J. Ye
TL;DR
Systematic shifts, especially blackbody-radiation effects, limit the accuracy evaluation of optical lattice clocks. This work combines improved stability with measurements and controls targeting these shifts, achieving 2.1 × 10-18 overall systematic uncertainty in the JILA 87Sr clock.
Problem
Accurate evaluation of the 87Sr clock remains limited by systematic shifts, with blackbody-radiation effects constituting the largest uncertainty.
Method
The study combines improved laser-referenced clock stability with lattice-shift control, BBR thermometry and atomic-structure measurements, and active electric- and magnetic-field stabilization.
Results
2.1 × 10-18 overall systematic uncertainty was achieved, alongside record fractional frequency stability of 2.2 × 10-16 at 1 s.
Takeaways & Limitations
The achieved uncertainty corresponds to a gravitational redshift for a height change of 2 cm on Earth.
Takeaways & Limitations
Line pulling from off-resonant spectroscopic features is bounded conservatively at 1 × 10-19.
Abstract
from arXiv · showhide
The pursuit of better atomic clocks has advanced many research areas, providing better quantum state control, new insights in quantum science, tighter limits on fundamental constant variation, and improved tests of relativity. The record for the best stability and accuracy is currently held by optical lattice clocks. This work takes an important step towards realizing the full potential of a many-particle clock with a state-of-the-art stable laser. Our 87Sr optical lattice clock now achieves fractional stability of 2.2e-16 at 1 s. With this improved stability, we perform a new accuracy evaluation of our clock, reducing many systematic uncertainties that limited our previous measurements, such as those in the lattice ac Stark shift, the atoms' thermal environment, and the atomic response to room-temperature BBR. Our combined measurements have reduced the total uncertainty of the JILA Sr clock to 2.1e-18 in fractional frequency units.
Introduction
Optical atomic clocks support advances in precision measurement and fundamental research, while this work combines an ultrastable laser and accuracy improvements to achieve 2.1 × 10-18 overall systematic uncertainty.
- Introduction: Optical atomic clocks can improve measurement precision and sensor resolution while advancing quantum control, quantum science, fundamental-constant tests, and relativity tests.The introduction frames these clocks as relevant to both scientific and technological applications.
- Introduction: 10 s coherence time and 60% duty-cycle referencing connect an ultrastable laser to thousands of strontium atoms in an optical lattice.The laser serves as the local oscillator, while the atomic transition extends stability from seconds to hours.
- Introduction: The accuracy improvements include an optical lattice with no measurable ac Stark shift at 1 × 10-18, millikelvin-level BBR thermometry, atomic structure measurements, and active field stabilization.These developments target lattice shifts, blackbody-radiation response, and electric and magnetic field effects.
- Introduction: 2.1 × 10-18 overall systematic uncertainty marks more than a threefold improvement over the previous best atomic clock.This uncertainty corresponds to a gravitational redshift from a 2 cm height change on Earth.
Results · Clock stability
The 87Sr optical lattice clock achieves best independent stability of 2.2 × 10^-16/τ^1/2 and reaches 1 × 10^-17 stability in less than 500 s. Short-term stability is limited by the Dick effect, while controlled systematic drifts do not limit stability at 2 × 10^-18 after thousands of seconds.
- Clock stability: Fourier-limited probe times of ≤1 s are used to study clock stability and systematics with Rabi spectroscopy of the 1S0 → 3P0 1 mHz transition.The transition is probed using a 698 nm laser stabilized to 26 mHz.
- Clock stability: The Dick effect limits short-term stability by aliasing high-frequency clock-laser noise above quantum projection noise with 2000 atoms.At long averaging times, drifting systematic shifts are the only mechanism identified as capable of limiting stability.
- Clock stability: 2 × 10^-18 stability is maintained after thousands of seconds of averaging because residual systematic drifts do not affect the clock stability.This result follows careful control of systematic effects.
- Clock stability: QPN and the Dick effect are confirmed by self-comparison, agreeing with measurements from a two-clock comparison.Self-comparison uses two independent frequency locks operating on alternate experimental cycles.
- Clock stability: 2.2 × 10^-16/τ^1/2 is the best independent clock stability achieved with 1-s probe pulses.Here, τ is the averaging time in seconds, and the result agrees with the estimated Dick effect from the laser-noise spectrum.
- Clock stability: 1 × 10^-17 stability is reached in less than 500 s, compared with the previous record of 1000 s.The comparison is shown between the current result and the previous record described for the clock stability measurement.
- Clock stability: Improved stability motivates new strategies to reduce systematic uncertainties, including lock-in detection of frequency shifts caused by modulating experimental parameters.The uncertainty budget includes systematic shifts such as the lattice ac Stark shift.
Lattice ac Stark shift
The lattice ac Stark shift is evaluated using lock-in detection across lattice intensities and operation at a magic wavelength. The measured shift is (-1.3 ± 1.1) × 10-18 for a 12 μK trap depth.
- Measurement method: Lock-in detection measures the frequency shift between different lattice intensities while tight confinement eliminates Doppler and recoil shifts during spectroscopy.At the magic wavelength, both clock states experience identical ac Stark shifts, making the transition frequency independent of trap intensity.
- Magic-wavelength operation: At the magic wavelength for m_F = ±9/2, scalar and tensor differential Stark-shift components cancel.The lattice wavelength and trap depth U0 are varied to identify this operating point.
- Measured shift: (-1.3 ± 1.1) × 10-18 is the measured ac Stark shift for a 12 μK trap depth.The operating wavelength is c/(368.5544849(1) THz), with the lattice laser referenced through an optical frequency comb to the NIST Boulder hydrogen maser.
- Systematic correction: Density-shift cancellation accounts for parasitic shifts caused by lattice-depth modulation changing the sample density.The cancellation uses the experimentally verified proportionality to NU0^3/2 while monitoring the corresponding atom-number change.
Dc Stark shift
The study actively controls the dc Stark shift along an axis with a measurable background electric field. External electrodes change the applied field direction, enabling frequency-difference measurements because the shift depends on the square of the total field.
- The dc Stark shift is an important systematic effect in lattice clocks.
- External electrodes outside the vacuum chamber enable active control of the dc Stark shift along the axis with a measurable background field.
- Reversing the applied field direction produces a frequency difference because the dc Stark shift is proportional to the square of the total electric field.
Radiation thermometry
Radiation thermometry addresses the clock’s largest systematic uncertainty, the blackbody-radiation Stark shift, by characterizing and homogenizing the atoms’ thermal environment. Calibrated platinum resistance thermometers and a blackbody-radiation shield enable millikelvin-scale temperature control and uncertainty assessment.
- Radiation thermometry: The blackbody-radiation Stark shift ΔνBBR is the clock’s largest systematic uncertainty.This shift arises from the background blackbody-radiation field.
- Radiation thermometry: The static blackbody-radiation shift scales as T^4, while the dynamic shift depends on atomic transitions and deviations from an ideal spectrum.T is ambient temperature, with T0 = 300 K; higher-order terms are negligible.
- Radiation thermometry: Two blackened platinum resistance thermometers measure the atoms’ blackbody-radiation environment and are calibrated on their vacuum-flange mounts against NIST-traceable standards.Four-wire electrical feedthroughs support the measurements, while secondary sensors calibrate immersion error from flange-to-sensor heat conduction.
- Radiation thermometry: A surrounding blackbody-radiation shield achieves ≤ 1 K spatial temperature inhomogeneity, ensuring a sufficiently uniform thermal environment for predicting the dynamic shift.A movable sensor measures a 1.5 mK temperature difference between locations in the chamber.
- Radiation thermometry: Final temperature uncertainties are 5 mK for the movable sensor and 11 mK for the fixed sensor, whose agreement supports negligible chamber gradients and no installation-related calibration shifts.The sensors have markedly different immersion-error coefficients, providing an independent consistency check.
3D1 decay rate
The largest systematic uncertainty comes from the BBR dynamic coefficient νdyn, dominated by the oscillator strength of the 2.6 µm 3P0→3D1 transition. The transition is characterized through time-resolved decay fluorescence to extract τ3D1 and τ3P1, while fitting and other shifts are carefully controlled.
- 3D1 decay rate: The dominant νdyn uncertainty arises from the oscillator strength of the 2.6 µm transition between the 3P0 clock state and 3D1 state.This is the only clock-state transition that significantly overlaps the room-temperature BBR spectrum.
- 3D1 decay rate: A 200 ns 2.6 µm pulse drives 3P0→3D1, and 689 nm photons from subsequent 3P1→1S0 decay are time-binned to extract τ3D1 and τ3P1.The decay signal is fitted to a double exponential function.
- 3D1 decay rate: The double-exponential fit is unbiased when t0 is free after the 200 ns excitation pulse, as confirmed by analytical modeling and numerical simulation.Potential density-dependent effects include radiation trapping and superradiance.
- 3D1 decay rate: First- and second-order Zeeman shifts and the probe Stark shift are reduced to the low 10^-19 level or better.The passage refers to the Methods for these uncertainty reductions.
Discussion
Stable lasers with >10 s coherence time and many-particle clocks are enabling clock accuracy near the 1 x 10-18 level. This coherence supports alternating interrogation of two atomic samples at >50% duty cycle to eliminate the Dick effect, while next-generation lasers are expected to approach the 160 s natural lifetime of Sr.
- Discussion: >10 s coherence time and many-particle clocks have ushered in clock accuracy near the 1 x 10-18 level.The passage describes this as a new era of clock accuracy.
- Discussion: >50% duty cycle enables alternating interrogation of two separate atomic samples with a single laser, potentially eliminating the Dick effect.This capability is enabled by the current generation of stable lasers.
- Discussion: 160 s is the Sr natural lifetime that next-generation ultrastable lasers are expected to rival in coherence time.The passage states that the next generation of ultrastable lasers will soon come online.
METHODS
The clock uses laser-cooled 87Sr atoms in a cavity-enhanced optical lattice, interrogated with a stabilized 698 nm clock laser. Systematic shifts are measured with lock-in techniques and controlled operating conditions, including atom number, lattice intensity, temperature, and magnetic field.
- Clock apparatus: About 2000 strontium atoms are cooled to a few µK and loaded into a cavity-enhanced 1D optical lattice at 813.4 nm.Cooling uses a Zeeman slower and sequential 461 nm and 689 nm MOT stages.
- Clock apparatus: The 87Sr clock transition is interrogated with a 698 nm diode laser stabilized to 26 mHz using a 40 cm ULE cavity.The cavity system includes temperature control, heat shielding, vibration cancellation, and acoustic shielding.
- Spectroscopy and measurement: 160 ms to 4 s Rabi pulses determine the clock-laser offset, while fluorescence measurements determine the excited-state population fraction.Excited-state atoms are repumped to the ground state before a second fluorescence count.
- Systematic-shift evaluation: (-3.5 ± 0.4) × 10-18 is the density shift extrapolated to 2000 atoms and 71 Erec using atom-number modulation and lock-in detection.Spin-polarized fermions suppress s-wave interactions, while the measured p-wave density shift is reduced with the cavity-enhanced lattice.
- Systematic-shift evaluation: Lattice Stark shifts are measured versus trap depth U0 using resolved sideband spectroscopy, with atom-number modulation canceling parasitic density shifts.The lattice intensity is stabilized by monitoring cavity transmission, and a background magnetic-field servo controls polarization-dependent ac Stark shifts.
- Systematic-shift evaluation: 1 × 10-19 is the conservative upper bound assigned to line pulling from imperfect polarization, ellipticity-driven transitions, or lattice-tunneling sidebands.The bound is based on calculations and data for off-resonant spectroscopic features.