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arXiv:2407.04139 · Journal of Experimental and Theoretical Physics Letters

Synchronous Comparison of Two Thulium Optical Clocks

Artem A. Golovizin, D. Mishin, Daniil I. Provorchenko, Dmitry O. Tregubov, N. Kolachevsky

Published May 1, 2024• 4 citations
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Abstract

The experimental comparison of two thulium optical lattice clocks in a time interval of up to one hour has been carried out. The synchronous comparison of a clock transition in two independent atomic ensembles using a single ultrastable laser has allowed us to eliminate fluctuations of the laser frequency from the measured frequency difference and to reach a relative measurement error of 10–16 after 500-s averaging, which corresponds to a relative instability of $$2 \times {{10}^{{ - 15}}}{\text{/}}\sqrt \tau $$ . The successful demonstration of the long-term operation of two systems using the synchronous comparison of clock transitions opens the possibility of studying systematic shifts in thulium optical clocks with an uncertainty of 10–17.

DOI
10.1134/s0021364024600873

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The experimental comparison of two thulium optical lattice clocks in a time interval of up to one hour has been carried out. The synchronous comparison of a clock transition in two independent atomic ensembles using a single ultrastable laser has allowed us to eliminate fluctuations of the laser frequency from the measured frequency difference and to reach a relative measurement error of 10–16 after 500-s averaging, which corresponds to a relative instability of 2×10−15/τ2 \times {{10}^{{ - 15}}}{\text{/}}\sqrt \tau 2×10−15/τ​ . The successful demonstration of the long-term operation of two systems using the synchronous comparison of clock transitions opens the possibility of studying systematic shifts in thulium optical clocks with an uncertainty of 10–17.
Synchronous comparison of optical clocks using phase-coherent clock lasers makes it possible to determine the difference (ratio) of clock transition frequencies, which is not limited by the total noise of lasers in use. A detailed simulation of the comparison of two thulium optical clocks is performed using synchronous interrogation of atoms by the radiation of a common clock laser. Some critical parameters have been determined, specifically: the residual noncorrelated frequency and amplitude noises of test pulses and reading noises, which may deteriorate the comparison stability. At the same time, it is demonstrated that this way is insensitive to fluctuations in the number of atoms, calibration of feedback-loop parameters, individual ejections in measurement cycles, and fluctuations of laboratory magnetic field.
Abstract Synchronous comparison of optical clocks using phase-coherent clock lasers makes it possible to determine the difference (ratio) of clock transition frequencies, which is not limited by the total noise of lasers in use. A detailed simulation of the comparison of two thulium optical clocks is performed using synchronous interrogation of atoms by the radiation of a common clock laser. Some critical parameters have been determined, specifically: the residual noncorrelated frequency and amplitude noises of test pulses and reading noises, which may deteriorate the comparison stability. At the same time, it is demonstrated that this way is insensitive to fluctuations in the number of atoms, calibration of feedback-loop parameters, individual ejections in measurement cycles, and fluctuations of laboratory magnetic field.
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 $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, 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 $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$.
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.
Optical lattice clocks demonstrate advantages in metrology and frontier physics because of their high stability.Here, we present approaches to enhancing the stability by decoupling the noise related to the short-term and long-term stability.For the short-term stability, we optimize the clock laser by decoupling the frequency noise, and optimize each noise contribution individually until it is below the thermal noise limit.For the long-term stability, we introduce a method to decouple the instability caused by systematic effects.Having identified that the collision frequency shift was the main limiting factor in our systems, we thus optimized the atom number fluctuations in optical lattices.Through targeted optimization, we achieve a synchronous comparison of two clocks with an average stability of 3.2 × 10 -16 = τ p and a long-term stability of 2.4 × 10 -18 at 8000 s.This work provides an analytical framework for enhancing optical clock stability.
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.