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Журнал Экспериментальной и Теоретической Физики

Optimization of Feedback-Loop Parameters in Thulium Optical Clocks at Synchronous Comparison

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

Published Dec 15, 2023• 0 citations
Publisher

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.

DOI
10.31857/s0044451023080084

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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.
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.
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 consider designs of optical lattice clocks in view of the quantum statistics, relevant atomic spins, and atom-lattice interactions. The first two issues lead to two optimal constructions for the clock: a one-dimensional (1D) optical lattice loaded with spin-polarized fermions and a 3D optical lattice loaded with bosons. By taking atomic multipolar interactions with the lattice fields into account, an "atomic motion insensitive" wavelength is proposed to provide a precise definition of the "magic wavelength." We then present a frequency comparison of these two optical lattice clocks: spin-polarized fermionic 87 Sr and bosonic 88 Sr prepared in 1D and 3D optical lattices, respectively. Synchronous interrogations of these two optical lattice clocks by the same probe laser allowed canceling out its frequency noise as a common mode noise to achieve a relative stability of 3 × 10 −17 for an averaging time of τ = 350 s. The scheme, therefore, provides us with a powerful means to investigate intrinsic uncertainty of the clocks regardless of the probe laser stability. We discuss prospects of the synchronous operation of the clocks on the measurement of the geoid height difference and on the search of constancy of fundamental constants.
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 develop differential measurement protocols that circumvent the laser noise limit in the stability of optical clock comparisons by synchronous probing of two clocks using phase-locked local oscillators. This allows for probe times longer than the laser coherence time, avoids the Dick effect, and supports Heisenberg-limited measurement precision. We present protocols for such frequency comparisons and develop numerical simulations of the protocols with realistic noise sources. These methods provide a route to reduce frequency ratio measurement durations by more than an order of magnitude.