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Conference on Lasers and Electro-Optics

Elimination of second-order Zeeman shift in thulium optical clock by simultaneous interrogation of two clock transitions

Dmitry O. Tregubov, Artem A. Golovizin, E.S. Fedorova, D. Mishin, Daniil I. Provorchenko, Ksenia Yu. Khabarova, В. Н. Сорокин, N. Kolachevsky

Published Jan 1, 2021• 0 citations
Publisher

Abstract

We eliminate the largest systematic shift in thulium optical clock — the second-order Zeeman shift — using average frequency of two clock transitions. This reduces the total systematic shift down to mHz level.
DOI
10.1364/cleo_at.2021.jth3a.82

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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 Optical atomic clocks have already overcome the eighteenth decimal digit of instability and uncertainty, demonstrating incredible control over external perturbations of the clock transition frequency. At the same time, there is an increasing demand for atomic (ionic) transitions and new interrogation and readout protocols providing minimal sensitivity to external fields and possessing practical operational wavelengths. One of the goals is to simplify the clock operation while maintaining the relative uncertainty at a low 10−18 level achieved at the shortest averaging time. This is especially important for transportable and envisioned space-based optical clocks. Here, we demonstrate implementation of a synthetic frequency approach for a thulium optical clock with simultaneous optical interrogation of two clock transitions. Our experiment shows suppression of the quadratic Zeeman shift by at least three orders of magnitude. The effect of the tensor lattice Stark shift in thulium can also be reduced to below 10−18 in fractional frequency units. This makes the thulium optical clock almost free from hard-to-control systematic shifts. The “simultaneous” protocol demonstrates very low sensitivity to the cross-talks between individual clock transitions during interrogation and readout.
We discuss the extension of a recently proposed method based on continuous spectroscopy of 88 Sr atoms trapped in a moving optical lattice [Appl. Phys. Express, 14 , 072 006 (2021)] to the operation of bicolor thulium optical clocks. Simultaneous interrogation of two clock transitions at 1.14 μ m and build-up of a synthetic frequency provides a straightforward way to significantly suppress the first-order Doppler shift and cancel out the second-order Zeeman shift, the latter being one of the major sources of uncertainty in the originally proposed 88 Sr setup. In our configuration, the total systematic frequency shift is 4 × 10 −16 and instability is at or lower than 10 −18 after 1 h of integration.