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Measurement of magnetic field stability using 40Ca+ ion

Pham, Minh Tuan

Published Jan 1, 2022• 0 citations
OpenAlex

Abstract

One of the main limitations in the long-term measurement of the clock transition's absolute frequency is the magnetic field's fluctuation. The time-varying fluctuation of the external magnetic field leads to frequency shifts of the Zeeman components, thereby reducing the optical clock's frequency stability over time. Currently, optical atomic references are usually implemented with the help of a single ion. However, scaling the number of ions to higher values brings an indisputable benefit in the form of a high signal-to-noise ratio and, thus to the efficiency of the entire measurement process. In this case, the ions are spread over a large area, forming so-called ionic Coulomb crystals. In addition to the spatial stability of the magnetic field, the homogeneity of the magnetic field is also significant when working with Coulomb crystals. Excessive magnetic perturbation can be greatly reduced by covering the assembly with a magnetic shield or by using permanent magnets instead of conventionally used magnetic coils. Another method is averaging over multiple-level transitions. This contribution presents a simple method for measuring the stability of the magnetic field at the ion position.

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New Journal of Physics•Aug 20, 2026•0 citations
One of the main limitations in the long-term measurement of the clock transition's absolute frequency is the magnetic field's fluctuation. The time-varying fluctuation of the external magnetic field leads to frequency shifts of the Zeeman components, thereby reducing the optical clock's frequency stability over time. Currently, optical atomic references are usually implemented with the help of a single ion. However, scaling the number of ions to higher values brings an indisputable benefit in the form of a high signal-to-noise ratio and, thus to the efficiency of the entire measurement process. In this case, the ions are spread over a large area, forming so-called ionic Coulomb crystals. In addition to the spatial stability of the magnetic field, the homogeneity of the magnetic field is also significant when working with Coulomb crystals. Excessive magnetic perturbation can be greatly reduced by covering the assembly with a magnetic shield or by using permanent magnets instead of conventionally used magnetic coils. Another method is averaging over multiple-level transitions. This contribution presents a simple method for measuring the stability of the magnetic field at the ion position.
We developed an optical frequency standard with the 4 2S1/2-3 2D5/2 electric quadrupole transition of 40Ca+ ions. Its absolute transition frequency is 411 042 129 776 390(±7) Hz. The accuracy is limited by the electric quadrupole shift and the ambient magnetic field fluctuation. To determine the absolute transition frequency with a better accuracy, we have observed two pairs of the symmetrically-splitting Zeeman components and measured the transition frequency corrected for the electric quadrupole shift. In addition, we are developing a magnetic-shielded ion-trap chamber to suppress the transition-line broadening caused by the magnetic field fluctuation.
We developed an optical frequency standard using40Ca+with the 42S1/2-32D5/2electric quadrupole transition. Its absolute transition frequency is 411 042 129 776 390(7) Hz. The uncertainty is limited by the electric quadrupole shift and ambient magnetic field fluctuation. To determine the absolute transition frequency with a better uncertainty, we have observed two pairs of the symmetrically-splitting Zeeman components and measured the transition frequency which is corrected for the electric quadrupole shift. It will be used to determine the absolute transition frequency with respect to the SI base units of time and length. In addition, we are developing a magnetic-shielded ion-trap chamber to reduce the transition-line broadening caused by the magnetic field fluctuation.
Future applications of portable 40Ca+ optical clocks require reliable magnetic field stabilization to improve frequency stability, which can be achieved by implementing an active and passive magnetic field noise suppression system. On the one hand, we have optimized the magnetic shielding performance of the portable optical clock by reducing its apertures and optimizing its geometry; on the other hand, we have introduced an active magnetic field noise suppression system to further suppress the magnetic field noise experienced by the ions. These efforts reduced the ambient magnetic field noise by about 10000 times, significantly reduced the linewidth of the clock transition spectrum, improved the stability of the portable 40Ca+ optical clock, and created the conditions for using portable optical clocks in non-laboratory magnetic field environments. This active magnetic field suppression scheme has the advantages of simple installation and wide applicability.
Abstract We present a novel method for engineering an optical clock transition that is robust against external field fluctuations and is able to overcome limits resulting from field inhomogeneities. The technique is based on the application of continuous driving fields to form a pair of dressed states essentially free of all relevant shifts. Specifically, the clock transition is robust to magnetic field shifts, quadrupole and other tensor shifts, and amplitude fluctuations of the driving fields. The scheme is applicable to either a single ion or an ensemble of ions, and is relevant for several types of ions, such as 40 Ca + , 88 Sr + , 138 Ba + and 176 Lu + . Taking a spherically symmetric Coulomb crystal formed by 400 40 Ca + ions as an example, we show through numerical simulations that the inhomogeneous linewidth of tens of Hertz in such a crystal together with linear Zeeman shifts of order 10 MHz are reduced to form a linewidth of around 1 Hz. We estimate a two-order-of-magnitude reduction in averaging time compared to state-of-the art single ion frequency references, assuming a probe laser fractional instability of 10 − 15 . Furthermore, a statistical uncertainty reaching 2.9 × 10−16 in 1 s is estimated for a cascaded clock scheme in which the dynamically decoupled Coulomb crystal clock stabilizes the interrogation laser for an 27 Al + clock.
Progress of the 40Ca+ ion optical clock based on the 42S1/2 – 3d 2D5/2 electric quadrupole transition is reported. By setting the drive frequency to the “magic” frequency Ω 0, the frequency uncertainty caused by the scalar Stark shift and second-order Doppler shift induced by micromotion is reduced to the 10−19 level. By precisely measuring the differential static scalar polarizability Δα 0, the uncertainty due to the blackbody radiation (BBR) shift (coefficient) is reduced to the 10−19 level. With the help of a second-order integrating servo algorithm, the uncertainty due to the servo error is reduced to the 10−18 level. The total fractional uncertainty of the 40Ca+ ion optical clock is then improved to 2.2× 10−17, whereas this value is mainly restricted by the uncertainty of the BBR shift due to temperature fluctuations. The state preparation is introduced together with improvements in the pulse sequence, and furthermore, a better signal to noise ratio (SNR) and less dead time are achieved. The clock stability of a single clock is improved to 4.8 × 10 − 15 / τ ( in seconds ) .
Abstract Here, we develop a compact multilayer magnetic shield for a transportable optical clock, achieving shielding factors of up to 10 5 . To improve the frequency stability of the transportable optical clock, we improved the magnetic-field environment of a transportable 40 Ca + ion optical clock (TCIOC) using the newly developed magnetic shielding system and reduced the clock-laser frequency noise by transferring the stability of an ultrastable reference laser through an optical frequency comb. These improvements enabled the coherent interrogation time to be extended from 40 ms to 320 ms . A time-interleaved self-comparison yielded a measured short-term fractional frequency instability of 1.6 × 10 − 15 / τ , close to the estimated quantum projection noise-limited instability of 1.18 × 10 − 15 / τ . Meanwhile, the uncertainty contributions associated with the DC second-order Zeeman shift and the servo error were reduced to 1.1 × 10 − 21 and 4.5 × 10 − 19 . These results provide a practical basis for further improving the performance of transportable optical clocks.