Using the Thue-Morse Sequence to Cancel Low-Frequency Fluctuations

Schat, Jan

doi:10.1109/imtc.2007.379015

Cited by 3 publications

(4 citation statements)

References 8 publications

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“…Dotted lines are the analytical formulas for the normalized discriminator evaluated using numerical correlation functions (in (a), solid and dotted blue lines overlap). For RBBRBRRB probing, only the analytical result (16) for the normalized discriminator is shown (dash-dotted yellow line; overlaps with dashed red line in (a)).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In the simplest case, the red and blue sides of a transition are probed only once per servo cycle (but usually with multiple pulses in single-ion clocks) and in a fixed order, which we refer to as RB or BR probing depending on the order. In general, each side can be probed multiple times per cycle, e.g., in the order RBBR or using higherorder Thue-Morse sequences [16] in order to cancel the ; Formally, the expansion is done in the dimensionless detuning δ τ, but τ and τ 2 are absorbed into the coefficients a and b to simplify the notation.…”

Section: Modelmentioning

confidence: 99%

“…In general, each side can be probed multiple times per cycle, e.g. in the order RBBR or using higher-order Thue-Morse sequences [16] in order to cancel the error caused by laser amplitude drift [17]. The number of successful excitations are then summed, corresponding to averaging the transition probabilities (1) over all B (R) interrogations during a cycle.…”

Section: Figurementioning

confidence: 99%

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Noise-induced servo errors in optical clocks utilizing Rabi interrogation

et al. 2023

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We show that in optical clocks based on Rabi interrogation, both laser-frequency and magnetic-field flicker (1/f) noise with zero mean can lead to servo errors at the 10-18 level if the negative-detuning (red) and positive-detuning (blue) sides of the transition are always probed in the same order. This is due to the strong correlations of flicker noise in combination with an imbalance in the response of the servo discriminator to positive and negative differential frequency noise between the red- and blue-side probing. This imbalance is particularly large for a normalized discriminator. We derive an analytical expression for the servo error based on the correlation function of the laser-frequency or magnetic-field noise and compare it to numerical servo simulations to demonstrate how the error depends on the noise level, servo parameters, and probing sequence. We also show that the servo error can be avoided by normalizing the discriminator with a moving mean or by reversing the red/blue probing order for every second servo cycle.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: Figurementioning

confidence: 99%

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Noise-induced servo errors in optical clocks utilizing Rabi interrogation

et al. 2023

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“…In order to lock the 467 nm light to the clock transition, a servo control method is employed [13]. Rabi pulse probes are alternated in a Thue-Morse sequence [20] on the high and low frequency sides of the atomic resonance at the half maximum points. At the end of each servo cycle, typically made up of 4 probes on each side of the transition, this information is fed back via the aforementioned AOM, whose driving RF signal is responsible for applying the appropriate frequency in each probe.…”

Section: Methodsmentioning

confidence: 99%

¹⁷¹Yb⁺ optical clock with 2.2 × 10 − 18

Tofful,

Baynham,

Curtis

et al. 2024

Metrologia

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A full evaluation of the uncertainty budget for the ytterbium ion optical clock at the National Physical Laboratory (NPL) was performed on the electric octupole (E3) 2S1/2 → 2F7/2 transition. The total systematic frequency shift was measured with a fractional standard systematic uncertainty of 2.2 × 10−18. Furthermore, the absolute frequency of the E3 transition of the 171Yb+ ion was measured between 2019 and 2023 via a link to International Atomic Time (TAI) and against the local caesium fountain NPL-CsF2. The absolute frequencies were measured with fractional standard uncertainties between 3.7 × 10−16 and 1.1 × 10−15, and all were in agreement with the 2021 BIPM recommended frequency.

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