Robust optical clock transitions in trapped ions using dynamical decoupling
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Bibliographic record
Abstract
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>40</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi>Ca</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>88</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi>Sr</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>138</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi>Ba</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>176</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi>Lu</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> . Taking a spherically symmetric Coulomb crystal formed by 400 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>40</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi>Ca</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>15</mml:mn> </mml:mrow> </mml:msup> </mml:math> . 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>27</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi>Al</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> clock.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it