Progress in Atomic Fountains at LNE-SYRTE
Jocelyne Gu\'ena (1), Michel Abgrall (1), Daniele Rovera (1), Philippe, Laurent (1), Baptiste Chupin (1), Michel Lours (1), Giorgio Santarelli (1),, Peter Rosenbusch (1), Michael E. Tobar (2), Ruoxin Li (3), Kurt Gibble (3),, Andr\'e Clairon (1)

TL;DR
This paper reviews the recent progress, systematic studies, and applications of the LNE-SYRTE atomic fountain ensemble, highlighting advancements in accuracy, control of systematic shifts, and various metrological and fundamental physics applications.
Contribution
It provides a comprehensive overview of the developments in atomic fountain clocks at LNE-SYRTE over five years, including new systematic shift evaluations and application demonstrations.
Findings
Evaluation of distributed cavity phase shift for FO1 and FOM fountains
Calculations of microwave lensing frequency shift for all three fountains
Current accuracy budgets and control of systematic effects
Abstract
We give an overview of the work done with the Laboratoire National de M\'etrologie et d'Essais-Syst\`emes de R\'ef\'erence Temps-Espace (LNE-SYRTE) fountain ensemble during the last five years. After a description of the clock ensemble, comprising three fountains, FO1, FO2, and FOM, and the newest developments, we review recent studies of several systematic frequency shifts. This includes the distributed cavity phase shift, which we evaluate for the FO1 and FOM fountains, applying the techniques of our recent work on FO2. We also report calculations of the microwave lensing frequency shift for the three fountains, review the status of the blackbody radiation shift, and summarize recent experimental work to control microwave leakage and spurious phase perturbations. We give current accuracy budgets. We also describe several applications in time and frequency metrology: fountain…
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