Optical lattice clocks (OLCs) have progressed rapidly since the initial proposal in 2002, they now outperform even the best microwave clocks realizing the current definition of the SI second, as well as single ion optical clocks, thus becoming the best frequency references. While several groups worldwide are now pushing these new clocks towards their ultimate capabilities, one of the big challenges to face is to take full advantage of the statistical resolution -- or frequency stability -- that is intrinsically possible only with OLCs. Combining the benefit of a resonance with a quality factor of 10^15 and of 10^4 atoms probed simultaneously, a fractional resolution of 10^-17 could be achieved after only one second of integration. This would correspond to an integration time reduced by 6 orders of magnitude with respect to microwave clocks. The research project presented here aims at developing strategies to reach this unprecedented level of resolution, and explore ways to possibly overcome it. Such a resolution is an enabling property for the development and applications of OLCs. The rapid integration time it yields dramatically speeds-up the characterization of systematic effects, which opens the way to characterize the systematic frequency biases with an uncertainty below 10^-18. Also, OLCs offer numerous applications in both fundamental and applied science, in particular in relativistic geodesy, that will be reachable with such a statistical resolution, in particular with the remote comparisons between European using a fiber-based all optical clock network. This project combines two devices. The first one leverages a new generation of ultra-stable Fabry-Perot cavity. The ``clock laser'', stabilized on this new generation cavity, will dramatically push down the current limitation of the frequency stability of OLCs, namely the sampling of the clock laser noise, or Dick effect. But it also opens new challenges that this project aims at addressing. Transporting such a frequency stability to the atomic cloud, at the heart of an OLC, without degradation is, as of yet, unexplored. We propose to demonstrate this stability transfer on two OLC apparatus operated with strontium atoms available at SYRTE, and, as a consequence, to report for the first time on frequency stabilities of the clock in the 10^-17 range after 1 s of integration time. To further explore the clock stability, we will explore ways to combine the two Sr clock systems to optimally sample the residual laser noise by either synchronously interrogating the clock, either by combining them into a dead-time-free clock. As a consequence, the stability of OLCs is expected to reach a fundamental limit, the quantum projection noise (QPN). We will study ways to shrink down this limit by increasing the number of atoms, while keeping under control the effect of cold collisions on the clock accuracy. The second device under study in this project is more exploratory. It aims at bringing to clock techniques that allow for statistical resolutions beyond the QPN. For this, we will make use of cavity-based non-destructive detection systems which will be implemented in the two Sr OLCs. This detection system enables to generate non-classical atomic states whose correlations enable to overcome the QPN. The possibility to use such states, yet unexplored for optical transitions, is well adapted to OLCs, in which a significant number of atoms are confined in an optical lattice. In this project, the USC to uncover the QPN in OLCs, and the cavity-assisted detection system to overcome the QPN, are combined together to demonstrate unprecedented statistical resolution in any frequency standard. This project will demonstrate the possibility to improve OLCs with fundamental physics techniques, and enable the multiple applications of OLC beyond the field of metrology.

The objective of the CoQuIA project is to optimize the efficiency and robustness to environmental variations of laser beamsplitters in atomic interferometers, through novel pulse shaping methods that take advantage of unconventional optics and optimal quantum control methods. The new methods and key technologies that we propose to develop within the framework of this project, as well as the intimate knowledge of their limitations in terms of performance, will allow the development of atomic sensors which will be better able to meet the expectations of users in the most demanding applications, in particular for on-board applications, such as inertial navigation.