Study of the ultimate performances of a compact clock with laser-cooled atoms

This thesis context is the study of the ultimate performance of a microwave clock based on laser-cooled atoms. This clock, called MuClock, is fully integrated and automated within a volume of 0.7 m³. Its principle of operation is designed around its copper spherical cavity, which serves as both a microwave resonator and an integrating sphere to generate the isotropic cooling light field for the atoms. The MuClock measures the hyperfine transition frequency of the ⁵S_1/2 state of rubidium 87 using a sequence consisting of three distinct steps. First, by using 1,560 nm frequency doubling technologies, 10 million atoms are cooled to a temperature of about 70 µK through the isotropic cooling method. Next, the Ramsey spectroscopy method is used by applying two microwave pulses separated by an effective Ramsey time of 40 ms to interrogate the free falling atom cloud within the cavity. Finally, approximately 2 million atoms are detected through absorption of a vertical light beam. This sequence lasts about 150 ms and allows the MuClock to achieve a relative clock frequency stability performance of 3-5 ×10⁻¹³ at 1 second and 1×10⁻¹⁵ for over a month.

The goal of this thesis is to assess the clock frequency accuracy budget with a total uncertainty of less than 5×10⁻¹⁴. Each of the systematic effects contributing to the frequency shift of the MuClock is studied in this thesis. The largest of these, the quadratic Zeeman effect, is corrected by probing the magnetic transitions of the atoms. Another effect that cannot be measured by using the atoms is the phase transient effect, for which a specific measurement setup was designed. The measurements realized allow to optimize the clock sequence to reduce the contribution of this effect. This setup is also used to measure the dynamic end-to-end cavity phase shift during the interrogation of the atoms. This effect is eliminated by adjusting the MuClock's cavity heating method. Furthermore, a tomography imaging experiment is conducted to model the spatial distribution of the atoms. This model is validated by numerical simulations reconstructing the Rabi oscillation signals and Ramsey fringes of the MuClock. The spatial distribution of the atoms, as modelled, allows the estimation of several systematic effects such as the collisions between cold atoms or the distributed cavity phase shifts. This phase distribution is modeled from finite element simulations of the microwave resonance mode in the cavity. These simulations are also used to better understand the cavity pulling effect, whose contribution is made negligible by locking the cavity's resonance frequency. The Ramsey and Rabi pulling effects are measured using Ramsey spectroscopy with varying effective durations. The blackbody radiation effect is evaluated from measurements taken on atomic fountains. Finally, several effects, such as light shifts or off-resonance excitation phenomena are checked to ensure their contributions to the accuracy budget are negligible.

At the end of these studies, we estimate that the accuracy of a MuClock can be defined with an uncertainty of 1.4×10⁻¹⁴ at best. Frequency measurements of the MuClock against the frequency references of the Laboratoire Temps-Espace validate the evaluated clock frequency with a deviation of less than 1×10⁻¹⁴. The uncertainty for these measurements is 3×10⁻¹⁴, which is the current MuClock accuracy.

cold atoms, Rubidium, microwave clock, laser-cooling, accuracy budget.

Full document (FR) : not available because subject to an embargo until the 19^th May 2027.