Gravitational Ramsey spectroscopy applied to ultra cold neutrons in the qBounce experiment and application of numerical analysis techniques

Ultra-cold neutrons (UCNs) have been shown to be excellent probes for the study of gravity over short distances due to their electric neutrality and low polarizability. Over a mirror, they couple to the gravitational field of the Earth to form gravitationally bound quantum states. qBounce studies the transitions between those states using a technique called Gravitational Resonance Spectroscopy (GRS). State transitions are induced by mechanical oscillations, in a manner that is analogous to the Ramsey method of separated oscillatory fields. Here, it is performed without a coupling to electromagnetic field or potentials. The experiment is located in Grenoble (France) and uses the neutronsproduced by the Institut Laue-Langevin (ILL) high flux reactor. This thesis presents the first measurement of the transition pair |1⟩ → |7⟩ and |2⟩ → |9⟩. These are the transitions with the highest frequencies so far measured within the GRS framework, at approximately 1120 Hz and 1142 Hz respectively. A numerical procedure involving 30 quantum bound states was developed for the analysis of GRS measurements and applied to those data. The local acceleration of the neutron in the gravitational field of the Earth g was used as a fitting parameter. The experimental value measured with the experiment for the transition |1⟩ → |7⟩ and |2⟩ → |9⟩ shows a deviation of 2 σ relative to the value obtained from a corner-cube measurement. The result of a spin-dependentmeasurement (spin parallel and anti-parallel to −→g with corresponding frequency ν↑ and ν↓) for the transition |1⟩ → |6⟩, is also presented. This measurement is in agreement with the statement that the transition frequencies are statistically compatible. No spin dependence has been observed at the 0.5 σ level, with ν↑−ν↓ σ(ν↑−ν↓) = 0.49 for a relative error of σν↑ ν↑ ≈ 7.1 · 10−4 and σν↓ ν↓ ≈ 8.4 · 10−4. The obtained result corresponds to the lowest error reported so far for this type of measurement.