Condensed-matter physics with ultracold atoms: probing the Bogoliubov dispersion relation and the LMG model

Abstract
In this talk, I will report our investigation of a strongly interacting Bose-Einstein condensate of $^{39}$K trapped in a uniform box potential. We study the energy of particle-like excitations of such a system as a function of the interaction strength that we can vary using a Feshbach resonance acting on the collisional scattering length. While an excellent agreement is found with the Bogoliubov theory in the limit of vanishing interaction strength, a clear departure is observed as soon as the interaction strength becomes non-negligible. More surprisingly, we observe a non-monotonic evolution of the dispersion relation as a function of the interaction strength. A good agreement with the Feynman energy relation and the Wilson operator product expansion is found for different interaction regimes, but neither theory explains our observations across all interaction regimes, inviting further theoretical efforts.

I will also present our very recent investigation of the Lipkin-Meshkov-Glick model, induced by near-resonant light coupling with the J=8 ground state of an ultracold cloud of $^{162}$Dy. The paramagnetic to ferromagnetic phase transition expected from this model is investigated. We perform a full characterisation of the ground state properties as well as a quantitative study of the dynamics of the quantum critical regime, and find, away from the phase transition, a good agreement with mean-field predictions.